Conjectured formulas of the OEIS by Simon Plouffe as of Sept 6. 2014 There are 45691 unique sequence and more than 148403 expressions. Score = log(# of terms)*(length of sequence in charaters)/(length of the formula in characters). If the score is high the reliability of the formula is good. A score near 1 is not good, a score of 20+ is excellent. Some formulas are in double for many reasons, the sign or the factorization of the expression makes a change in length. The intention of the author is to keep the list as clean as possible, with time it will be done... These formulas are suggested, most of them are the true ones, in some cases the formula found automatically are better than the original reference. Some formulas are false positives, in some rare cases, even false the formula found is sometimes as interesting as the original. ---------------------------------------------------------------------------- OEIS # Score Formula Type --------------------------------------------------------------------------------------- ########################################################################### A000008 75.4905 1+x+x^4+x^9 ogf_with_Euler_Transform A000008 15.0981 1/(x^4-x^3+x^2-x+1)/(x+1)^2/(x^4+x^3+x^2+x+1)^2/(x-1)^4 ogf A000009 92.1358 1/(1-x^2) ogf_with_Euler_Transform A000009 30.7119 {a(n+2)-a(n),a(0)=1,a(1)=0} ogf_with_Euler_Transform A000023 26.9652 (1-2*x)*f(x)+(1-x)*f(x)^2 lgdegf A000023 42.1331 -(-1+2*x)/(-1+x) lgdegf A000023 42.1331 -exp(-2*x)/(x-1) egf A000023 11.6229 {(2*n+4)*a(n+1)+(n+1)*a(n+2)-a(n+3),a(0)=1,a(1)=-1,a(2)=2} ogf A000027 106.665 -2/(-1+x) lgdogf A000027 26.6662 1+(2*x-x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A000027 106.665 1/(x-1)^2 ogf A000032 46.942 (x-2)/(x^2-1+x) ogf A000032 24.2803 -(-1-4*x+x^2)/(x-2)/(x^2+x-1) lgdogf A000032 44.0081 -(2-x)/(x^2-1+x) ogf A000032 13.0394 -78+39*x+(79-59*x-39*x^2)*f(x)+(20*x^2-20+20*x)*f(x)^2 ogf A000032 20.118 {-a(n+2)+a(n+1)+a(n),a(0)=2,a(1)=1} ogf A000034 55.2276 -(-1-2*x)/(1-x^2) ogf A000034 46.9434 -(1+2*x)/(x-1)/(x+1) ogf A000034 28.4506 -2*(1+x+x^2)/(-1+x)/(2*x+1)/(x+1) lgdogf A000034 21.3379 -2-4*x+(-3-10*x-2*x^2)*f(x)+(5-5*x^2)*f(x)^2 ogf A000034 27.6138 1/2/(2+x)*(-1+(1+8*x+4*x^2)^(1/2)) revogf A000034 34.7729 {a(n+2)-a(n),a(0)=1,a(1)=2} ogf A000035 69.477 -1/(x-1)/(x+1) ogf A000035 57.2163 -2*x/(-1+x)/(x+1) lgdogf A000035 37.4107 1/2/x*(-1+(1+4*x^2)^(1/2)) revogf A000035 97.2678 arcsinh(x) revegf A000035 64.8452 x+(-1+x^2)*f(x) ogf A000035 108.075 x/(1-x^2) ogf A000035 36.0251 {a(n+2)-a(n),a(0)=0,a(1)=1} ogf A000038 60.7924 {-a(n+1),a(0)=2} ogf A000041 127.979 1/(1-x) ogf_with_Euler_Transform A000041 44.7926 {a(n+1)-a(n),a(0)=1} ogf_with_Euler_Transform A000042 20.1255 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A000042 28.5995 -1/(-1+11*x-10*x^2) ogf A000042 13.9331 -1/20*(-11*x-1+(81*x^2+22*x+1)^(1/2))/x revogf A000042 9.53315 -20+(-81-220*x+200*x^2)*f(x)+(101-1111*x+1010*x^2)*f(x)^2 ogf A000042 33.9618 1/(10*x-1)/(x-1) ogf A000042 12.9378 {-a(n+2)+11*a(n+1)-10*a(n),a(0)=1,a(1)=11} ogf A000044 18.3645 -(1+3*x^2+5*x^4+7*x^6+9*x^8+11*x^10)/(-1+x+x^3+x^5+x^7+x^9+x^11) lgdogf A000044 39.1777 -1/(-1+x+x^3+x^5+x^7+x^9+x^11) ogf A000045 40.7062 -(1+2*x)/(x^2-1+x) lgdogf A000045 61.0593 -1/(x^2-1+x) ogf A000045 56.3625 -x/(-1+x+x^2) ogf A000045 22.8972 1/2/x*(-x-1+(5*x^2+2*x+1)^(1/2)) revogf A000045 45.7945 x+(x^2+x-1)*f(x) ogf A000045 20.9346 {-a(n+2)+a(n+1)+a(n),a(0)=0,a(1)=1} ogf A000051 29.8355 -(-2+3*x)/(2*x-1)/(x-1) ogf A000051 29.8355 -(-2+3*x)/(2*x^2+1-3*x) ogf A000051 18.5464 -(3-8*x+6*x^2)/(-1+x)/(2*x-1)/(3*x-2) lgdogf A000051 12.0389 1/2*ln(2*x+3)-arctanh((2*x+4)^(1/2))-1/2*ln(3)+arctanh(2) revegf A000051 11.6308 106-159*x+(-25+117*x-106*x^2)*f(x)+(-28*x^2-14+42*x)*f(x)^2 ogf A000051 18.0583 {a(n+2)-3*a(n+1)+2*a(n),a(0)=2,a(1)=3} ogf A000064 7.56692 -(2+4*x+2*x^2+4*x^3+7*x^4+4*x^5+2*x^6+4*x^7+2*x^8+19*x^9)/(-1+x)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) lgdogf A000064 14.3231 -1/(x^4-x^3+x^2-x+1)/(x+1)^2/(x^4+x^3+x^2+x+1)^2/(x-1)^5 ogf A000064 72.9176 2+x+x^4+x^9 ogf_with_Euler_Transform A000070 64.4204 -(-2+x)/(1-x) ogf_with_Euler_Transform A000070 28.8781 {a(n+2)-a(n+1),a(0)=2,a(1)=1} ogf_with_Euler_Transform A000071 25.723 -(-2+3*x^2)/(-1+x)/(x^2+x-1) lgdogf A000071 34.2973 -x^2+(1-2*x+x^3)*f(x) ogf A000071 42.3672 1/(x-1)/(x^2-1+x) ogf A000071 48.0162 x^2/(1-2*x+x^3) ogf A000071 16.7498 {a(n+3)-2*a(n+2)+a(n),a(0)=0,a(1)=0,a(2)=1} ogf A000073 28.1913 -(1+2*x+3*x^2)/(x^2-1+x+x^3) lgdogf A000073 46.4328 -1/(-1+x+x^2+x^3) ogf A000073 34.3199 -x^2+(1-x-x^2-x^3)*f(x) ogf A000073 41.5451 -x^2/(-1+x+x^2+x^3) ogf A000073 16.1093 {-a(n+3)+a(n+2)+a(n+1)+a(n),a(0)=0,a(1)=0,a(2)=1} ogf A000078 21.1555 -(1+2*x+4*x^3+3*x^2)/(x^2-1+x+x^4+x^3) lgdogf A000078 38.2813 -1/(-1+x+x^2+x^3+x^4) ogf A000078 29.7743 -x^3+(1-x-x^2-x^3-x^4)*f(x) ogf A000078 34.9525 -x^3/(-1+x+x^2+x^3+x^4) ogf A000079 51.7199 -1+(1-2*x)*f(x) ogf A000079 70.5272 -2/(-1+2*x) lgdogf A000079 86.1999 1/(1-2*x) ogf A000079 59.6769 1/2*ln(1+2*x) revegf A000079 86.1999 x/(2*x+1) revogf A000079 35.2636 {a(n+1)-2*a(n),a(0)=1} ogf A000085 94.1346 1+x-f(x) lgdegf A000085 188.269 1+x] lgdegf A000085 47.0673 exp(1/2*x*(x+2)) egf A000085 15.0615 {(-n-2)*a(n+1)-a(n+2)+a(n+3),a(0)=1,a(1)=1,a(2)=2} ogf A000090 12.2717 (-3240+540*x^3+x^9-36*x^6)/(x-1)/(x^9+36*x^6+540*x^3+3240) egf A000090 37.4609 -(1-x^2+x^3)/(-1+x) lgdegf A000090 16.5525 {a(n+4)-a(n+3),a(0)=1,a(1)=1,a(2)=0,a(3)=1} lgdegf A000096 73.0821 (x-2)/(x-1)^3 ogf A000096 43.1849 -(-5+2*x)/(-1+x)/(x-2) lgdogf A000096 32.7609 -(2*x-x^2)/(-1+3*x-3*x^2+x^3) ogf A000096 12.6676 126*x-63*x^2+(-63+143*x-166*x^2+63*x^3)*f(x)+(23-69*x+69*x^2-23*x^3)*f(x)^2 ogf A000096 18.2705 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=2,a(2)=5} ogf A000097 54.6425 -(2-x^2)/(x-1) ogf_with_Euler_Transform A000097 20.6756 {-a(n+3)+a(n+2),a(0)=2,a(1)=2,a(2)=1} ogf_with_Euler_Transform A000098 45.5619 -(2-x^3)/(x-1) ogf_with_Euler_Transform A000098 14.497 {-a(n+4)+a(n+3),a(0)=2,a(1)=2,a(2)=2,a(3)=1} ogf_with_Euler_Transform A000100 16.3595 -(1+x)*(5*x^3+3*x^2-2)/(x^2+x-1)/(x^3+x^2+x-1) lgdogf A000100 10.7506 -x^3+(1-2*x-x^2+2*x^3+2*x^4+x^5)*f(x)+(x^2-1+2*x-2*x^4-x^3-x^5)*f(x)^2 ogf A000100 28.9438 1/(x^2-1+x)/(-1+x+x^2+x^3) ogf A000100 25.9496 x^3/(1-2*x-x^2+x^3+2*x^4+x^5) ogf A000102 10.8252 -(-2-2*x+15*x^4+8*x^3+7*x^6+12*x^5)/(x^3+x^2+x-1)/(x^4+x^3+x^2+x-1) lgdogf A000102 18.5972 -x^4/(-1+2*x+x^2-2*x^4-3*x^5-2*x^6-x^7) ogf A000102 20.7226 1/(-1+x+x^2+x^3)/(-1+x+x^2+x^3+x^4) ogf A000108 57.734 -1+f(x)-x*f(x)^2 ogf A000108 102.638 -x*(-1+x) revogf A000108 48.6181 2/(1+(1-4*x)^(1/2)) ogf A000108 27.9922 2/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A000108 20.9942 {(-4*n-6)*a(n+1)+(n+3)*a(n+2),a(0)=1,a(1)=1} ogf A000110 143.369 exp(x) lgdegf A000110 23.8948 {(-n-2)*a(n+2)+a(n+1),a(0)=1,a(1)=1} lgdegf A000115 14.0985 -(1+4*x+9*x^4+4*x^3+8*x^5+4*x^2)/(-1+x)/(1+x)/(x^4+x^3+x^2+x+1) lgdogf A000115 26.1237 -1/(x+1)/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A000115 126.887 1+x+x^4 ogf_with_Euler_Transform A000115 28.6518 1/(1-x-x^2+x^3-x^5+x^6+x^7-x^8) ogf A000115 20.1865 {-a(n+5),a(0)=1,a(1)=1,a(2)=0,a(3)=0,a(4)=1} ogf_with_Euler_Transform A000118 29.2773 -(8-4*x+4*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000118 16.6479 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=8,a(1)=-12,a(2)=8} ogf_with_Euler_Transform A000122 38.9071 -(2-x+x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000122 19.4536 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=2,a(1)=-3,a(2)=2} ogf_with_Euler_Transform A000124 31.9211 -(2+x^2)/(-1+x)/(x^2-x+1) lgdogf A000124 44.3349 -(x^2-x+1)/(x-1)^3 ogf A000124 72.548 2+x+x^2-x^5 ogf_with_Euler_Transform A000124 11.9109 5-5*x+5*x^2+(-2+12*x-12*x^2+5*x^3)*f(x)+(-9*x^2-3+9*x+3*x^3)*f(x)^2 ogf A000124 15.3467 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=2,a(2)=4} ogf A000125 37.0102 (1-2*x+2*x^2)/(x-1)^4 ogf A000125 18.9564 -1+2*x-2*x^2+(1-4*x+x^4+6*x^2-4*x^3)*f(x) ogf A000125 22.2061 -2*(1-x+2*x^2)/(-1+x)/(2*x^2-2*x+1) lgdogf A000125 8.54081 {(n+4)*a(n+4)+(-11-3*n)*a(n+3)+(10+4*n)*a(n+2)+(-6-2*n)*a(n+1),a(0)=1,a(1)=2,a(2)=4,a(3)=8} ogf A000126 16.2887 (-1+x-x^3)*f(x)+(2*x^2+1-3*x-x^4+x^3)*f(x)^2 ogf A000126 16.2887 -(-2+2*x+x^4+x^5)/(-1+x)/(x^2+x-1)/(x^3-x+1) lgdogf A000126 25.5966 -(1-x+x^3)/(x^2-1+x)/(x-1)^2 ogf A000126 9.0722 {(-3-n)*a(n+1)-a(n+2)+(2*n+5)*a(n+3)+(-n-2)*a(n+4),a(0)=1,a(1)=2,a(2)=4,a(3)=8} ogf A000127 10.813 (-1+3*x-4*x^2+2*x^3-x^4)*f(x)+(10*x^2+1-5*x+5*x^4-10*x^3-x^5)*f(x)^2 ogf A000127 22.9777 -(1-3*x+4*x^2-2*x^3+x^4)/(x-1)^5 ogf A000127 15.0059 -(2-4*x+x^4+6*x^2)/(-1+x)/(x^4-2*x^3+4*x^2-3*x+1) lgdogf A000127 8.26165 {(2*n+4)*a(n+1)+(-3*n+2)*a(n+2)+(n-2)*a(n+3),a(0)=1,a(1)=2,a(2)=4,a(3)=8,a(4)=16,a(5)=31} ogf A000128 12.7895 (1-2*x+x^2+x^3)*f(x)^2+(-5*x^2-1+4*x+2*x^4-x^5+x^3)*f(x)^3 ogf A000128 22.4784 (1-2*x+x^2+x^3)/(x^2-1+x)/(x-1)^3 ogf A000128 16.4842 -(-1+2*x-x^2-x^3)/(5*x^2+1-4*x-2*x^4+x^5-x^3) ogf A000128 11.2392 -(-2+4*x+5*x^4-4*x^3+2*x^5-2*x^2)/(-1+x)/(x^2+x-1)/(x^3+x^2-2*x+1) lgdogf A000128 7.06465 {(n^2+5*n+8)*a(n+1)+(2*n+4)*a(n+2)+(-2*n^2-8*n-12)*a(n+3)+(n^2+3*n+4)*a(n+4),a(0)=1,a(1)=2,a(2)=4,a(3)=8} ogf A000129 51.7551 -1/(-1+2*x+x^2) ogf A000129 38.8163 -2*(1+x)/(x^2-1+2*x) lgdogf A000129 40.8593 -x+(1-2*x-x^2)*f(x) ogf A000129 22.8331 1/2/x*(-2*x-1+(8*x^2+4*x+1)^(1/2)) revogf A000129 20.9818 {-a(n+2)+2*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A000132 26.8227 -(10-5*x+5*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000132 15.1827 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=10,a(1)=-15,a(2)=10} ogf_with_Euler_Transform A000134 10.1125 (2+4*x+3*x^2+3*x^3+3*x^4+x^9+3*x^5+3*x^6+x^7-x^8)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A000134 12.9129 -(-2-4*x-3*x^2-x^7+x^8-3*x^5-3*x^6-3*x^3-3*x^4-x^9)/(1-x+x^8-x^7) ogf A000138 29.644 -(1-x^3+x^4)/(-1+x) lgdegf A000138 26.8208 -1+x^3-x^4+(1-x)*f(x) lgdegf A000138 6.3285 {(-16+4*n^2)*a(n+1)+(16-9*n-7*n^2)*a(n+2)+(9*n+3*n^2)*a(n+3),a(0)=1,a(1)=1,a(2)=1,a(3)=0} lgdegf A000139 17.9787 1/27+1/3*x-1/27*(-(-1+3*x)^3)^(1/2) revogf A000139 14.6338 2-27*x+(-1+18*x)*f(x)-2*x*f(x)^2-x^2*f(x)^3 ogf A000139 9.98816 {(27*n^2+81*n+60)*a(n+1)+(-4*n^2-22*n-30)*a(n+2),a(0)=2,a(1)=1} ogf A000141 23.9182 -(-6*x+12+6*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000141 24.7155 -(12-6*x+6*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000141 13.9899 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=12,a(1)=-18,a(2)=12} ogf_with_Euler_Transform A000142 55.7152 -1+(1-x)*f(x) egf A000142 80.4776 -1/(-1+x) lgdegf A000142 90.5373 -1/(x-1) egf A000142 80.4776 1-exp(-x) revegf A000142 103.471 1/(1-x) egf A000142 20.1194 {(-n-2)*a(n+1)+a(n+2),a(0)=1,a(1)=1} ogf A000143 26.8412 -(16-8*x+8*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000143 15.1931 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=16,a(1)=-24,a(2)=16} ogf_with_Euler_Transform A000144 21.1512 -(20-10*x+10*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000144 12.7705 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=20,a(1)=-30,a(2)=20} ogf_with_Euler_Transform A000145 20.187 -(24-12*x+12*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000145 12.1884 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=24,a(1)=-36,a(2)=24} ogf_with_Euler_Transform A000152 19.8628 -(32-16*x+16*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000152 11.9926 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=32,a(1)=-48,a(2)=32} ogf_with_Euler_Transform A000153 37.1051 -exp(-x)/(x-1)^3 egf A000153 14.1353 {a(n)*n+(n+2)*a(n+1)-a(n+2),a(0)=0,a(1)=1} ogf A000156 19.5991 -(48-24*x+24*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A000156 11.8334 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=48,a(1)=-72,a(2)=48} ogf_with_Euler_Transform A000165 44.7362 -1+(1-2*x)*f(x) egf A000165 67.1044 -1/(2*x-1) egf A000165 61.004 -2/(-1+2*x) lgdegf A000165 74.5604 1/(1-2*x) egf A000165 17.659 {(-2*n-4)*a(n+1)+a(n+2),a(0)=1,a(1)=2} ogf A000166 44.5993 -exp(-x)/(x-1) egf A000166 48.03 -x+(1-x)*f(x) lgdegf A000166 69.3767 -x/(-1+x) lgdegf A000166 11.3525 {(n+2)*a(n+1)+(n+2)*a(n+2)-a(n+3),a(0)=1,a(1)=0,a(2)=1} ogf A000168 25.2428 -1+16*x+(1-18*x)*f(x)+27*x^2*f(x)^2 ogf A000168 17.67 1/32+9/16*x-27/32*x^2-1/32*((x-1)*(9*x-1)^3)^(1/2) revogf A000168 10.6446 1/9*(1-12*x-(1-12*x)^(1/2)+24*(1-12*x)^(1/2)*x)/(1+(1-12*x)^(1/2))/x/(1-12*x)^(1/2) ogf A000168 19.2065 {(-12*n-18)*a(n+1)+(n+4)*a(n+2),a(0)=1,a(1)=2} ogf A000172 22.7168 HeunG(-1/8,1/4,1,1,1,1,-x) ogf A000172 6.63637 {(32+32*n+8*n^2)*a(n+1)+(44+35*n+7*n^2)*a(n+2)+(-6*n-n^2-9)*a(n+3),a(0)=1,a(1)=2,a(2)=10} ogf A000172 6.63637 {(32+32*n+8*n^2)*a(n+1)+(44+35*n+7*n^2)*a(n+2)+(-n^2-6*n-9)*a(n+3),a(0)=1,a(1)=2,a(2)=10} ogf A000180 34.5144 -(2+3*x)/(-1+3*x) lgdegf A000180 30.8813 -2-3*x+(1-3*x)*f(x) lgdegf A000180 36.6716 -exp(-x)/(3*x-1) egf A000180 9.46363 {(-3*n-6)*a(n+1)+(-3*n-8)*a(n+2)+a(n+3),a(0)=1,a(1)=2,a(2)=13} ogf A000184 12.8334 {(-288-136*n-16*n^2)*a(n+1)+(114+62*n+8*n^2)*a(n+2)+(-7*n-12-n^2)*a(n+3),a(0)=2,a(1)=22,a(2)=164} ogf A000193 6.72679 (-1+2*x^3-11*x^10-3*x^2-32*x^31+31*x^32+10*x^11)/(-1+x)/(1+x)/(x^2-x+1)/(x^29-x^26+x^23-x^20+x^17-x^14+x^11+1) lgdogf A000193 29.5979 -(-x-x^12-x^4-x^33)/(1-x) ogf A000193 12.1303 -(x+1)*(x^2-x+1)*(x^29-x^26+x^23-x^20+x^17-x^14+x^11+1)/(x-1) ogf A000194 48.9868 -(-1-x-x^2)/(1+x^2) ogf_with_Euler_Transform A000194 25.8541 {a(n+3)+a(n+1),a(0)=1,a(1)=1,a(2)=0} ogf_with_Euler_Transform A000195 17.6178 -(-x^2-x^7-x^20+x^36+x^41)/(1-x-x^34+x^35) ogf A000202 12.1237 (1+2*x+x^2+2*x^3+2*x^4+x^5+2*x^6+x^7+x^8)/(x+1)/(x^4+1)/(x^2+1)/(x-1)^2 ogf A000202 15.1014 -(1+2*x+x^7+x^2+x^8+x^5+2*x^3+2*x^4+2*x^6)/(-x^9-1+x+x^8) ogf A000204 40.4823 -(-1-2*x)/(-x^2+1-x) ogf A000204 44.9804 -(1+2*x)/(x^2-1+x) ogf A000204 25.3015 -(3+2*x+2*x^2)/(2*x+1)/(x^2+x-1) lgdogf A000204 40.4823 1+2*x+(x^2-1+x)*f(x) ogf A000204 21.8823 1/2/(2+x)*(-x-1+(5*x^2+10*x+1)^(1/2)) revogf A000204 23.8131 {a(n+2)-a(n+1)-a(n),a(0)=1,a(1)=3} ogf A000211 23.6971 -(-4+5*x+x^2)/(1-2*x+x^3) ogf A000211 20.4286 -(-4+5*x+x^2)/(x-1)/(x^2-1+x) ogf A000211 10.7714 -(3-2*x+x^4+10*x^3-10*x^2)/(-1+x)/(x^2+5*x-4)/(x^2+x-1) lgdogf A000211 8.11546 -1572+1965*x+393*x^2+(373-761*x+5*x^2+393*x^3)*f(x)+(5-10*x+5*x^3)*f(x)^2 ogf A000211 13.7774 {a(n+3)-2*a(n+2)+a(n),a(0)=4,a(1)=3,a(2)=5} ogf A000212 20.5918 -(-x^2-x^3)/(1-2*x+x^2-x^5-x^3+2*x^4) ogf A000212 17.7185 -(3+4*x+4*x^3+7*x^2)/(-1+x)/(1+x)/(x^2+x+1) lgdogf A000212 31.7456 -(x+1)/(x^2+x+1)/(x-1)^3 ogf A000212 108.842 3-x+x^2 ogf_with_Euler_Transform A000212 7.61895 {(-n^2-6*n-9)*a(n+1)+(-2*n-5)*a(n+2)+(-2*n-5)*a(n+3)+(n^2+4*n+4)*a(n+4),a(0)=0,a(1)=0,a(2)=1,a(3)=3} ogf A000213 30.4151 (x-1)*(x+1)/(-1+x+x^2+x^3) ogf A000213 34.3822 -(-1+x^2)/(1-x-x^2-x^3) ogf A000213 18.8284 -(-1+x^4-4*x^2)/(-1+x)/(1+x)/(x^3+x^2+x-1) lgdogf A000213 16.1386 -1+x^2+(2-x-2*x^2-x^3)*f(x)+(-1+x^3+x+x^2)*f(x)^2 ogf A000213 16.1386 {-a(n+3)+a(n+2)+a(n+1)+a(n),a(0)=1,a(1)=1,a(2)=1} ogf A000216 9.86188 -(2+4*x+16*x^2+37*x^3+58*x^4+89*x^5+145*x^6+42*x^7+18*x^8)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A000216 12.6585 -(2+4*x+42*x^7+16*x^2+18*x^8+89*x^5+37*x^3+145*x^6+58*x^4)/(-1+x^8) ogf A000217 82.173 -1/(x-1)^3 ogf A000217 91.3033 -3/(-1+x) lgdogf A000217 32.8692 x+(-1+3*x-3*x^2+x^3)*f(x) ogf A000217 43.2489 x/(1-3*x+3*x^2-x^3) ogf A000217 15.8025 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=3} ogf A000218 8.97387 -(3+9*x+89*x^7+81*x^2-61*x^10+142*x^8+37*x^5+65*x^3+58*x^6+33*x^9-45*x^12-61*x^11+61*x^4)/(-1+x^8) ogf A000219 62.388 -1/(-1+2*x-x^2) ogf_with_Euler_Transform A000219 25.2924 {-a(n+2)+2*a(n+1)-a(n),a(0)=1,a(1)=2} ogf_with_Euler_Transform A000221 8.45654 (-5-25*x-29*x^2-85*x^3-89*x^4+9*x^9+27*x^11-145*x^5-42*x^6-20*x^7+x^8-8*x^10)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A000221 10.3248 -(5+25*x+20*x^7+29*x^2+8*x^10-x^8+145*x^5+85*x^3+42*x^6-9*x^9-27*x^11+89*x^4)/(-1+x^8) ogf A000225 30.4488 -(-3+4*x)/(2*x-1)/(-1+x) lgdogf A000225 22.1446 -1/4*(-1-3*x+(1+6*x+x^2)^(1/2))/x revogf A000225 48.718 1/(2*x-1)/(x-1) ogf A000225 34.7986 x+(-1+3*x-2*x^2)*f(x) ogf A000225 48.718 x/(1-3*x+2*x^2) ogf A000225 19.2308 {a(n+2)-3*a(n+1)+2*a(n),a(0)=0,a(1)=1} ogf A000240 8.36843 -336*x-112*x^3+224*x^2+(112-233*x-115*x^3+230*x^2)*f(x)+(3-6*x+6*x^2-3*x^3)*f(x)^2 lgdegf A000240 22.1358 -x*(3+x^2-2*x)/(-1+x)/(x^2-x+1) lgdegf A000240 27.4484 exp(-x)*(x^2-x+1)/(x-1)^2 egf A000240 9.14948 {(12+7*n+n^2)*a(n+1)+(6*n+8+n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=0,a(2)=3} ogf A000241 4.85693 -1/(x+1)^3/(x-1)^5*(x^2+x+1) ogf A000241 15.1105 3+3*x-x^2 ogf_with_Euler_Transform A000241 5.23054 x^5*f(x)^2+(-1+3*x)*f(x)^3 ogf A000241 1.4782 {(-n-n^2)*a(n)+(-2*n+2)*a(n+1)+(n^2-5*n+6)*a(n+2),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=1} ogf A000244 49.0944 -1+(1-3*x)*f(x) ogf A000244 73.6416 -1/(3*x-1) ogf A000244 66.9469 -3/(-1+3*x) lgdogf A000244 81.824 1/(1-3*x) ogf A000244 56.6474 1/3*ln(1+3*x) revegf A000244 81.824 x/(1+3*x) revogf A000244 33.4735 {a(n+1)-3*a(n),a(0)=1} ogf A000245 23.1234 6/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A000245 33.1771 8*x/(1+(1+4*x)^(1/2))^3 revogf A000245 36.3368 8/(1+(1-4*x)^(1/2))^3 ogf A000245 29.349 x+(-1+3*x)*f(x)+x^2*f(x)^2 ogf A000245 13.1564 {(12+14*n+4*n^2)*a(n+1)+(-5*n-n^2-4)*a(n+2),a(0)=0,a(1)=1} ogf A000246 31.6988 -1-x+(1-x)*f(x)^2 egf A000246 35.9253 -1/(-1+x)/(1+x) lgdegf A000246 18.5821 -1/(x-1)*(-(x-1)*(x+1))^(1/2) egf A000246 12.8305 {(n^2+n)*a(n)-a(n+2)+a(n+1),a(0)=1,a(1)=1} ogf A000247 27.493 (-3+2*x)/(2*x-1)/(x-1)^2 ogf A000247 19.9949 -(-3*x+2*x^2)/(1-4*x+5*x^2-2*x^3) ogf A000247 16.4958 -2*(5-10*x+4*x^2)/(-1+x)/(2*x-1)/(2*x-3) lgdogf A000247 7.33148 4350*x-2900*x^2+(-1450+4453*x-6352*x^2+2900*x^3)*f(x)+(449-1796*x+2245*x^2-898*x^3)*f(x)^2 ogf A000247 11.997 {a(n+3)-4*a(n+2)+5*a(n+1)-2*a(n),a(0)=0,a(1)=3,a(2)=10} ogf A000248 45.9215 exp(x)*(1+x) lgdegf A000248 10.3973 {(n+3)*a(n+3)+n*a(n+2)-a(n+1),a(0)=1,a(1)=2,a(2)=3/2} lgdegf A000253 15.9725 -(-4+10*x+8*x^3-9*x^2)/(2*x-1)/(x^3-x^2+2*x-1) lgdogf A000253 29.3895 1/(2*x-1)/(x^3-x^2+2*x-1) ogf A000253 8.44525 28*x+(-28+239*x-140*x^2+84*x^3-56*x^4)*f(x)+(-127+508*x-635*x^2+381*x^3-254*x^4)*f(x)^2 ogf A000253 27.2125 x/(1-4*x+5*x^2-3*x^3+2*x^4) ogf A000254 10.6737 {(n^2+4*n+4)*a(n+1)+(-2*n-5)*a(n+2)+a(n+3),a(0)=0,a(1)=1,a(2)=3} ogf A000255 41.4793 -(1+x)/(-1+x) lgdegf A000255 35.9488 -1-x+(1-x)*f(x) lgdegf A000255 35.9488 exp(-x)/(x-1)^2 egf A000255 9.4602 {(-n-2)*a(n+1)+(-n-3)*a(n+2)+a(n+3),a(0)=1,a(1)=1,a(2)=3} ogf A000256 6.24841 -1+54*x+76*x^2+8*x^3+(1-115*x-108*x^2-12*x^3)*f(x)+(76*x+51*x^2+6*x^3)*f(x)^2+(-16*x-8*x^2-x^3)*f(x)^3 ogf A000256 6.24841 -1+54*x+8*x^3+76*x^2+(1-115*x-12*x^3-108*x^2)*f(x)+(76*x+6*x^3+51*x^2)*f(x)^2+(-16*x-8*x^2-x^3)*f(x)^3 ogf A000257 15.749 -1+11*x+x^2+(1-12*x-8*x^2)*f(x)+16*x^2*f(x)^2 ogf A000257 8.85881 {(4*n+8*n^2)*a(n)+(-48-59*n-17*n^2)*a(n+1)+(12*n+16+2*n^2)*a(n+2),a(0)=1,a(1)=1} ogf A000259 9.1843 1+(-1+5*x)*f(x)+(-2*x+11*x^2)*f(x)^2+(11*x^3+x^4-x^2)*f(x)^3 ogf A000260 14.6456 1/32+5/8*x-1/4*x^2-1/32*(-(8*x-1)^3)^(1/2) revogf A000260 6.98997 {(-2544*n-256*n^3-1408*n^2-1512)*a(n+1)+(27*n^3+216*n^2+573*n+504)*a(n+2),a(0)=1,a(1)=1} ogf A000261 46.9838 exp(-x)/(x-1)^4 egf A000261 16.0172 {-a(n)*n+(-n-3)*a(n+1)+a(n+2),a(0)=0,a(1)=1} ogf A000262 15.7276 1+(2*x-x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 lgdegf A000262 56.6193 1/(-1+x)^2 lgdegf A000262 25.736 1/exp(1)*exp(-1/(x-1)) egf A000262 11.1018 {(n^2+n)*a(n)+(-2*n-3)*a(n+1)+a(n+2),a(0)=1,a(1)=1} ogf A000266 41.868 -(1-x+x^2)/(-1+x) lgdegf A000266 37.4609 -1+x-x^2+(1-x)*f(x) lgdegf A000266 35.5878 -exp(-1/2*x^2)/(x-1) egf A000266 8.57538 {(-n^2-5*n-6)*a(n+1)+(n+3)*a(n+2)+(-n-4)*a(n+3)+a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=3} ogf A000271 8.55636 {a(n+1)+(n+3)*a(n+2)+(n+3)*a(n+3)-a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=1} ogf A000274 10.4384 -(6+12*x-3*x^4+9*x^3+x^5-x^2)/(-1+x)/(x^4-2*x^3+5*x^2+2) lgdegf A000274 14.9884 1/2*exp(-x)/(x-1)^4*(x^4-2*x^3+5*x^2+2) egf A000274 7.59153 {(20+9*n+n^2)*a(n+1)+(15+8*n+n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=3,a(2)=18} ogf A000276 4.97118 {(120+94*n+24*n^2+2*n^3)*a(n+1)+(366+219*n+44*n^2+3*n^3)*a(n+2)+(-149-61*n-6*n^2)*a(n+3)+(3*n+12)*a(n+4),a(0)=3,a(1)=20,a(2)=130,a(3)=924} ogf A000285 29.5455 -(-1-3*x)/(-x^2+1-x) ogf A000285 32.8283 -(1+3*x)/(x^2-1+x) ogf A000285 18.4659 -(4+2*x+3*x^2)/(3*x+1)/(x^2+x-1) lgdogf A000285 15.9705 1/2/(3+x)*(-x-1+(5*x^2+14*x+1)^(1/2)) revogf A000285 12.0594 5+15*x+(-2+14*x+5*x^2)*f(x)+(-3+3*x+3*x^2)*f(x)^2 ogf A000285 17.3797 {a(n+2)-a(n+1)-a(n),a(0)=1,a(1)=4} ogf A000287 4.91301 {(150+50*n+4*n^2)*a(n+1)+(306+119*n+11*n^2)*a(n+2)+(43*n+84+5*n^2)*a(n+3)+(-26*n-72-2*n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=4,a(3)=6} ogf A000288 21.7631 (-1+x^2+2*x^3)/(-1+x+x^2+x^3+x^4) ogf A000288 11.0489 -(-1-x^4-8*x^3+2*x^6+2*x^5+2*x^2)/(2*x^3+x^2-1)/(x^4+x^3+x^2+x-1) lgdogf A000288 21.7631 -(1-x^2-2*x^3)/(-1+x+x^2+x^3+x^4) ogf A000288 9.09089 -4+4*x^2+8*x^3+(7-4*x-7*x^2-10*x^3-4*x^4)*f(x)+(3*x^2+3*x^4-3+3*x+3*x^3)*f(x)^2 ogf A000290 58.4158 -(x+1)/(x-1)^3 ogf A000290 30.2897 -(x+x^2)/(-1+3*x-3*x^2+x^3) ogf A000290 38.9438 -2*(x+2)/(-1+x)/(1+x) lgdogf A000290 272.607 4-x ogf_with_Euler_Transform A000290 10.9043 63*x+63*x^2+(-63+97*x-281*x^2+63*x^3)*f(x)+(92-276*x+276*x^2-92*x^3)*f(x)^2 ogf A000290 15.7273 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=4} ogf A000292 85.0154 -4/(-1+x) lgdogf A000292 85.0154 1/(x-1)^4 ogf A000292 9.93687 9*x+(-9+50*x-54*x^2+36*x^3-9*x^4)*f(x)+(-14+56*x-84*x^2+56*x^3-14*x^4)*f(x)^2 ogf A000292 30.6055 x/(1-4*x+6*x^2-4*x^3+x^4) ogf A000292 18.2176 {(n+1)*a(n+2)+(-4-n)*a(n+1),a(0)=0,a(1)=1} ogf A000294 62.1534 1/(1-3*x+3*x^2-x^3) ogf_with_Euler_Transform A000294 22.7099 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=3,a(2)=6} ogf_with_Euler_Transform A000295 43.1 -1/(2*x-1)/(x-1)^2 ogf A000295 29.8384 -2*(-2+3*x)/(2*x-1)/(-1+x) lgdogf A000295 26.7517 x^2+(-1+4*x-5*x^2+2*x^3)*f(x) ogf A000295 33.7304 x^2/(1-4*x+5*x^2-2*x^3) ogf A000295 14.3667 {a(n+3)-4*a(n+2)+5*a(n+1)-2*a(n),a(0)=0,a(1)=0,a(2)=1} ogf A000296 17.1054 {-a(n)+(n+1)*a(n+1),a(0)=0,a(1)=1} lgdegf A000297 52.7857 (x-2)^2/(x-1)^4 ogf A000297 19.3118 -(-4*x+4*x^2-x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A000297 35.9902 -2*(-3+x)/(-1+x)/(x-2) lgdogf A000297 6.71004 -7172*x+7172*x^2-1793*x^3+(1793-8244*x+11830*x^2-7440*x^3+1793*x^4)*f(x)+(268-1072*x+1608*x^2-1072*x^3+268*x^4)*f(x)^2 ogf A000297 11.6439 {(-4-2*n)*a(n+3)+(9+3*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=4,a(2)=12} ogf A000302 46.9956 -1+(1-4*x)*f(x) ogf A000302 64.085 -1/(-1+4*x) ogf A000302 64.085 -4/(-1+4*x) lgdogf A000302 78.3261 1/(1-4*x) ogf A000302 54.2257 1/4*ln(1+4*x) revegf A000302 78.3261 x/(1+4*x) revogf A000302 32.0425 {a(n+1)-4*a(n),a(0)=1} ogf A000305 9.38727 1/2/(x+1)^2*(-11*x^2-15*x-4+((x+1)*(5*x+1)*(4+5*x)^2)^(1/2)) revogf A000305 7.411 4+x+(-4+19*x+3*x^2)*f(x)+(-4*x+26*x^2+3*x^3)*f(x)^2+(-x^2+11*x^3+x^4)*f(x)^3 ogf A000305 7.411 4+x+(-4+19*x+3*x^2)*f(x)+(-4*x+3*x^3+26*x^2)*f(x)^2+(-x^2+11*x^3+x^4)*f(x)^3 ogf A000309 12.5039 1-27*x+(-1+36*x)*f(x)-8*x*f(x)^2-16*x^2*f(x)^3 ogf A000309 16.4337 1/54+2/3*x-1/54*(-(12*x-1)^3)^(1/2) revogf A000309 9.12984 {(27*n^2+81*n+60)*a(n+1)+(-2*n^2-11*n-15)*a(n+2),a(0)=1,a(1)=1} ogf A000311 51.6763 1+2*x-exp(x) revegf A000311 8.05346 {2*n*a(n+1)+(-5*n-2-2*n^2)*a(n+2)+(5*n+6+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=-1/2} revegf A000313 7.97808 -(24+60*x+x^7-52*x^4+77*x^3-8*x^6+30*x^5-12*x^2)/(-1+x)/(x^6-6*x^5+18*x^4-22*x^3+27*x^2+6) lgdegf A000313 13.055 -1/6/(x-1)^5*exp(-x)*(6+27*x^2-22*x^3+18*x^4-6*x^5+x^6) egf A000313 9.20548 {(30+11*n+n^2)*a(n+1)+(18+9*n+n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=4,a(2)=30} ogf A000321 71.0104 -1-2*x-f(x) lgdegf A000321 111.588 -1-2*x] lgdegf A000321 60.0857 exp(-(x+1)*x) egf A000321 14.738 {(2*n+4)*a(n+1)+a(n+2)+a(n+3),a(0)=1,a(1)=-1,a(2)=-1} ogf A000322 16.5365 (-1+x^2+2*x^3+3*x^4)/(-1+x+x^2+x^3+x^4+x^5) ogf A000322 7.90078 -(-1+4*x^7-15*x^4+4*x^3+3*x^8+2*x^6-4*x^5+2*x^2)/(3*x^4+2*x^3+x^2-1)/(x^5+x^4+x^3+x^2+x-1) lgdogf A000322 16.5365 -(1-x^2-2*x^3-3*x^4)/(-1+x+x^2+x^3+x^4+x^5) ogf A000322 7.0403 -5+5*x^2+10*x^3+15*x^4+(8-5*x-8*x^2-11*x^3-14*x^4-5*x^5)*f(x)+(-3+3*x^3+3*x+3*x^2+3*x^5+3*x^4)*f(x)^2 ogf A000325 13.7243 -(-1+3*x+6*x^3-6*x^2)/(-1+x)/(2*x-1)/(3*x^2-3*x+1) lgdogf A000325 19.6062 -(-1+3*x-3*x^2)/(5*x^2+1-4*x-2*x^3) ogf A000325 22.8739 -(1-3*x+3*x^2)/(2*x-1)/(x-1)^2 ogf A000325 10.0914 1-3*x+3*x^2+(-4+13*x-14*x^2+2*x^3)*f(x)+(3-12*x+15*x^2-6*x^3)*f(x)^2 ogf A000325 12.4767 {-a(n+3)+4*a(n+2)-5*a(n+1)+2*a(n),a(0)=1,a(1)=1,a(2)=2} ogf A000326 47.1643 -(1+2*x)/(x-1)^3 ogf A000326 32.81 -(5+4*x)/(2*x+1)/(-1+x) lgdogf A000326 26.0217 -(x+2*x^2)/(-1+3*x-3*x^2+x^3) ogf A000326 10.3374 26*x+52*x^2+(-26+51*x-132*x^2+26*x^3)*f(x)+(27-81*x+81*x^2-27*x^3)*f(x)^2 ogf A000326 14.5121 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=5} ogf A000330 62.6635 (x+1)/(x-1)^4 ogf A000330 38.7917 -(3*x+5)/(-1+x)/(1+x) lgdogf A000330 24.6856 -(x+x^2)/(-1+4*x-x^4-6*x^2+4*x^3) ogf A000330 7.27344 1793*x+1793*x^2+(-1793+9316*x-8614*x^2+7172*x^3-1793*x^4)*f(x)+(-2144*x^4-2144+8576*x+8576*x^3-12864*x^2)*f(x)^2 ogf A000330 271.542 5-x ogf_with_Euler_Transform A000330 14.0453 {(n+2)*a(n+3)-5*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=1,a(2)=5} ogf A000332 80.6032 -1/(x-1)^5 ogf A000332 89.5592 -5/(-1+x) lgdogf A000332 19.6593 x^4+(-1+5*x-10*x^2+10*x^3-5*x^4+x^5)*f(x) ogf A000332 12.5943 {(-2+n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=1} ogf A000332 12.5943 {(-2+n)*a(n+2)+(-n-2)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=1} ogf A000332 12.7942 {(n-2)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=1} ogf A000337 26.7981 -(-5+6*x)/(2*x-1)/(-1+x) lgdogf A000337 35.7308 -1/(x-1)/(2*x-1)^2 ogf A000337 27.9632 -x/(-1+5*x-8*x^2+4*x^3) ogf A000337 10.9009 x+(-1+10*x-8*x^2+4*x^3)*f(x)+(-40*x^2-5+25*x+20*x^3)*f(x)^2 ogf A000337 11.9103 {a(n+3)-5*a(n+2)+8*a(n+1)-4*a(n),a(0)=0,a(1)=1,a(2)=5} ogf A000338 37.7456 (2*x-5)*(x^2+x+1)/(x-1)^3 ogf A000338 23.591 -3*(-6-4*x+x^2)/(2*x-5)/(-1+x)/(x^2+x+1) lgdogf A000338 9.16155 -7525-4515*x-4515*x^2+3010*x^3+(2090-4164*x+4866*x^2-1739*x^3)*f(x)+(-117+351*x-351*x^2+117*x^3)*f(x)^2 ogf A000338 14.7444 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=5,a(1)=18,a(2)=42,a(3)=75} ogf A000340 25.2146 -(-5+9*x)/(3*x-1)/(-1+x) lgdogf A000340 33.6194 -1/(3*x-1)/(x-1)^2 ogf A000340 7.20416 -1053+(3058-5265*x+7371*x^2-3159*x^3)*f(x)+(-14035*x^2+6015*x^3-2005+10025*x)*f(x)^2 ogf A000340 28.8166 1/(1-5*x+7*x^2-3*x^3) ogf A000340 11.0027 {a(n+3)-5*a(n+2)+7*a(n+1)-3*a(n),a(0)=1,a(1)=5,a(2)=18} ogf A000344 21.7526 -25+(5-20*x)*f(x)+(x-4*x^2)*f(x)^2 lgdogf A000344 21.7526 10/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A000344 33.6177 32/(1+(1-4*x)^(1/2))^5 ogf A000344 12.5354 {(-56-30*n-4*n^2)*a(n+1)+(9*n+14+n^2)*a(n+2),a(0)=1,a(1)=5} ogf A000346 18.4054 1+(-1+4*x)*f(x)+(16*x^3+x-8*x^2)*f(x)^2 ogf A000346 11.7674 2*x*(8*x+1+3*(1+8*x)^(1/2))/(1+8*x)^(1/2)/(1+(1+8*x)^(1/2))^3 revogf A000346 10.11 {(-16*n-40)*a(n+1)+(8*n+26)*a(n+2)+(-n-4)*a(n+3),a(0)=1,a(1)=5,a(2)=22} ogf A000351 48.3064 -1+(1-5*x)*f(x) ogf A000351 65.8723 -1/(-1+5*x) ogf A000351 65.8723 -5/(-1+5*x) lgdogf A000351 80.5106 1/(1-5*x) ogf A000351 55.7381 1/5*ln(1+5*x) revegf A000351 80.5106 x/(1+5*x) revogf A000351 32.9362 {a(n+1)-5*a(n),a(0)=1} ogf A000352 10.6115 -(-29+141*x+108*x^3-216*x^2)/(6*x-5)/(-1+x)/(3*x-1)/(2*x-1) lgdogf A000352 16.921 -(5-6*x)/(-17*x^2-1+7*x+17*x^3-6*x^4) ogf A000352 19.5649 -(6*x-5)/(3*x-1)/(2*x-1)/(x-1)^2 ogf A000352 4.89122 {(-6*n+6)*a(n+1)+(11*n-17)*a(n+2)+(-6*n+11)*a(n+3)+(n-2)*a(n+4),a(0)=5,a(1)=29,a(2)=118,a(3)=418,a(4)=1383,a(5)=4407,a(6)=13736} ogf A000354 36.2534 -(1+2*x)/(2*x-1) lgdegf A000354 30.5292 -1-2*x+(1-2*x)*f(x) lgdegf A000354 36.2534 -exp(-x)/(2*x-1) egf A000354 9.50909 {(-2*n-4)*a(n+1)+(-2*n-5)*a(n+2)+a(n+3),a(0)=1,a(1)=1,a(2)=5} ogf A000356 8.33943 {(16*n^2+96*n+140)*a(n+1)+(-n^2-9*n-20)*a(n+2),a(0)=1,a(1)=5} ogf A000363 9.69804 -(-61+445*x+675*x^3-963*x^2)/(-1+x)/(9*x-5)/(3*x-1)/(5*x-1) lgdogf A000363 16.3481 -(9*x-5)/(-1+5*x)/(3*x-1)^2/(x-1)^3 ogf A000363 4.30214 {(-360-150*n-15*n^2)*a(n+1)+(387+195*n+23*n^2)*a(n+2)+(-68*n-123-9*n^2)*a(n+3)+(7*n+12+n^2)*a(n+4),a(0)=5,a(1)=61,a(2)=479,a(3)=3111} ogf A000381 6.49807 -(-2+x+2*x^2)/(x-1)/(x^2-1+x) ogf A000381 7.53777 -(2-x-2*x^2)/(-1+2*x-x^3) ogf A000381 3.42626 -(3-4*x+2*x^4+2*x^3-2*x^2)/(-1+x)/(x^2+x-1)/(2*x^2+x-2) lgdogf A000381 3.14074 -12+6*x+12*x^2+(8-13*x-2*x^2+6*x^3)*f(x)+(-1-x^3+2*x)*f(x)^2 ogf A000381 4.28282 {-a(n+3)+2*a(n+2)-a(n),a(0)=2,a(1)=3,a(2)=4} ogf A000382 18.8379 -(-6+x+2*x^2+4*x^3+x^4)/(1-2*x+x^4) ogf A000382 14.9847 -(-6+x+2*x^2+4*x^3+x^4)/(x-1)/(-1+x+x^2+x^3) ogf A000382 7.94369 -(11-4*x+9*x^4-12*x^3+4*x^6+4*x^5-8*x^2)/(-1+x)/(x^3+x^2+x-1)/(x^4+4*x^3+2*x^2+x-6) lgdogf A000382 5.99387 -5490+915*x+1830*x^2+3660*x^3+915*x^4+(6591-2776*x-1892*x^2-3784*x^3-31*x^4)*f(x)+(-946+1892*x-946*x^4)*f(x)^2 ogf A000383 14.8525 (-1+x^2+2*x^3+3*x^4+4*x^5)/(-1+x+x^2+x^3+x^4+x^5+x^6) ogf A000383 7.28871 -(-1+6*x^9+5*x^4+4*x^3+4*x^10+5*x^8-10*x^6-26*x^5+2*x^2)/(4*x^5+3*x^4+2*x^3+x^2-1)/(x^6+x^5+x^4+x^3+x^2+x-1) lgdogf A000384 51.0801 -(1+3*x)/(x-1)^3 ogf A000384 15.1349 -(x+3*x^2-158*x^21+81*x^20+77*x^22)/(-1+3*x-3*x^2+x^3) ogf A000384 35.534 -6*(1+x)/(3*x+1)/(-1+x) lgdogf A000384 8.8835 1365*x+4095*x^2+(-1365+3023*x-7311*x^2+1365*x^3)*f(x)+(1072-3216*x+3216*x^2-1072*x^3)*f(x)^2 ogf A000384 15.717 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=6} ogf A000387 14.6691 -1/2*exp(-x)*(x^4-4*x^3+7*x^2-4*x+2)/(x-1)^3 egf A000387 10.7573 -x*(12-6*x^3+15*x^2+x^4-16*x)/(-1+x)/(x^4-4*x^3+7*x^2-4*x+2) lgdegf A000387 8.49261 {(20+9*n+n^2)*a(n+1)+(7*n+10+n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=0,a(2)=6} ogf A000389 89.7041 -6/(-1+x) lgdogf A000389 20.1834 1/(1-6*x+15*x^2-20*x^3+15*x^4-6*x^5+x^6) ogf A000389 89.7041 1/(x-1)^6 ogf A000389 11.3709 {(-3+n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=1} ogf A000389 11.5334 {(n-3)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=1} ogf A000392 27.6295 -1/(x-1)/(3*x-1)/(2*x-1) ogf A000392 16.5777 -2*(3-11*x+9*x^2)/(-1+x)/(3*x-1)/(2*x-1) lgdogf A000392 17.9218 -x^3*f(x)+(1-6*x+11*x^2-6*x^3)*f(x)^2 ogf A000392 25.5041 -x^3/(-1+6*x-11*x^2+6*x^3) ogf A000392 10.2017 {-a(n+4)+6*a(n+3)-11*a(n+2)+6*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A000399 3.74747 {(-64-48*n-12*n^2-n^3)*a(n+1)+(115*n+122+33*n^2+3*n^3)*a(n+2)+(-93*n-90-30*n^2-3*n^3)*a(n+3)+(26*n+24+9*n^2+n^3)*a(n+4),a(0)=1,a(1)=6,a(2)=35/2,a(3)=75/2} egf A000399 5.34361 {(-n^3-12*n^2-48*n-64)*a(n+1)+(3*n^2+27*n+61)*a(n+2)+(-3*n-15)*a(n+3)+a(n+4),a(0)=1,a(1)=6,a(2)=35,a(3)=225} ogf A000400 48.4956 -1+(1-6*x)*f(x) ogf A000400 66.1303 -1/(-1+6*x) ogf A000400 72.7434 -6/(6*x-1) lgdogf A000400 80.826 1/(1-6*x) ogf A000400 55.9564 1/6*ln(1+6*x) revegf A000400 80.826 x/(1+6*x) revogf A000400 33.0652 {a(n+1)-6*a(n),a(0)=1} ogf A000407 18.0617 -1+(1-12*x+48*x^2-64*x^3)*f(x)^2 egf A000407 52.5432 -6/(-1+4*x) lgdegf A000407 38.5317 1/(1-4*x)^(3/2) egf A000407 33.9985 x*(1+x)/(1+2*x)^2 revegf A000407 14.8199 {(-4*n-10)*a(n+1)+a(n+2),a(0)=1,a(1)=6} ogf A000420 46.7777 -1+(1-7*x)*f(x) ogf A000420 63.7878 -1/(-1+7*x) ogf A000420 63.7878 -7/(-1+7*x) lgdogf A000420 77.9629 1/(1-7*x) ogf A000420 53.9743 1/7*ln(1+7*x) revegf A000420 77.9629 x/(1+7*x) revogf A000420 31.8939 {a(n+1)-7*a(n),a(0)=1} ogf A000422 7.32018 441-1260*x+900*x^2+(-42+522*x+600*x^3-1080*x^2)*f(x)+(100*x^4+141*x^2+1-22*x-220*x^3)*f(x)^2 lgdogf A000425 5.4155 {(20+9*n+n^2)*a(n+1)+(38*n+40+11*n^2+n^3)*a(n+2)+(31*n+30+10*n^2+n^3)*a(n+3)+(-6*n-8-n^2)*a(n+4),a(0)=2,a(1)=0,a(2)=0,a(3)=8} ogf A000431 18.7039 -2*x^3*f(x)+(1-8*x+20*x^2-16*x^3)*f(x)^2 ogf A000431 25.7985 -2*x^3/(-1+8*x-20*x^2+16*x^3) ogf A000431 35.6265 -2/(-1+4*x)/(2*x-1)^2 ogf A000431 26.7198 -8*(-1+3*x)/(-1+4*x)/(2*x-1) lgdogf A000431 11.3357 {-a(n+4)+8*a(n+3)-20*a(n+2)+16*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=2} ogf A000439 31.5672 (-3+2*x)*(x^2-3*x+3)/(x-1)^5 ogf A000439 17.331 -(-30+42*x+4*x^3-21*x^2)/(-1+x)/(2*x-3)/(x^2-3*x+3) lgdogf A000439 16.3682 -(-9+15*x-9*x^2+2*x^3)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A000439 9.30402 {(60+29*n+3*n^2)*a(n+1)+(-188-80*n-8*n^2)*a(n+2)+(43*n+84+5*n^2)*a(n+3),a(0)=9,a(1)=30,a(2)=69} ogf A000442 9.85608 {(-n^3-6*n^2-12*n-8)*a(n+1)+a(n+2),a(0)=1,a(1)=1} ogf A000442 11.7792 {(n^2+4*n+4)*a(n+1)-a(n+2),a(0)=1,a(1)=1} egf A000447 48.5633 (1+6*x+x^2)/(x-1)^4 ogf A000447 23.659 -(-x-6*x^2-x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A000447 27.1383 -2*(5+10*x+x^2)/(-1+x)/(x^2+6*x+1) lgdogf A000447 8.09388 969*x+5814*x^2+969*x^3+(-969+4276*x-3414*x^2+4276*x^3-969*x^4)*f(x)+(-2400*x^2-400+1600*x-400*x^4+1600*x^3)*f(x)^2 ogf A000447 10.7291 {(n+3)*a(n+4)+5*a(n+3)*n+(-25-5*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=10,a(3)=35} ogf A000447 10.7291 {(n+3)*a(n+4)+5*n*a(n+3)+(-25-5*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=10,a(3)=35} ogf A000449 6.4695 -x*(60+x^6-124*x^3+165*x^2-12*x^5+54*x^4-120*x)/(-1+x)/(x^6-9*x^5+30*x^4-49*x^3+45*x^2-18*x+6) lgdegf A000449 10.3073 1/6*exp(-x)/(x-1)^4*(6-18*x+45*x^2-49*x^3+30*x^4-9*x^5+x^6) egf A000449 7.79658 {(30+11*n+n^2)*a(n+1)+(8*n+12+n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=0,a(2)=10} ogf A000453 21.5722 -1/(-1+10*x-35*x^2+50*x^3-24*x^4) ogf A000453 12.2738 -2*(-5+35*x+48*x^3-75*x^2)/(-1+x)/(3*x-1)/(2*x-1)/(-1+4*x) lgdogf A000453 22.2463 1/(x-1)/(3*x-1)/(2*x-1)/(-1+4*x) ogf A000457 25.9036 (1+3*x)/(1-2*x)^(7/2) egf A000457 25.9036 (3*x+1)/(1-2*x)^(7/2) egf A000457 7.66164 -25350-38025*x+(5075+6345*x-15210*x^2)*f(x)+(1524*x^2-254-254*x)*f(x)^2 lgdegf A000457 20.9222 -5*(2+3*x)/(3*x+1)/(2*x-1) lgdegf A000457 10.2637 {(-21-13*n-2*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=10} ogf A000460 14.8735 -(-1-x+4*x^2)/(3*x-1)/(2*x-1)^2/(x-1)^3 ogf A000460 10.1766 -(-1-x+4*x^2)/(40*x^2+1-10*x+91*x^4-52*x^5+12*x^6-82*x^3) ogf A000460 8.53038 -(-11+44*x+96*x^4-102*x^3-15*x^2)/(-1+x)/(3*x-1)/(2*x-1)/(4*x^2-x-1) lgdogf A000463 28.7148 -(-1-x+x^2-x^3)/(1+3*x^4-3*x^2-x^6) ogf A000463 18.9626 -(1+4*x+3*x^4-4*x^3+8*x^2)/(-1+x)/(1+x)/(x^3-x^2+x+1) lgdogf A000463 33.5006 -(1+x-x^2+x^3)/(x-1)^3/(x+1)^3 ogf A000466 32.2479 -(-1+6*x+3*x^2)/(x-1)^3 ogf A000466 21.1915 -(-1-9*x^2+2*x^3)/(1-3*x+3*x^2-x^3) ogf A000466 23.1782 -(1-6*x-3*x^2)/(3*x^2+1-3*x-x^3) ogf A000466 21.1915 -3*(1+6*x+x^2)/(-1+x)/(3*x^2+6*x-1) lgdogf A000466 9.15681 103-618*x-309*x^2+(71-117*x+405*x^2-103*x^3)*f(x)+(-32+96*x-96*x^2+32*x^3)*f(x)^2 ogf A000466 13.7352 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=-1,a(1)=3,a(2)=15} ogf A000475 8.06543 {(42+13*n+n^2)*a(n+1)+(9*n+14+n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=0,a(2)=15} ogf A000478 8.43676 -(-105+700*x-1044*x^4+1974*x^3+216*x^5-1729*x^2)/(-1+x)/(3*x-1)/(2*x-1)/(12*x^3-40*x^2+45*x-15) lgdogf A000478 15.7155 -(-15+45*x-40*x^2+12*x^3)/(3*x-1)/(2*x-1)^2/(x-1)^3 ogf A000478 11.6158 -(-15+45*x-40*x^2+12*x^3)/(40*x^2+1-10*x+91*x^4-52*x^5-82*x^3+12*x^6) ogf A000478 5.93698 {(6*n^2+102*n+432)*a(n+1)+(-11*n^2-172*n-657)*a(n+2)+(6*n^2+88*n+315)*a(n+3)+(-n^2-14*n-48)*a(n+4),a(0)=15,a(1)=105,a(2)=490,a(3)=1918} ogf A000480 7.78593 (-1+x+x^2-x^11+x^15-x^18+x^23-x^22+x^21-x^5+x^8)/(x-1)/(x^2+1)/(x^20-x^18+x^16-x^14+x^12-x^10+x^8-x^6+x^4-x^2+1) ogf A000481 28.5742 -(15-170*x+600*x^4-1096*x^3+675*x^2)/(-1+x)/(-1+4*x)/(3*x-1)/(2*x-1)/(5*x-1) lgdogf A000481 51.7057 -1/(x-1)/(-1+4*x)/(3*x-1)/(2*x-1)/(-1+5*x) ogf A000481 52.9669 1/(1-15*x+85*x^2-225*x^3+274*x^4-120*x^5) ogf A000486 6.31104 -(-75+799*x-6216*x^4+6508*x^3+2304*x^5-3284*x^2)/(-1+x)/(3*x-1)/(2*x-1)/(-1+4*x)/(24*x^2-29*x+8) lgdogf A000486 9.32092 -(16-58*x+48*x^2)/(-67*x^2-1+13*x-244*x^4+172*x^5-48*x^6+175*x^3) ogf A000486 11.6511 2*(8-29*x+24*x^2)/(-1+4*x)/(3*x-1)/(2*x-1)^2/(x-1)^2 ogf A000487 10.7266 -(-16+48*x)/(160*x^2+1-20*x-1664*x^5+768*x^6-656*x^3+1456*x^4) ogf A000487 10.9025 -(-17+184*x+720*x^3-636*x^2)/(6*x-1)/(3*x-1)/(2*x-1)/(-1+4*x) lgdogf A000487 16.2208 -16*(3*x-1)/(-1+6*x)/(-1+4*x)^2/(2*x-1)^3 ogf A000487 4.78455 {(1152+480*n+48*n^2)*a(n+1)+(-768-380*n-44*n^2)*a(n+2)+(92*n+168+12*n^2)*a(n+3)+(-7*n-12-n^2)*a(n+4),a(0)=16,a(1)=272,a(2)=2880,a(3)=24576} ogf A000493 17.7233 -(-x^19+x^16+x^22-x^13+x^4-x^7+x^10)/(1-x-x^23+x^22) ogf A000493 18.0708 -(x^7-x^10-x^4+x^19-x^22+x^13-x^16)/(1-x-x^23+x^22) ogf A000496 9.88706 -(11-4*x+9*x^4-12*x^3+4*x^6+4*x^5-8*x^2)/(-1+x)/(x^3+x^2+x-1)/(x^4+4*x^3+2*x^2+x-6) lgdogf A000496 20.0153 -(24-4*x-8*x^2-16*x^3-4*x^4)/(-1+2*x-x^4) ogf A000496 17.8397 -4*(-6+x+2*x^2+4*x^3+x^4)/(x-1)/(-1+x+x^2+x^3) ogf A000496 7.13588 -43920+7320*x+14640*x^2+29280*x^3+7320*x^4+(13182-5552*x-3784*x^2-7568*x^3-62*x^4)*f(x)+(-473+946*x-473*x^4)*f(x)^2 ogf A000497 9.47722 -5*(10+66*x+4*x^3+57*x^2)/(2*x-1)/(4*x^3+39*x^2+28*x+2) lgdegf A000497 6.06101 {(-56-30*n-4*n^2)*a(n+1)+(-55-19*n-2*n^2)*a(n+2)+(n+3)*a(n+3),a(0)=1,a(1)=25,a(2)=490} ogf A000504 8.21981 -21*(16+276*x+60*x^4+585*x^3+864*x^2)/(2*x-1)/(180*x^4+1285*x^3+1299*x^2+246*x+6) lgdegf A000504 4.89562 {(-864-408*n-48*n^2)*a(n+1)+(-4712-1586*n-140*n^2)*a(n+2)+(-415-75*n-10*n^2)*a(n+3)+(5*n+20)*a(n+4),a(0)=1,a(1)=56,a(2)=1918,a(3)=56980} ogf A000507 4.66906 -(1385-25654*x+1278063*x^4-669204*x^3+496125*x^6-1247670*x^5+185387*x^2)/(-1+x)/(3*x-1)/(7*x-1)/(5*x-1)/(675*x^3-963*x^2+445*x-61) lgdogf A000507 9.05937 -1/(-1+7*x)/(3*x-1)^3*(675*x^3-963*x^2+445*x-61)/(x-1)^4/(-1+5*x)^2 ogf A000515 15.8707 hypergeom([1/2,3/2],[1],16*x) ogf A000515 7.67083 {(60+64*n+16*n^2)*a(n+1)+(-4-n^2-4*n)*a(n+2),a(0)=1,a(1)=12} ogf A000515 7.67083 {(60+64*n+16*n^2)*a(n+1)+(-n^2-4*n-4)*a(n+2),a(0)=1,a(1)=12} ogf A000520 11.5314 (-1-28*x^27+27*x^28)/(-1+x)/(x^4+1)/(x^24-x^20+x^16-x^12+x^8-x^4+1) lgdogf A000520 42.9224 -(x^3+x^31)/(-1+x) ogf A000520 16.7957 -(x^4+1)*(x^24-x^20+x^16-x^12+x^8-x^4+1)/(x-1) ogf A000522 49.7272 (x-2)/(-1+x) lgdegf A000522 39.7817 -2+x+(1-x)*f(x) lgdegf A000522 45.902 -exp(x)/(x-1) egf A000522 10.6558 {(-n-2)*a(n+1)+(n+4)*a(n+2)-a(n+3),a(0)=1,a(1)=2,a(2)=5} ogf A000529 35.4255 (x-2)*(3*x^3-12*x^2+18*x-10)/(x-1)^6 ogf A000529 18.2188 -(20-46*x+42*x^2-18*x^3+3*x^4)/(-15*x^2-1+6*x-x^6-15*x^4+20*x^3+6*x^5) ogf A000529 18.7547 -2*(37-73*x+3*x^4-21*x^3+57*x^2)/(-1+x)/(x-2)/(3*x^3-12*x^2+18*x-10) lgdogf A000531 10.6469 -1+(1-8*x+16*x^2)*f(x)+(48*x^3+x-12*x^2-64*x^4)*f(x)^2 ogf A000531 8.09765 {(-16*n-56)*a(n+1)+(8*n+30)*a(n+2)+(-n-4)*a(n+3),a(0)=1,a(1)=7,a(2)=38} ogf A000533 17.1004 -(-1+10*x^2)/(1-11*x+10*x^2) ogf A000533 17.7338 -(-1+10*x^2)/(10*x-1)/(x-1) ogf A000533 10.6403 -(11-40*x+110*x^2)/(-1+x)/(10*x-1)/(10*x^2-1) lgdogf A000533 7.72278 40-400*x^2+(41+440*x-1210*x^2)*f(x)+(-81+891*x-810*x^2)*f(x)^2 ogf A000533 9.20793 {a(n+3)-11*a(n+2)+10*a(n+1),a(0)=1,a(1)=11,a(2)=101} ogf A000534 5.90626 -(-x+4*x^6+55*x^14-2*x^2+13*x^8+2*x^5-3*x^3+27*x^12-x^4+18*x^9+36*x^13+19*x^10+11*x^7+20*x^11+60*x^15+36*x^17+32*x^16)/(1-4*x^3) ogf A000536 15.6506 -(240+840*x+x^9+50*x^7-86*x^4+620*x^3-10*x^8-120*x^6+265*x^5+720*x^2)/(-1+x)/(x^8-8*x^7+34*x^6-64*x^5+125*x^4-16*x^3+168*x^2+96*x+24) lgdegf A000536 27.7538 -1/(x-1)^7*exp(-x)*(24+96*x+168*x^2-16*x^3+125*x^4-64*x^5+34*x^6-8*x^7+x^8) egf A000536 24.4886 {(-42-13*n-n^2)*a(n+1)+(-28-11*n-n^2)*a(n+2)+(n+3)*a(n+3),a(0)=24,a(1)=240,a(2)=2520} ogf A000537 16.9927 -(-x-4*x^2-x^3)/(1-5*x+10*x^2-x^5-10*x^3+5*x^4) ogf A000537 39.9328 -(1+4*x+x^2)/(x-1)^5 ogf A000537 24.2017 -3*(3+6*x+x^2)/(-1+x)/(x^2+4*x+1) lgdogf A000537 8.87396 {(n+3)*a(n+4)+(-3+3*n)*a(n+3)+(-21-3*n)*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=1,a(2)=9,a(3)=36} ogf A000537 8.87396 {(n+3)*a(n+4)+(-3+3*n)*a(n+3)+(-21-3*n)*a(n+2)+(-n-3)*a(n+1),a(0)=0,a(1)=1,a(2)=9,a(3)=36} ogf A000538 30.3572 (x+1)*(x^2+10*x+1)/(x-1)^6 ogf A000538 12.7304 -(-x-11*x^2-11*x^3-x^4)/(1-6*x+x^6+15*x^2-20*x^3+15*x^4-6*x^5) ogf A000538 16.1079 -(17+77*x+3*x^3+47*x^2)/(-1+x)/(1+x)/(x^2+10*x+1) lgdogf A000538 8.39668 {(-39-25*n-4*n^2)*a(n+1)+(83+40*n+8*n^2)*a(n+2)+(-14-15*n-4*n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=17} ogf A000539 21.8794 -(1+26*x+66*x^2+26*x^3+x^4)/(x-1)^7 ogf A000539 10.076 -(x+26*x^2+x^5+66*x^3+26*x^4)/(-1+7*x-21*x^2+x^7+35*x^3-35*x^4+21*x^5-7*x^6) ogf A000539 11.7812 -3*(11+96*x+x^4+36*x^3+136*x^2)/(-1+x)/(x^4+26*x^3+66*x^2+26*x+1) lgdogf A000540 17.7988 (x+1)*(x^4+56*x^3+246*x^2+56*x+1)/(x-1)^8 ogf A000540 7.93208 -(-x-x^6-57*x^2-57*x^5-302*x^3-302*x^4)/(1-8*x+x^8+28*x^2-56*x^3+70*x^4-56*x^5+28*x^6-8*x^7) ogf A000540 8.58532 -(65+1003*x+233*x^4+1738*x^3+3*x^5+2718*x^2)/(-1+x)/(1+x)/(x^4+56*x^3+246*x^2+56*x+1) lgdogf A000540 5.03277 {(-312-197*n-31*n^2)*a(n+1)+(11328+4559*n+513*n^2)*a(n+2)+(-2442-1597*n-513*n^2)*a(n+3)+(246+175*n+31*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=65,a(3)=794} ogf A000541 6.40188 -(-x-120*x^6-120*x^2-1191*x^5-1191*x^3-2416*x^4-x^7)/(1-9*x+9*x^8+36*x^2-x^9-84*x^3+126*x^4-126*x^5+84*x^6-36*x^7) ogf A000541 12.8038 -(1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/(x-1)^9 ogf A000541 6.69554 -3*(43+1114*x+2185*x^4+6420*x^3+x^6+162*x^5+5195*x^2)/(-1+x)/(x^6+120*x^5+1191*x^4+2416*x^3+1191*x^2+120*x+1) lgdogf A000542 10.9245 (x+1)*(x^6+246*x^5+4047*x^4+11572*x^3+4047*x^2+246*x+1)/(x-1)^10 ogf A000542 5.06646 -(-x-4293*x^6-247*x^2-x^8-15619*x^5-4293*x^3-15619*x^4-247*x^7)/(1-10*x+45*x^8+45*x^2-10*x^9-120*x^3+x^10+210*x^4-252*x^5+210*x^6-120*x^7) ogf A000543 5.41982 -(-x-162*x^6-14*x^2-x^8-663*x^5-162*x^3-663*x^4-14*x^7)/(1-9*x+9*x^8+36*x^2-x^9-84*x^3+126*x^4-126*x^5+84*x^6-36*x^7) ogf A000543 5.46655 -(23+436*x+2*x^7+4125*x^4+6630*x^3+49*x^6+732*x^5+3123*x^2)/(-1+x)/(1+x)/(x^6+13*x^5+149*x^4+514*x^3+149*x^2+13*x+1) lgdogf A000543 10.9331 -(x+1)*(x^6+13*x^5+149*x^4+514*x^3+149*x^2+13*x+1)/(x-1)^9 ogf A000554 7.72852 -(-30+150*x-96*x^4+248*x^3+16*x^5-285*x^2)/(-1+x)/(2*x-1)/(4*x^4-18*x^3+33*x^2-24*x+6) lgdogf A000554 9.10483 -(12-48*x+66*x^2-36*x^3+8*x^4)/(-33*x^2-1+9*x-8*x^6-66*x^4+63*x^3+36*x^5) ogf A000554 13.8469 2*(6-24*x+33*x^2-18*x^3+4*x^4)/(2*x-1)^3/(x-1)^3 ogf A000554 7.07077 {(-26*n-2*n^2-84)*a(n+1)+(3*n^2+33*n+84)*a(n+2)+(-n^2-9*n-20)*a(n+3),a(0)=12,a(1)=60,a(2)=210} ogf A000561 30.6489 -(-6-20*x-5*x^2+4*x^3)/(x-1)^4 ogf A000561 18.0288 -2*(-22-35*x+2*x^3+x^2)/(-1+x)/(4*x^3-5*x^2-20*x-6) lgdogf A000561 8.0655 {(-3210-2203*n-299*n^2)*a(n+1)+(-9384-2980*n-167*n^2)*a(n+2)+(2888*n+4470+466*n^2)*a(n+3),a(0)=6,a(1)=44,a(2)=145} ogf A000562 20.0844 (-9-50*x-35*x^2+15*x^3-4*x^4+2*x^5)/(x-1)^5 ogf A000562 11.6707 -(-95-270*x+6*x^4+14*x^3-60*x^2)/(-1+x)/(2*x^5-4*x^4+15*x^3-35*x^2-50*x-9) lgdogf A000563 15.117 -(-13-114*x-128*x^2+10*x^3-6*x^4+8*x^5)/(x-1)^6 ogf A000563 9.10898 -(13+114*x+128*x^2-8*x^5-10*x^3+6*x^4)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A000563 8.26163 -2*(-96-413*x+14*x^4+3*x^3+4*x^5-241*x^2)/(-1+x)/(8*x^5-6*x^4+10*x^3-128*x^2-114*x-13) lgdogf A000564 10.4614 (-20-231*x-411*x^2-72*x^3-29*x^4+36*x^5-4*x^6+2*x^7)/(x-1)^7 ogf A000564 6.34022 -(-20-231*x-4*x^6-411*x^2+36*x^5-72*x^3-29*x^4+2*x^7)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A000564 5.65479 -(-371-2208*x+93*x^4-404*x^3+10*x^6+48*x^5-2271*x^2)/(-1+x)/(2*x^7-4*x^6+36*x^5-29*x^4-72*x^3-411*x^2-231*x-20) lgdogf A000565 9.8764 -(-31-448*x-1123*x^2-548*x^3-131*x^4+88*x^5-6*x^6+12*x^7)/(x-1)^8 ogf A000565 5.83606 -(31+448*x+6*x^6+1123*x^2-88*x^5+548*x^3+131*x^4-12*x^7)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A000565 5.26202 -6*(-116-897*x+2*x^7-14*x^4-544*x^3+12*x^6+38*x^5-1397*x^2)/(-1+x)/(12*x^7-6*x^6+88*x^5-131*x^4-548*x^3-1123*x^2-448*x-31) lgdogf A000566 15.072 -(-x-4*x^2-96*x^22+197*x^21-101*x^20)/(1-3*x+3*x^2-x^3) ogf A000566 51.8099 -(1+4*x)/(x-1)^3 ogf A000566 36.0416 -(7+8*x)/(4*x+1)/(-1+x) lgdogf A000566 9.86854 279*x+1116*x^2+(-279+662*x-1537*x^2+279*x^3)*f(x)+(175-525*x+525*x^2-175*x^3)*f(x)^2 ogf A000566 15.9415 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=7} ogf A000567 44.9373 -(1+5*x)/(x-1)^3 ogf A000567 24.793 -(x+5*x^2)/(-1+3*x-3*x^2+x^3) ogf A000567 28.7598 -2*(4+5*x)/(5*x+1)/(-1+x) lgdogf A000567 7.41233 9331*x+46655*x^2+(-9331+23133*x-52293*x^2+9331*x^3)*f(x)+(4860-14580*x+14580*x^2-4860*x^3)*f(x)^2 ogf A000567 13.8268 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=8} ogf A000570 8.93923 -(1+2*x+2*x^7+3*x^4+6*x^3+x^8+3*x^6+2*x^5+5*x^2)/(x^4+x^3+x^2+1)/(x^5+x^4+x^3+x-1) lgdogf A000570 21.5593 -(1+x^2+x^3+x^4)/(x^3-1+x+x^5+x^4) ogf A000574 43.213 -(-3+2*x)/(x-1)^6 ogf A000574 15.3046 -(3-2*x)/(-15*x^2-1+6*x+6*x^5-x^6+20*x^3-15*x^4) ogf A000574 28.2547 -2*(-8+5*x)/(-1+x)/(2*x-3) lgdogf A000574 10.2031 {(3*n+9)*a(n+3)+(-26-5*n)*a(n+2)+(12+2*n)*a(n+1),a(0)=3,a(1)=16,a(2)=51} ogf A000575 22.7777 -(-10+20*x-15*x^2+4*x^3)/(x-1)^10 ogf A000575 7.67005 -(10-20*x+15*x^2-4*x^3)/(10*x^9-1+10*x+120*x^7-45*x^2+252*x^5+120*x^3-210*x^4-210*x^6-45*x^8-x^10) ogf A000575 13.1871 -2*(-40+75*x+14*x^3-54*x^2)/(-1+x)/(4*x^3-15*x^2+20*x-10) lgdogf A000575 8.17027 {(104+21*n+n^2)*a(n+1)+(-74-29*n-2*n^2)*a(n+2)+(8*n+15+n^2)*a(n+3),a(0)=10,a(1)=80,a(2)=365} ogf A000578 40.0675 (1+4*x+x^2)/(x-1)^4 ogf A000578 19.52 -(-x-4*x^2-x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A000578 23.0691 -2*(4+7*x+x^2)/(-1+x)/(x^2+4*x+1) lgdogf A000578 6.45154 1087*x+4348*x^2+1087*x^3+(-1087+5008*x-3882*x^2+5008*x^3-1087*x^4)*f(x)+(-3960*x^2-660+2640*x-660*x^4+2640*x^3)*f(x)^2 ogf A000578 8.45869 {(n+3)*a(n+4)+(-2+3*n)*a(n+3)+(-17-3*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=8,a(3)=27} ogf A000578 8.45869 {(n+3)*a(n+4)+(-2+3*n)*a(n+3)+(-17-3*n)*a(n+2)+(-n-2)*a(n+1),a(0)=0,a(1)=1,a(2)=8,a(3)=27} ogf A000579 79.3109 -1/(x-1)^7 ogf A000579 88.1232 -7/(-1+x) lgdogf A000579 16.8747 1/(1-7*x+21*x^2-35*x^3+35*x^4-21*x^5+7*x^6-x^7) ogf A000579 10.3001 {(n-4)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=1} ogf A000579 10.3001 {(n-4)*a(n+2)+(-n-2)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=1} ogf A000580 73.64 -8/(-1+x) lgdogf A000580 12.2733 1/(1-8*x+28*x^2-56*x^3+70*x^4-56*x^5+28*x^6-8*x^7+x^8) ogf A000580 73.64 1/(x-1)^8 ogf A000580 15.78 {(-n-2)*a(n+2)+(9+n)*a(n+1),a(0)=1,a(1)=8} ogf A000580 41.4225 {-a(n+1),a(0)=8} ogf_with_Euler_Transform A000581 10.3606 -1/(-1+9*x-36*x^2+84*x^3-126*x^4+126*x^5-84*x^6+36*x^7-9*x^8+x^9) ogf A000581 67.3438 -1/(x-1)^9 ogf A000581 74.8264 -9/(-1+x) lgdogf A000581 15.6613 {(-n-2)*a(n+2)+(10+n)*a(n+1),a(0)=1,a(1)=9} ogf A000581 42.0898 {-a(n+1),a(0)=9} ogf_with_Euler_Transform A000582 9.64159 -1/(-1+10*x-45*x^2+120*x^3-210*x^4+252*x^5-210*x^6+120*x^7-45*x^8+10*x^9-x^10) ogf A000582 75.2044 -10/(-1+x) lgdogf A000582 75.2044 1/(x-1)^10 ogf A000582 17.0919 {(-n-2)*a(n+2)+(11+n)*a(n+1),a(0)=1,a(1)=10} ogf A000582 44.2379 {-a(n+1),a(0)=10} ogf_with_Euler_Transform A000583 25.9906 -(x+1)*(x^2+10*x+1)/(x-1)^5 ogf A000583 12.759 -(x+11*x^2+11*x^3+x^4)/(-1+5*x-10*x^2+10*x^3-5*x^4+x^5) ogf A000583 14.6197 -2*(8+33*x+x^3+18*x^2)/(-1+x)/(1+x)/(x^2+10*x+1) lgdogf A000583 7.46538 {(-18-17*n-4*n^2)*a(n+1)+(72+8*n^2+32*n)*a(n+2)+(-14-15*n-4*n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=16} ogf A000584 20.1071 (1+26*x+66*x^2+26*x^3+x^4)/(x-1)^6 ogf A000584 9.90784 -(-x-26*x^2-x^5-66*x^3-26*x^4)/(1-6*x+15*x^2-20*x^3+15*x^4-6*x^5+x^6) ogf A000584 10.3582 -2*(16+131*x+x^4+41*x^3+171*x^2)/(-1+x)/(x^4+26*x^3+66*x^2+26*x+1) lgdogf A000587 87.0378 -exp(x) lgdegf A000587 16.4666 {(n+2)*a(n+2)-a(n+1),a(0)=-1,a(1)=-1} lgdegf A000588 22.3453 -49+(7-28*x)*f(x)+(x-4*x^2)*f(x)^2 lgdogf A000588 33.0322 128/(1+(1-4*x)^(1/2))^7 ogf A000588 22.3453 14/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A000588 18.5303 x^3+(-1+7*x-14*x^2+7*x^3)*f(x)+x^4*f(x)^2 ogf A000588 10.4074 {(-12-14*n-4*n^2)*a(n+1)+(-6+5*n+n^2)*a(n+2),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A000589 20.1276 -121+(11-44*x)*f(x)+(x-4*x^2)*f(x)^2 lgdogf A000589 28.9838 2048/(1+(1-4*x)^(1/2))^11 ogf A000589 21.3116 22/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A000589 11.687 {(-182-54*n-4*n^2)*a(n+1)+(15*n+26+n^2)*a(n+2),a(0)=1,a(1)=11} ogf A000590 20.7456 -169+(13-52*x)*f(x)+(x-4*x^2)*f(x)^2 lgdogf A000590 21.9659 26/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A000590 29.8737 8192/(1+(1-4*x)^(1/2))^13 ogf A000590 12.0458 {(-240-62*n-4*n^2)*a(n+1)+(17*n+30+n^2)*a(n+2),a(0)=1,a(1)=13} ogf A000594 77.7513 24/(-1+x) ogf_with_Euler_Transform A000594 87.4702 24/(x-1) ogf_with_Euler_Transform A000594 30.4244 {-a(n+1)+a(n),a(0)=-24} ogf_with_Euler_Transform A000596 5.95272 -(-4-21*x-14*x^2-x^3)/(21*x^2+1-7*x-x^7+35*x^4-21*x^5-35*x^3+7*x^6) ogf A000596 14.244 -(4+21*x+14*x^2+x^3)/(x-1)^7 ogf A000596 7.82024 -(49+154*x+4*x^3+73*x^2)/(-1+x)/(x^3+14*x^2+21*x+4) lgdogf A000596 3.91012 {(45+19*n+2*n^2)*a(n+1)+(-2841-907*n-74*n^2)*a(n+2)+(468*n+756+72*n^2)*a(n+3),a(0)=4,a(1)=49,a(2)=273} ogf A000597 7.37391 (x^5+75*x^4+603*x^3+1065*x^2+460*x+36)/(x-1)^10 ogf A000597 3.76711 -(820+6270*x+455*x^4+4521*x^3+5*x^5+10329*x^2)/(-1+x)/(x^5+75*x^4+603*x^3+1065*x^2+460*x+36) lgdogf A000601 18.4684 -(2+6*x+7*x^3+9*x^2)/(-1+x)/(1+x)/(x^2+x+1) lgdogf A000601 29.4126 1/(1-2*x+x^3+x^4-2*x^6+x^7) ogf A000601 31.7656 1/(x+1)/(x^2+x+1)/(x-1)^4 ogf A000601 113.449 2+x+x^2 ogf_with_Euler_Transform A000601 26.4713 {-a(n+3),a(0)=2,a(1)=1,a(2)=1} ogf_with_Euler_Transform A000611 1.70397 -2+(-x^2+6)*f(x)+(2*x^2-6)*f(x)^2+(-x^2+2)*f(x)^3 egf A000655 29.0309 (-1-2*x-2*x^2+x^3)/(x-1) ogf A000655 15.8351 (3+4*x+2*x^3-5*x^2)/(-1+x)/(x^3-2*x^2-2*x-1) lgdogf A000655 27.8697 -(-1-2*x-2*x^2+x^3)/(1-x) ogf A000655 9.04861 -649-1298*x-1298*x^2+649*x^3+(570-807*x-158*x^2+79*x^3)*f(x)+(79-79*x)*f(x)^2 ogf A000655 16.2033 {a(n+4)-a(n+3),a(0)=1,a(1)=3,a(2)=5,a(3)=4} ogf A000680 15.4838 {(2*n^2+7*n+6)*a(n+1)-a(n+2),a(0)=1,a(1)=1} ogf A000681 10.6757 {(n+2)*a(n+1)+(-2*n-6)*a(n+2)+2*a(n+3),a(0)=1,a(1)=1,a(2)=3/2} egf A000681 8.07189 {(n^3+7*n^2+16*n+12)*a(n+1)+(-2*n^2-12*n-18)*a(n+2)+2*a(n+3),a(0)=1,a(1)=1,a(2)=3} ogf A000689 21.4396 -(1+x+3*x^2+5*x^3)/(-x^2-1+x+x^3) ogf A000689 22.1096 -(1+x+3*x^2+5*x^3)/(x^2+1)/(x-1) ogf A000689 11.9916 -1-x-3*x^2-5*x^3+(2+4*x^2+4*x^3)*f(x)+(-1+x-x^2+x^3)*f(x)^2 ogf A000689 11.5985 -2*(1+2*x+4*x^4-4*x^3+7*x^2)/(-1+x)/(x^2+1)/(5*x^3+3*x^2+x+1) lgdogf A000689 12.1984 {-a(n+4)+a(n+3)-a(n+2)+a(n+1),a(0)=1,a(1)=2,a(2)=4,a(3)=8} ogf A000700 45.6155 -(-1+x-x^2)/(1-x^4) ogf_with_Euler_Transform A000700 20.6356 {a(n+4)-a(n),a(0)=1,a(1)=-1,a(2)=1,a(3)=0} ogf_with_Euler_Transform A000710 52.3821 -(2-x^4)/(-1+x) ogf_with_Euler_Transform A000710 56.1237 -(2-x^4)/(x-1) ogf_with_Euler_Transform A000710 15.7146 {a(n+2)-a(n+1),a(0)=2,a(1)=2,a(2)=2,a(3)=2,a(4)=1} ogf_with_Euler_Transform A000711 52.5583 -(3-x^4)/(-1+x) ogf_with_Euler_Transform A000711 56.3125 -(3-x^4)/(x-1) ogf_with_Euler_Transform A000711 15.7675 {a(n+2)-a(n+1),a(0)=3,a(1)=3,a(2)=3,a(3)=3,a(4)=2} ogf_with_Euler_Transform A000712 112 2/(1-x) ogf_with_Euler_Transform A000712 39.2001 {a(n+1)-a(n),a(0)=2} ogf_with_Euler_Transform A000713 62.1188 -(-3+x)/(1-x) ogf_with_Euler_Transform A000713 27.8464 {a(n+2)-a(n+1),a(0)=3,a(1)=2} ogf_with_Euler_Transform A000714 43.3567 -(3-x^2)/(-1+x) ogf_with_Euler_Transform A000714 46.4536 -(3-x^2)/(x-1) ogf_with_Euler_Transform A000714 17.5771 {-a(n+3)+a(n+2),a(0)=3,a(1)=3,a(2)=2} ogf_with_Euler_Transform A000715 52.0805 -(3-x^3)/(-1+x) ogf_with_Euler_Transform A000715 55.8005 -(3-x^3)/(x-1) ogf_with_Euler_Transform A000715 17.7547 {-a(n+4)+a(n+3),a(0)=3,a(1)=3,a(2)=3,a(3)=2} ogf_with_Euler_Transform A000716 132.412 3/(1-x) ogf_with_Euler_Transform A000716 46.344 {a(n+1)-a(n),a(0)=3} ogf_with_Euler_Transform A000726 54.2593 -(-1-x)/(1-x^3) ogf_with_Euler_Transform A000726 23.9379 {a(n+3)-a(n),a(0)=1,a(1)=1,a(2)=0} ogf_with_Euler_Transform A000727 133.303 4/(-1+x) ogf_with_Euler_Transform A000727 152.347 4/(x-1) ogf_with_Euler_Transform A000727 48.4739 {-a(n+1)+a(n),a(0)=-4} ogf_with_Euler_Transform A000728 95.5171 5/(-1+x) ogf_with_Euler_Transform A000728 109.162 5/(x-1) ogf_with_Euler_Transform A000728 34.7335 {-a(n+1)+a(n),a(0)=-5} ogf_with_Euler_Transform A000729 121.201 6/(-1+x) ogf_with_Euler_Transform A000729 138.516 6/(x-1) ogf_with_Euler_Transform A000729 44.0732 {-a(n+1)+a(n),a(0)=-6} ogf_with_Euler_Transform A000730 88.5373 7/(-1+x) ogf_with_Euler_Transform A000730 101.185 7/(x-1) ogf_with_Euler_Transform A000730 32.1954 {-a(n+1)+a(n),a(0)=-7} ogf_with_Euler_Transform A000731 114.077 8/(-1+x) ogf_with_Euler_Transform A000731 130.373 8/(x-1) ogf_with_Euler_Transform A000731 41.4824 {-a(n+1)+a(n),a(0)=-8} ogf_with_Euler_Transform A000735 95.1029 12/(-1+x) ogf_with_Euler_Transform A000735 106.991 12/(x-1) ogf_with_Euler_Transform A000735 37.2142 {-a(n+1)+a(n),a(0)=-12} ogf_with_Euler_Transform A000739 69.8245 16/(-1+x) ogf_with_Euler_Transform A000739 78.5525 16/(x-1) ogf_with_Euler_Transform A000739 27.3226 {-a(n+1)+a(n),a(0)=-16} ogf_with_Euler_Transform A000748 20.964 -(1+3*x+6*x^2+9*x^3+9*x^4)/(-1+27*x^6) ogf A000748 18.9674 -2+(1+6*x+6*x^2)*f(x)+(1+3*x+3*x^2)*f(x)^2 ogf A000748 33.193 -3*(2*x+1)/(3*x^2+1+3*x) lgdogf A000748 53.1088 1/(3*x^2+3*x+1) ogf A000748 20.4265 {a(n+2)+3*a(n+1)+3*a(n),a(0)=1,a(1)=-3} ogf A000749 29.8271 -1/(2*x-1)/(1-2*x+2*x^2) ogf A000749 18.3552 -4*(-3*x+1+3*x^2)/(2*x-1)/(2*x^2-2*x+1) lgdogf A000749 19.8848 -x^3*f(x)+(1-4*x+6*x^2-4*x^3)*f(x)^2 ogf A000749 28.634 -x^3/(-1+4*x-6*x^2+4*x^3) ogf A000749 11.1852 {-a(n+4)+4*a(n+3)-6*a(n+2)+4*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A000750 4.97737 -(-8-995*x^6-340*x^4-6050*x^10-29*x-76*x^2-170*x^3-1375*x^7-1375*x^8-615*x^5)/(11*x^2+8-11*x-6875*x^12-4975*x^10+6875*x^11) ogf A000750 11.7734 -5*(2*x+1)*(2*x^2+2*x+1)/(10*x^2+1+5*x+5*x^4+10*x^3) lgdogf A000750 17.4919 1+(-1-5*x-10*x^2-10*x^3-5*x^4)*f(x) ogf A000750 21.1109 1/(1+5*x+10*x^2+10*x^3+5*x^4) ogf A000757 7.07075 {(-n-2)*a(n+1)+(-2*n-4)*a(n+2)+(-n-1)*a(n+3)+a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=1} ogf A000770 7.13559 -(-21+350*x-8820*x^4+6496*x^3+4320*x^5-2205*x^2)/(-1+x)/(6*x-1)/(-1+4*x)/(3*x-1)/(2*x-1)/(5*x-1) lgdogf A000770 12.6855 -1/(-1+21*x-175*x^2+735*x^3-1624*x^4+1764*x^5-720*x^6) ogf A000770 13.7003 1/(x-1)/(-1+6*x)/(-1+4*x)/(3*x-1)/(2*x-1)/(-1+5*x) ogf A000771 11.1341 -1/(x-1)/(-1+6*x)/(-1+4*x)/(3*x-1)/(2*x-1)/(-1+7*x)/(-1+5*x) ogf A000771 5.80911 -4*(7-161*x+16415*x^4-6769*x^3+8820*x^6-19602*x^5+1470*x^2)/(-1+x)/(6*x-1)/(-1+4*x)/(3*x-1)/(2*x-1)/(7*x-1)/(5*x-1) lgdogf A000771 10.2777 1/(1-28*x+322*x^2-1960*x^3+6769*x^4-13132*x^5+13068*x^6-5040*x^7) ogf A000773 16.1125 -(-1-10*x+24*x^3+9*x^2)/(2*x-1)/(1+x)/(3*x^2-1) lgdogf A000773 11.1366 -x^3+(1-x-5*x^2+6*x^3+6*x^4)*f(x)+(15*x^2-3+3*x-18*x^4-9*x^3)*f(x)^2 ogf A000773 26.1134 -x^3/(-1+x+5*x^2-3*x^3-6*x^4) ogf A000773 29.1265 1/(2*x-1)/(x+1)/(-1+3*x^2) ogf A000774 5.62468 {(-8-12*n-6*n^2-n^3)*a(n+1)+(-26-24*n-8*n^2-n^3)*a(n+2)+(26+14*n+2*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=2,a(2)=5,a(3)=17} ogf A000775 5.78324 {(8+8*n+2*n^2)*a(n+1)+(-50-37*n-7*n^2)*a(n+2)+(50*n+78+8*n^2)*a(n+3)+(-21*n-36-3*n^2)*a(n+4),a(0)=1,a(1)=4,a(2)=6,a(3)=23/3} egf A000776 5.58381 {(16+24*n+12*n^2+2*n^3)*a(n+1)+(16+15*n+n^3+6*n^2)*a(n+2)+(-24-13*n-2*n^2)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=3,a(2)=8,a(3)=28} ogf A000777 10.1951 1-7*x+12*x^2-9*x^3+(-1+8*x-19*x^2+12*x^3)*f(x)+(x-6*x^2+9*x^3-4*x^4)*f(x)^2 ogf A000777 10.1951 1-7*x-9*x^3+12*x^2+(-1+8*x+12*x^3-19*x^2)*f(x)+(x-6*x^2+9*x^3-4*x^4)*f(x)^2 ogf A000778 13.8806 1-x+x^3+(-1+3*x-x^2-x^3)*f(x)+(x^4-2*x^3+x^2)*f(x)^2 ogf A000778 13.8806 1-x+x^3+(-1+3*x-x^3-x^2)*f(x)+(x^4-2*x^3+x^2)*f(x)^2 ogf A000779 14.2295 ((1-2*x)^(1/2)-2)/(1-2*x)^(1/2)/(2*x-1) egf A000779 13.5354 -2*(2*x+5+(1-2*x)^(1/2))/(2*x+3)/(-1+2*x) lgdegf A000779 10.4708 -3-2*x+(2-8*x+8*x^2)*f(x)+(1+12*x^2-8*x^3-6*x)*f(x)^2 egf A000779 4.17256 {(-40-56*n-26*n^2-4*n^3)*a(n+1)+(-146-127*n-38*n^2-4*n^3)*a(n+2)+(58+30*n+4*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=4,a(2)=22,a(3)=162} ogf A000780 39.9369 (x^2-x-1)/(x-1)^3 egf A000780 23.4113 -(-1-x+x^2)/(3*x^2+1-3*x-x^3) egf A000780 23.4113 -(x-2)*(x+2)/(-1+x)/(x^2-x-1) lgdegf A000780 9.1747 -29-29*x+29*x^2+(34-82*x+82*x^2-29*x^3)*f(x)+(-15*x^2-5+15*x+5*x^3)*f(x)^2 egf A000780 6.2287 {(8+8*n+2*n^2)*a(n+1)+(34+19*n+3*n^2)*a(n+2)+(16+7*n+n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=4,a(2)=16,a(3)=78} ogf A000781 10.6765 -3+x+2*x^2-x^3+(3-13*x+15*x^2-5*x^3)*f(x)+(-x^2+2*x^3-x^4)*f(x)^2 ogf A000781 10.6765 -3+x-x^3+2*x^2+(3-13*x-5*x^3+15*x^2)*f(x)+(-x^2+2*x^3-x^4)*f(x)^2 ogf A000782 15.3119 -1-5/2*x-1/2*x^2+1/2*((1+6*x+x^2)*(2+x)^2)^(1/2) revogf A000782 26.249 -2-x+(2-5*x)*f(x)-x^2*f(x)^2 ogf A000782 7.65596 {(-60-70*n-20*n^2)*a(n+1)+(-150-79*n-11*n^2)*a(n+2)+(32*n+60+4*n^2)*a(n+3),a(0)=1,a(1)=3,a(2)=8} ogf A000792 13.1961 (-1-4*x-6*x^4-10*x^3+3*x^6-9*x^2)/(3*x^3-1)/(x^4+2*x^2+x+1) lgdogf A000792 28.8359 -(1+x+2*x^2+x^4)/(-1+3*x^3) ogf A000792 11.6204 3+3*x+6*x^2+3*x^4+(-7-4*x-8*x^2+9*x^3-4*x^4)*f(x)+(4-12*x^3)*f(x)^2 ogf A000792 14.69 {-a(n+5)+3*a(n+2),a(0)=1,a(1)=1,a(2)=2,a(3)=3,a(4)=4} ogf A000803 24.1808 -(-8*x^2+12*x^3)/(1-2*x+x^4) ogf A000803 15.0458 -(1+9*x^4-8*x^3)/(-1+x)/(3*x-2)/(x^3+x^2+x-1) lgdogf A000803 9.27481 -256*x^2+384*x^3+(32-64*x-24*x^2+36*x^3+32*x^4)*f(x)+(3-6*x+3*x^4)*f(x)^2 ogf A000803 21.1582 -4*(-2+3*x)/(x-1)/(-1+x+x^2+x^3) ogf A000806 27.752 (-1+(1+2*x)^(1/2))/(1+2*x) lgdegf A000806 18.9882 -2*x+(2+4*x)*f(x)+(4*x^2+1+4*x)*f(x)^2 lgdegf A000806 31.3718 1/2*ln(1+x)*(ln(1+x)+2) revegf A000806 7.00535 {(n+2)*a(n+1)+(-6-2*n^2-8*n)*a(n+2)+(-16*n-30-2*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=0,a(2)=1,a(3)=-5} ogf A000852 5.39652 (8-2*x-415*x^4+216*x^3-270*x^14+183*x^5+140*x^13+12*x^2+130*x^15)/(-1+x)/(10*x^15-10*x^14+61*x^5-55*x^4-4*x^3+4*x^2-6*x-1) lgdogf A000852 11.1589 -(-1-6*x+4*x^2-4*x^3-55*x^4-10*x^14+10*x^15+61*x^5)/(x-1)^2 ogf A000852 10.4504 -(1+55*x^4+6*x+10*x^14-61*x^5-10*x^15-4*x^2+4*x^3)/(-x^2-1+2*x) ogf A000855 8.14365 -(x+1+4*x^3+16*x^5+2*x^2-36*x^7+8*x^4-44*x^9+32*x^6+13*x^10+28*x^8+25*x^11+50*x^12)/(-x^10-1+x+x^11) ogf A000865 20.9433 -(-1-98*x+98*x^2)/(x-1)^2 ogf A000865 18.0546 -(1+98*x-98*x^2)/(-x^2-1+2*x) ogf A000865 14.544 -2*(-50+49*x)/(-1+x)/(98*x^2-98*x-1) lgdogf A000865 7.17238 -4999-489902*x+489902*x^2+(4998-10096*x+5097*x^2)*f(x)+(1-2*x+x^2)*f(x)^2 ogf A000865 10.4717 {-a(n+3)+2*a(n+2)-a(n+1),a(0)=1,a(1)=100,a(2)=101} ogf A000873 5.09059 (11+3*x+122*x^4-299*x^3+8520*x^14+9230*x^12-17750*x^13+165*x^2)/(-1+x)/(710*x^14-710*x^13+61*x^4-55*x^3-4*x^2+5*x-8) lgdogf A000873 10.7365 -(-8+5*x-4*x^2-55*x^3+61*x^4-710*x^13+710*x^14)/(x-1)^2 ogf A000873 10.0086 -(-8+61*x^4+5*x+710*x^14-710*x^13-4*x^2-55*x^3)/(x^2+1-2*x) ogf A000888 17.3422 hypergeom([1/2,1/2],[2],16*x) ogf A000888 8.52414 {(-36-48*n-16*n^2)*a(n+1)+(6+5*n+n^2)*a(n+2),a(0)=1,a(1)=2} ogf A000891 8.67111 {(16*n^2+64*n+60)*a(n+1)+(-n^2-6*n-9)*a(n+2),a(0)=1,a(1)=3} ogf A000894 9.26242 1/4*(EllipticK(4*x^(1/2))-EllipticE(4*x^(1/2)))/Pi/x ogf A000894 8.16349 1/4/x*EllipticK(4*x^(1/2))/Pi-1/4/x*EllipticE(4*x^(1/2))/Pi ogf A000894 8.16349 {(-60-64*n-16*n^2)*a(n+1)+(6+5*n+n^2)*a(n+2),a(0)=1,a(1)=6} ogf A000897 17.8358 hypergeom([1/4,3/4],[1],64*x) ogf A000897 8.34254 {(-140-192*n-64*n^2)*a(n+1)+(n^2+4*n+4)*a(n+2),a(0)=1,a(1)=12} ogf A000898 82.7557 2+2*x-f(x) lgdegf A000898 137.926 2+2*x] lgdegf A000898 68.9631 exp(x*(x+2)) egf A000898 15.6143 {(2*n+4)*a(n+1)+2*a(n+2)-a(n+3),a(0)=1,a(1)=2,a(2)=6} ogf A000902 29.9439 1/2+1/2*exp(x*(x+2)) egf A000904 7.3611 {-a(n+1)+(-n-7)*a(n+2)+(-n-6)*a(n+3)+a(n+4),a(0)=0,a(1)=3,a(2)=13,a(3)=83} ogf A000906 20.4621 -5*(2+3*x)/(3*x+1)/(-1+2*x) lgdegf A000906 24.0207 2*(1+3*x)/(1-2*x)^(7/2) egf A000906 24.0207 2*(3*x+1)/(1-2*x)^(7/2) egf A000906 10.4241 {(-21-13*n-2*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=2,a(1)=20} ogf A000907 9.67974 -5*(26+138*x+2*x^3+81*x^2)/(-1+2*x)/(2*x^3+57*x^2+64*x+6) lgdegf A000907 5.86963 {(-28-15*n-2*n^2)*a(n+1)+(-332-125*n-12*n^2)*a(n+2)+(6*n+18)*a(n+3),a(0)=6,a(1)=130,a(2)=2380} ogf A000909 10.8601 {(16*n^2+64*n+60)*a(n+1)-a(n+2),a(0)=1,a(1)=12} ogf A000910 83.8955 -5/(x-1)^7 ogf A000910 93.2172 -7/(-1+x) lgdogf A000910 16.4501 5*x^6/(1-7*x+21*x^2-35*x^3+35*x^4-21*x^5+7*x^6-x^7) ogf A000910 10.7558 {(-4+n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=5} ogf A000910 10.7558 {(-4+n)*a(n+2)+(-n-2)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=5} ogf A000911 61.1421 -10/(-1+4*x) lgdogf A000911 48.9136 6/(1-4*x)^(5/2) ogf A000911 15.9501 {(-n-2)*a(n+2)+(14+4*n)*a(n+1),a(0)=6,a(1)=60} ogf A000914 33.7304 -(11+4*x)/(x+2)/(-1+x) lgdogf A000914 17.2574 -(2*x+x^2)/(-1+5*x-5*x^4-10*x^2+10*x^3+x^5) ogf A000914 53.0049 -(x+2)/(x-1)^5 ogf A000914 11.0756 {(2*n+4)*a(n+3)+(-12-n)*a(n+2)+(-4-n)*a(n+1),a(0)=0,a(1)=2,a(2)=11} ogf A000914 11.0756 {(4+2*n)*a(n+3)+(-12-n)*a(n+2)+(-4-n)*a(n+1),a(0)=0,a(1)=2,a(2)=11} ogf A000915 8.97734 -(-24-58*x-x^3-22*x^2)/(-x^9+1-9*x-36*x^7+36*x^2-126*x^5-84*x^3+126*x^4+84*x^6+9*x^8) ogf A000915 26.3129 -(24+58*x+22*x^2+x^3)/(x-1)^9 ogf A000915 14.131 -(274+508*x+6*x^3+157*x^2)/(-1+x)/(x^3+22*x^2+58*x+24) lgdogf A000915 7.33725 {(-203-57*n-4*n^2)*a(n+1)+(-691-154*n-7*n^2)*a(n+2)+(91*n+174+11*n^2)*a(n+3),a(0)=24,a(1)=274,a(2)=1624} ogf A000917 11.552 -1/2*(-6*x+1+4*(1-4*x)^(1/2)*x-(1-4*x)^(1/2))/(1-4*x)^(3/2)/x^2 ogf A000917 11.552 -1/2*(-6*x+1-(1-4*x)^(1/2)+4*(1-4*x)^(1/2)*x)/(1-4*x)^(3/2)/x^2 ogf A000917 12.3351 {(-42-26*n-4*n^2)*a(n+1)+(6*n+8+n^2)*a(n+2),a(0)=3,a(1)=20} ogf A000918 46.769 (3*x-1)/(2*x-1)/(x-1) ogf A000918 32.7383 -(-3*x+1+4*x^2)/(-2*x^2-1+3*x) ogf A000918 42.7021 -(3*x-1)/(-2*x^2-1+3*x) ogf A000918 26.5446 -2*x*(-2+3*x)/(-1+x)/(3*x-1)/(-1+2*x) lgdogf A000918 40.9229 1-3*x+(2*x^2+1-3*x)*f(x) ogf A000918 25.1833 1/2/(-3+2*x)*(-1+3*x+(1+6*x+x^2)^(1/2)) revogf A000918 24.5537 {-a(n+2)+3*a(n+1)-2*a(n),a(0)=-1,a(1)=0} ogf A000919 12.4391 -2*(-5+35*x+48*x^3-75*x^2)/(-1+x)/(3*x-1)/(-1+2*x)/(-1+4*x) lgdogf A000919 17.4739 24*x^3+(-1+10*x-35*x^2+50*x^3-24*x^4)*f(x) ogf A000919 22.2395 24/(x-1)/(3*x-1)/(2*x-1)/(-1+4*x) ogf A000920 6.78754 -(-21+350*x-8820*x^4+6496*x^3+4320*x^5-2205*x^2)/(-1+x)/(6*x-1)/(-1+4*x)/(3*x-1)/(-1+2*x)/(5*x-1) lgdogf A000920 11.3516 720*x^5/(1-21*x+175*x^2-735*x^3+1624*x^4-1764*x^5+720*x^6) ogf A000920 12.6614 720/(x-1)/(-1+6*x)/(-1+4*x)/(3*x-1)/(2*x-1)/(-1+5*x) ogf A000930 38.3825 -(1+3*x^2)/(-1+x+x^3) lgdogf A000930 62.0025 -1/(-1+x+x^3) ogf A000930 23.0295 1+(-2+x+x^3)*f(x)+(-x^3+1-x)*f(x)^2 ogf A000930 73.2757 1/(1-x-x^3) ogf A000930 19.1912 {-a(n+3)+a(n+2)+a(n),a(0)=1,a(1)=1,a(2)=1} ogf A000931 31.4592 (x-1)*(x+1)/(-1+x^3+x^2) ogf A000931 35.9533 -(-x^2+1)/(x^3-1+x^2) ogf A000931 20.4059 -x^2*(x^2-3)/(-1+x)/(1+x)/(x^3+x^2-1) lgdogf A000931 32.827 -x^2+1+(x^3-1+x^2)*f(x) ogf A000931 17.9767 {-a(n+3)+a(n+1)+a(n),a(0)=1,a(1)=0,a(2)=0} ogf A000932 14.5017 {(-3-n)*a(n+1)-a(n+2)+a(n+3),a(0)=1,a(1)=1,a(2)=3} ogf A000933 10.2719 -(1-2*x^7+9*x^4+3*x^8+6*x^6-4*x^5+5*x^2)/(-1+x)/(x^2+x+1)/(x^4-x^3+x^2-x+1)/(1+x^2) lgdogf A000933 19.3766 -(x^4-x^3+x^2-x+1)/(x^2+1)/(x^2+x+1)/(x-1)^3 ogf A000933 13.1165 -(x^4-x^5+x^6-x^7+x^8)/(-1+2*x-2*x^2+3*x^3-3*x^4+2*x^5-2*x^6+x^7) ogf A000933 50.1512 1+x^2+x^3+x^4-x^9 ogf_with_Euler_Transform A000957 35.6934 -x*(-1+2*x)/(-1+x)^2 revogf A000957 24.6161 -x+(1+2*x)*f(x)+(-2-x)*f(x)^2 ogf A000957 6.48971 {(2*n+4*n^2)*a(n)+(-12-12*n+3*n^2)*a(n+1)+(-27*n-18-9*n^2)*a(n+2)+(10*n+12+2*n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=0} ogf A000958 23.5337 1+(-1+x)*f(x)+(2*x^2+x^3)*f(x)^2 ogf A000958 14.209 1/2*((4*x^2+1)^(1/2)*x+(4*x^2+1)^(1/2)-1-x-2*x^2)/x^2 revogf A000958 5.88342 {(-30-22*n-4*n^2)*a(n+1)+(234+99*n+9*n^2)*a(n+2)+(492+246*n+30*n^2)*a(n+3)+(-80*n-192-8*n^2)*a(n+4),a(0)=1,a(1)=1,a(2)=3,a(3)=8} ogf A000962 16.0554 (x+1)*(2*x^4-7*x^3+6*x^2+x-1)/(x^6-1+7*x^2-3*x^4) ogf A000962 17.1025 -(1+5*x^4+x^3-2*x^5-7*x^2)/(x^6-1+7*x^2-3*x^4) ogf A000962 7.15195 -x^2*(-10*x^7+28*x^5+17*x^2-8*x+2*x^8+3*x^6-39*x^4+22*x^3-3)/(1+x)/(2*x^4-7*x^3+6*x^2+x-1)/(x^6-3*x^4+7*x^2-1) lgdogf A000963 10.8829 (-1+4*x^2-7*x^3+2*x^4)/(x^6-1+7*x^2-3*x^4) ogf A000963 10.6298 -(-7*x^4-x+4*x^3+2*x^5)/(1-7*x^2-x^6+3*x^4) ogf A000963 4.48119 -x*(-6+4*x^8+16*x^6+49*x^3+20*x^2-21*x^7+21*x^5-58*x^4-21*x)/(2*x^4-7*x^3+4*x^2-1)/(x^6-3*x^4+7*x^2-1) lgdogf A000964 16.7611 -(-3*x^4+x^3+x^5+x^2)/(-1+7*x^2+x^6-3*x^4) ogf A000964 7.48902 -(1+8*x-12*x^7-16*x^4-12*x^3+3*x^8+2*x^6+24*x^5+10*x^2)/(-1+x)/(x^2-2*x-1)/(x^6-3*x^4+7*x^2-1) lgdogf A000964 18.5255 -(x-1)*(x^2-2*x-1)/(x^6-1+7*x^2-3*x^4) ogf A000969 21.5821 -(-1-x-2*x^2)/(x^2+1-2*x+2*x^4-x^5-x^3) ogf A000969 15.0304 -(3+8*x+6*x^4+8*x^3+11*x^2)/(-1+x)/(x^2+x+1)/(2*x^2+x+1) lgdogf A000969 28.0567 -(x+1+2*x^2)/(x^2+x+1)/(x-1)^3 ogf A000969 7.5829 {(-2*n^2-17*n-37)*a(n+1)+(-4*n-15)*a(n+2)+(-4*n-15)*a(n+3)+(2*n^2+13*n+22)*a(n+4),a(0)=1,a(1)=3,a(2)=7,a(3)=12} ogf A000970 8.64042 -(-1-2*x^4-3*x-4*x^3-3*x^5-3*x^2)/(-6*x^7+1-4*x-x^9+6*x^2-4*x^3+x^4-x^5+4*x^6+4*x^8) ogf A000970 12.5137 -(1+3*x+3*x^2+4*x^3+2*x^4+3*x^5)/(x^4+x^3+x^2+x+1)/(x-1)^5 ogf A000970 5.94914 -(7+22*x+12*x^9+44*x^7+72*x^4+52*x^3+22*x^8+57*x^6+72*x^5+40*x^2)/(-1+x)/(3*x^5+2*x^4+4*x^3+3*x^2+3*x+1)/(x^4+x^3+x^2+x+1) lgdogf A000972 7.59338 -(1+6*x+9*x^2+9*x^3+10*x^4+7*x^5+12*x^6+6*x^7+4*x^8)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^7 ogf A000973 25.458 (x+1)*(1+6*x+x^2)/(x-1)^8 ogf A000973 8.83959 -(1+7*x+x^3+7*x^2)/(-28*x^2-1+8*x+8*x^7-70*x^4+56*x^5+56*x^3-x^8-28*x^6) ogf A000973 13.2594 -(15+63*x+5*x^3+45*x^2)/(-1+x)/(1+x)/(x^2+6*x+1) lgdogf A000973 10.2653 {(66+23*n+2*n^2)*a(n+1)+(-9*n-10-2*n^2)*a(n+2),a(0)=1,a(1)=15} ogf A000975 19.1836 -2*(-1-x+3*x^2)/(-1+x)/(-1+2*x)/(1+x) lgdogf A000975 28.3917 -x+(1-2*x-x^2+2*x^3)*f(x) ogf A000975 33.7996 -x/(-1+2*x+x^2-2*x^3) ogf A000975 33.7996 1/(x-1)/(2*x-1)/(x+1) ogf A000975 13.3923 {-a(n+3)+2*a(n+2)+a(n+1)-2*a(n),a(0)=0,a(1)=1,a(2)=2} ogf A000981 5.88386 (19+8800*x^13+123*x+9600*x^11+70*x^3-18400*x^12-210*x^2)/(-1+x)/(800*x^13-800*x^12+70*x^3-61*x^2-x-9) lgdogf A000981 12.644 -(-9-x-61*x^2+70*x^3-800*x^12+800*x^13)/(x-1)^2 ogf A000981 11.6523 -(9+x-800*x^13-70*x^3+800*x^12+61*x^2)/(-x^2-1+2*x) ogf A000982 30.139 -(-x-x^3)/(1-2*x+2*x^3-x^4) ogf A000982 36.9887 -(x^2+1)/(x+1)/(x-1)^3 ogf A000982 20.8654 -2*(1+3*x+x^2+x^3)/(-1+x)/(1+x)/(1+x^2) lgdogf A000982 90.4169 2+2*x-x^3 ogf_with_Euler_Transform A000982 9.68752 527*x+527*x^3+(-527+1205*x-903*x^3+527*x^4)*f(x)+(-151+302*x-302*x^3+151*x^4)*f(x)^2 ogf A000982 6.07278 {(412+360*n+77*n^2)*a(n+1)+(943+406*n+25*n^2)*a(n+2)+(150-156*n-77*n^2)*a(n+3)+(-381-202*n-25*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=2,a(3)=5} ogf A000984 34.4327 (-2*x+(4*x^2+1)^(1/2))*x revogf A000984 48.6109 -1+(1-4*x)*f(x)^2 ogf A000984 75.126 -2/(-1+4*x) lgdogf A000984 55.0924 1/(1-4*x)^(1/2) ogf A000984 18.7815 {(-n-2)*a(n+2)+(6+4*n)*a(n+1),a(0)=1,a(1)=2} ogf A000985 22.7341 -2-x^3+2*x^2+(2-4*x+2*x^2)*f(x) lgdegf A000985 27.106 1/2*(2+x^3-2*x^2)/(-1+x)^2 lgdegf A000985 6.52553 {(-2*n-10)*a(n+5)+(18+4*n)*a(n+4)+(-2*n-6)*a(n+3)-2*a(n+2)+a(n+1),a(0)=1,a(1)=1,a(2)=3/2,a(3)=11/6,a(4)=7/3} egf A000986 18.718 (-2*x+x^3)*f(x)+(2-4*x+2*x^2)*f(x)^2 lgdegf A000986 28.0769 -1/2*x*(-2+x^2)/(-1+x)^2 lgdegf A000986 12.2518 {-a(n+4)+2*a(n+3)-a(n+2),a(0)=0,a(1)=1,a(2)=2,a(3)=5/2} lgdegf A000990 65.6763 -(-1-x)/(1-x) ogf_with_Euler_Transform A000990 29.4411 {a(n+2)-a(n+1),a(0)=1,a(1)=2} ogf_with_Euler_Transform A000993 6.06085 -(-1+4*x+68*x^2-59*x^3-723*x^4+5*x^5+1700*x^6+500*x^7)/(x-1)/(-1+5*x)/(1+2*x)/(2*x-1)/(1+5*x)/(10*x-1)/(x+1) ogf A000993 5.89704 -(1-4*x-1700*x^6-500*x^7-5*x^5+59*x^3+723*x^4-68*x^2)/(30*x^2-1+10*x-129*x^4-300*x^3+100*x^6+1290*x^5-1000*x^7) ogf A001002 23.0703 -1+f(x)-x*f(x)^2-x^2*f(x)^3 ogf A001002 47.9152 -x*(-1+x+x^2) revogf A001002 6.2919 {(-108*n-27*n^2-105)*a(n+1)+(-22*n^2-121*n-165)*a(n+2)+(5*n^2+35*n+60)*a(n+3),a(0)=1,a(1)=1,a(2)=3} ogf A001003 27.0134 -1+(1+x)*f(x)-2*x*f(x)^2 ogf A001003 13.2311 -1/2*(-1+x+(1-6*x+x^2)^(1/2))/(1-6*x+x^2)^(1/2)/x lgdogf A001003 20.9136 -1/4*(-x-1+(1-6*x+x^2)^(1/2))/x ogf A001003 38.1366 x*(-1+2*x)/(-1+x) revogf A001003 6.29439 {(n+n^2)*a(n)+(-19*n-12-7*n^2)*a(n+1)+(48+37*n+7*n^2)*a(n+2)+(-7*n-12-n^2)*a(n+3),a(0)=1,a(1)=1,a(2)=3} ogf A001005 30.3981 -1+f(x)-x^2*f(x)^2-x^3*f(x)^3 ogf A001005 67.8112 x/(1+x^2+x^3) revogf A001006 29.3353 1+(-1+x)*f(x)+x^2*f(x)^2 ogf A001006 64.0044 x/(1+x+x^2) revogf A001006 10.5082 {(-3*n-6)*a(n+1)+(-2*n-7)*a(n+2)+(n+5)*a(n+3),a(0)=1,a(1)=1,a(2)=2} ogf A001014 17.7184 -(x+1)*(x^4+56*x^3+246*x^2+56*x+1)/(x-1)^7 ogf A001014 8.75498 -(x+57*x^5+x^6+302*x^3+302*x^4+57*x^2)/(-1+7*x-21*x^2+35*x^3-35*x^4+21*x^5-7*x^6+x^7) ogf A001014 9.07528 -2*(32+473*x+88*x^4+718*x^3+x^5+1208*x^2)/(-1+x)/(1+x)/(x^4+56*x^3+246*x^2+56*x+1) lgdogf A001014 5.13223 {(-402-365*n-82*n^2)*a(n+1)+(10521+4545*n+666*n^2)*a(n+2)+(-4446-2115*n-666*n^2)*a(n+3)+(627+455*n+82*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=64,a(3)=729} ogf A001015 13.3599 (1+120*x+1191*x^2+2416*x^3+1191*x^4+120*x^5+x^6)/(x-1)^8 ogf A001015 7.12529 -(-x-1191*x^5-120*x^6-x^7-1191*x^3-2416*x^4-120*x^2)/(1-8*x+x^8+28*x^2-56*x^3+70*x^4-56*x^5+28*x^6-8*x^7) ogf A001015 6.86381 -2*(64+1611*x+2682*x^4+8422*x^3+x^6+183*x^5+7197*x^2)/(-1+x)/(x^6+120*x^5+1191*x^4+2416*x^3+1191*x^2+120*x+1) lgdogf A001016 5.87124 -(-x-15619*x^5-4293*x^6-247*x^7-4293*x^3-15619*x^4-247*x^2-x^8)/(1-9*x+9*x^8+36*x^2-x^9-84*x^3+126*x^4-126*x^5+84*x^6-36*x^7) ogf A001016 11.4673 -(x+1)*(x^6+246*x^5+4047*x^4+11572*x^3+4047*x^2+246*x+1)/(x-1)^9 ogf A001017 8.5376 1/(x-1)^10*(1+502*x+14608*x^2+88234*x^3+156190*x^4+88234*x^5+14608*x^6+502*x^7+x^8) ogf A001017 8.5376 x*(1+156190*x^4+88234*x^5+14608*x^6+14608*x^2+88234*x^3+x^8+502*x+502*x^7)/(x-1)^10 ogf A001018 65.8797 -1+(1-8*x)*f(x) ogf A001018 98.8196 -1/(8*x-1) ogf A001018 89.836 -8/(-1+8*x) lgdogf A001018 109.8 1/(1-8*x) ogf A001018 76.0151 1/8*ln(8*x+1) revegf A001018 44.918 {a(n+1)-8*a(n),a(0)=1} ogf A001019 41.9402 -1+(1-9*x)*f(x) ogf A001019 57.1912 -1/(-1+9*x) ogf A001019 57.1912 -9/(-1+9*x) lgdogf A001019 69.9004 1/(1-9*x) ogf A001019 48.3926 1/9*ln(1+9*x) revegf A001019 69.9004 x/(1+9*x) revogf A001019 28.5956 {a(n+1)-9*a(n),a(0)=1} ogf A001020 42.8764 -1+(1-11*x)*f(x) ogf A001020 57.1685 -1/(-1+11*x) ogf A001020 52.7709 -11/(-1+11*x) lgdogf A001020 68.6022 1/(1-11*x) ogf A001020 45.7348 1/11*ln(1+11*x) revegf A001020 68.6022 x/(11*x+1) revogf A001020 29.8271 {a(n+1)-11*a(n),a(0)=1} ogf A001021 34.8651 -1+(1-12*x)*f(x) ogf A001021 46.4868 -1/(-1+12*x) ogf A001021 42.9109 -12/(-1+12*x) lgdogf A001021 55.7841 1/(1-12*x) ogf A001021 37.1894 1/12*ln(1+12*x) revegf A001021 55.7841 x/(12*x+1) revogf A001021 24.254 {a(n+1)-12*a(n),a(0)=1} ogf A001022 50.6151 -1+(1-13*x)*f(x) ogf A001022 67.4869 -1/(-1+13*x) ogf A001022 67.4869 -13/(13*x-1) lgdogf A001022 80.9842 1/(1-13*x) ogf A001022 53.9895 1/13*ln(1+13*x) revegf A001022 80.9842 x/(1+13*x) revogf A001022 35.2105 {a(n+1)-13*a(n),a(0)=1} ogf A001023 51.7568 -1+(1-14*x)*f(x) ogf A001023 69.0091 -1/(-1+14*x) ogf A001023 63.7007 -14/(-1+14*x) lgdogf A001023 82.8109 1/(1-14*x) ogf A001023 55.2073 1/14*ln(1+14*x) revegf A001023 82.8109 x/(1+14*x) revogf A001023 36.0048 {a(n+1)-14*a(n),a(0)=1} ogf A001024 52.8985 -1+(1-15*x)*f(x) ogf A001024 70.5314 -1/(-1+15*x) ogf A001024 65.1059 -15/(-1+15*x) lgdogf A001024 84.6377 1/(1-15*x) ogf A001024 56.4251 1/15*ln(1+15*x) revegf A001024 84.6377 x/(1+15*x) revogf A001024 36.799 {a(n+1)-15*a(n),a(0)=1} ogf A001025 54.2305 -1+(1-16*x)*f(x) ogf A001025 72.3073 -1/(-1+16*x) ogf A001025 66.7452 -16/(-1+16*x) lgdogf A001025 86.7688 1/(1-16*x) ogf A001025 57.8459 1/16*ln(1+16*x) revegf A001025 86.7688 x/(16*x+1) revogf A001025 37.7256 {a(n+1)-16*a(n),a(0)=1} ogf A001026 54.9916 -1+(1-17*x)*f(x) ogf A001026 73.3222 -1/(-1+17*x) ogf A001026 67.682 -17/(-1+17*x) lgdogf A001026 87.9866 1/(1-17*x) ogf A001026 58.6578 1/17*ln(1+17*x) revegf A001026 87.9866 x/(1+17*x) revogf A001026 38.2551 {a(n+1)-17*a(n),a(0)=1} ogf A001027 56.3236 -1+(1-18*x)*f(x) ogf A001027 75.0982 -1/(-1+18*x) ogf A001027 69.3214 -18/(-1+18*x) lgdogf A001027 90.1178 1/(1-18*x) ogf A001027 60.0785 1/18*ln(1+18*x) revegf A001027 90.1178 x/(1+18*x) revogf A001027 39.1816 {a(n+1)-18*a(n),a(0)=1} ogf A001029 57.0847 -1+(1-19*x)*f(x) ogf A001029 76.113 -1/(-1+19*x) ogf A001029 70.2582 -19/(-1+19*x) lgdogf A001029 91.3356 1/(1-19*x) ogf A001029 60.8904 1/19*ln(1+19*x) revegf A001029 91.3356 x/(1+19*x) revogf A001029 39.7111 {a(n+1)-19*a(n),a(0)=1} ogf A001040 14.9555 {-a(n+1)+(-2-n)*a(n+2)+a(n+3),a(0)=0,a(1)=1,a(2)=1} ogf A001044 12.1047 {(n^2+4*n+4)*a(n+1)-a(n+2),a(0)=1,a(1)=1} ogf A001045 33.3894 -(1+4*x)/(1+x)/(-1+2*x) lgdogf A001045 47.9972 -1/(2*x-1)/(x+1) ogf A001045 51.197 -x/(-1+x+2*x^2) ogf A001045 23.9986 1/4/x*(-x-1+(9*x^2+2*x+1)^(1/2)) revogf A001045 19.1989 x+(-1+2*x+2*x^2)*f(x)+(2*x^2-1+x)*f(x)^2 ogf A001045 20.7556 {-a(n+2)+a(n+1)+2*a(n),a(0)=0,a(1)=1} ogf A001046 5.50482 {(2*n+4)*a(n+1)+(20+18*n+7*n^2+n^3)*a(n+2)+(44+38*n+11*n^2+n^3)*a(n+3)+(-2*n-8)*a(n+4),a(0)=1,a(1)=1,a(2)=2,a(3)=7} ogf A001047 29.4327 -(-5+12*x)/(3*x-1)/(-1+2*x) lgdogf A001047 22.7052 -1/12*(-1-5*x+(1+10*x+x^2)^(1/2))/x revogf A001047 46.746 1/(3*x-1)/(2*x-1) ogf A001047 37.842 x+(-1+5*x-6*x^2)*f(x) ogf A001047 52.9789 x/(1-5*x+6*x^2) ogf A001047 20.9127 {a(n+2)-5*a(n+1)+6*a(n),a(0)=0,a(1)=1} ogf A001048 27.7105 -(-3+x)/(-1+x)/(x-2) lgdegf A001048 29.1689 -(2-x)/(-x^2-1+2*x) egf A001048 39.5864 -(x-2)/(x-1)^2 egf A001048 11.7917 -10+5*x+(1-8*x+5*x^2)*f(x)+(2-4*x+2*x^2)*f(x)^2 egf A001048 6.8421 {(-4-4*n-n^2)*a(n+1)+(-21-13*n-2*n^2)*a(n+2)+(2*n+6)*a(n+3),a(0)=2,a(1)=3,a(2)=8} ogf A001052 5.30486 {(-8-4*n)*a(n+1)+(-32-34*n-14*n^2-2*n^3)*a(n+2)+(-40-36*n-11*n^2-n^3)*a(n+3)+(2*n+8)*a(n+4),a(0)=1,a(1)=2,a(2)=3,a(3)=11} ogf A001053 11.5156 {-a(n+1)+(-n-2)*a(n+2)+a(n+3),a(0)=1,a(1)=0,a(2)=1} ogf A001057 39.4584 -(3*x-1)/(-1+x)/(1+x) lgdogf A001057 51.7891 -1/(x-1)/(x+1)^2 ogf A001057 39.4584 -x+(1+x-x^2-x^3)*f(x) ogf A001057 48.7427 -x/(-1+x+x^2-x^3) ogf A001057 48.7427 -x/(-1-x+x^2+x^3) ogf A001057 165.725 2*x-1 ogf_with_Euler_Transform A001057 16.5725 {-a(n+3)-a(n+2)+a(n+1)+a(n),a(0)=0,a(1)=1,a(2)=-1} ogf A001060 35.8352 -(-2-3*x)/(-x^2+1-x) ogf A001060 39.8169 -(3*x+2)/(x^2-1+x) ogf A001060 22.397 -(5+4*x+3*x^2)/(3*x+2)/(x^2+x-1) lgdogf A001060 19.3704 1/2/(3+x)*(-2-x+(4+16*x+5*x^2)^(1/2)) revogf A001060 14.3341 14+21*x+(11+34*x+7*x^2)*f(x)+(-9+9*x+9*x^2)*f(x)^2 ogf A001060 21.0795 {a(n+2)-a(n+1)-a(n),a(0)=2,a(1)=5} ogf A001068 23.9262 (1+x+x^2+2*x^3)/(x^2+1)/(x+1)/(x-1)^2 ogf A001068 26.8264 -(-x-x^3-2*x^4-x^2)/(1-x+x^5-x^4) ogf A001068 11.8036 -(2+4*x+7*x^4+9*x^3+4*x^6+5*x^5+9*x^2)/(-1+x)/(1+x)/(x^2+1)/(2*x^3+x^2+x+1) lgdogf A001069 16.0959 (-1-2*x-14*x^13+13*x^14+x^2)/(-1+x)/(1+x^14+x^2) lgdogf A001069 38.6301 -(-x-x^15-x^3)/(1-x) ogf A001069 40.6633 -(1+x^2+x^14)/(x-1) ogf A001075 36.2542 -(-1+2*x)/(x^2+1-4*x) ogf A001075 38.067 -(2*x-1)/(x^2+1-4*x) ogf A001075 16.1987 -1+2*x+(4-10*x+x^2)*f(x)+(-3+12*x-3*x^2)*f(x)^2 ogf A001075 23.0709 -2*(1-x+x^2)/(-1+2*x)/(x^2-4*x+1) lgdogf A001075 21.1483 {a(n+2)-4*a(n+1)+a(n),a(0)=1,a(1)=2} ogf A001076 49.3059 -1/(-1+4*x+x^2) ogf A001076 36.9794 -2*(x+2)/(x^2-1+4*x) lgdogf A001076 38.9257 -x+(1-4*x-x^2)*f(x) ogf A001076 49.3059 -x/(-1+4*x+x^2) ogf A001076 21.1311 1/2/x*(-1-4*x+(1+8*x+20*x^2)^(1/2)) revogf A001076 19.9889 {-a(n+2)+4*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A001077 29.0033 (2*x-1)/(-1+4*x+x^2) ogf A001077 27.6222 -(1-2*x)/(-1+4*x+x^2) ogf A001077 17.0608 -2*(-1-x+x^2)/(-1+2*x)/(x^2-1+4*x) lgdogf A001077 16.5733 1/2/(x-2)*(-1-4*x+(20*x^2+1)^(1/2)) revogf A001077 12.0847 3-6*x+(-8+22*x+3*x^2)*f(x)+(5-20*x-5*x^2)*f(x)^2 ogf A001077 15.6775 {-a(n+2)+4*a(n+1)+a(n),a(0)=1,a(1)=2} ogf A001078 16.1309 -(-1-5*x+(1+4*x)^(1/2)*(6*x+1)^(1/2))/x revogf A001078 29.9573 -2*(x-5)/(x^2+1-10*x) lgdogf A001078 28.5956 2*x+(-1+10*x-x^2)*f(x) ogf A001078 39.319 2*x/(1-10*x+x^2) ogf A001078 44.9359 2/(1-10*x+x^2) ogf A001078 17.0028 {a(n+2)-10*a(n+1)+a(n),a(0)=0,a(1)=2} ogf A001079 25.4293 -(-1+5*x)/(1-10*x+x^2) ogf A001079 15.9841 -(5-2*x+5*x^2)/(5*x-1)/(x^2+1-10*x) lgdogf A001079 15.1201 -1/2*(-10*x-1+(96*x^2+1)^(1/2))/(x+5) revogf A001079 9.64558 -23+115*x+(71-470*x+23*x^2)*f(x)+(-48+480*x-48*x^2)*f(x)^2 ogf A001079 15.1201 {a(n+2)-10*a(n+1)+a(n),a(0)=1,a(1)=5} ogf A001080 12.2222 -1/2*(-16*x-3+(14*x+3)^(1/2)*(6*x+1)^(1/2)*3^(1/2))/x revogf A001080 29.4444 -2*(-8+x)/(x^2+1-16*x) lgdogf A001080 29.4444 3*x+(-1+16*x-x^2)*f(x) ogf A001080 40.4861 3*x/(1-16*x+x^2) ogf A001080 46.2698 3/(1-16*x+x^2) ogf A001080 17.5075 {a(n+2)-16*a(n+1)+a(n),a(0)=0,a(1)=3} ogf A001081 23.5672 -(-1+8*x)/(1-16*x+x^2) ogf A001081 24.6894 -(8*x-1)/(1-16*x+x^2) ogf A001081 14.4022 -2*(4-x+4*x^2)/(-1+8*x)/(x^2+1-16*x) lgdogf A001081 8.64129 -31+248*x+(94-1000*x+31*x^2)*f(x)+(-63+1008*x-63*x^2)*f(x)^2 ogf A001081 14.0129 {a(n+2)-16*a(n+1)+a(n),a(0)=1,a(1)=8} ogf A001082 19.9489 -(-x-x^3-4*x^2)/(1-x-2*x^2-x^5+2*x^3+x^4) ogf A001082 29.211 -(1+4*x+x^2)/(x+1)^2/(x-1)^3 ogf A001082 18.1757 -(x+5)*(3*x^2+2*x+1)/(-1+x)/(1+x)/(x^2+4*x+1) lgdogf A001082 5.17662 {(-9651-6628*n-1137*n^2)*a(n+1)+(-112801-57260*n-6849*n^2)*a(n+2)+(-18467-3632*n+1137*n^2)*a(n+3)+(45087+35576*n+6849*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=5,a(3)=8} ogf A001084 13.0555 -1/2*(-20*x-3+(6*x+1)^(1/2)*(22*x+3)^(1/2)*3^(1/2))/x revogf A001084 31.452 -2*(x-10)/(x^2+1-20*x) lgdogf A001084 31.452 3*x+(-1+20*x-x^2)*f(x) ogf A001084 43.2465 3*x/(1-20*x+x^2) ogf A001084 49.4245 3/(1-20*x+x^2) ogf A001084 18.7012 {a(n+2)-20*a(n+1)+a(n),a(0)=0,a(1)=3} ogf A001085 27.647 -(-1+10*x)/(1-20*x+x^2) ogf A001085 28.9037 -(10*x-1)/(1-20*x+x^2) ogf A001085 17.6634 -2*(5-x+5*x^2)/(10*x-1)/(x^2+1-20*x) lgdogf A001085 10.4243 -49+490*x+(148-1970*x+49*x^2)*f(x)+(-99+1980*x-99*x^2)*f(x)^2 ogf A001085 16.7337 {a(n+2)-20*a(n+1)+a(n),a(0)=1,a(1)=10} ogf A001090 13.9771 -1/2*(-1-8*x+(10*x+1)^(1/2)*(6*x+1)^(1/2))/x revogf A001090 30.7497 -2*(x-4)/(x^2+1-8*x) lgdogf A001090 47.3072 1/(1-8*x+x^2) ogf A001090 32.3681 x+(-1+8*x-x^2)*f(x) ogf A001090 47.3072 x/(1-8*x+x^2) ogf A001090 17.0831 {a(n+2)-8*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A001091 27.6748 -(-1+4*x)/(1-8*x+x^2) ogf A001091 16.6049 -2*(2-x+2*x^2)/(-1+4*x)/(x^2+1-8*x) lgdogf A001091 10.5668 -7+28*x+(22-116*x+7*x^2)*f(x)+(-15+120*x-15*x^2)*f(x)^2 ogf A001091 16.1437 {a(n+2)-8*a(n+1)+a(n),a(0)=1,a(1)=4} ogf A001093 35.5442 (1-2*x+7*x^2)/(x-1)^4 ogf A001093 18.2056 -(-x-7*x^3+2*x^2)/(1-4*x+6*x^2-4*x^3+x^4) ogf A001093 20.1737 -2*(1+4*x+7*x^2)/(-1+x)/(7*x^2-2*x+1) lgdogf A001093 7.31792 61*x-122*x^2+427*x^3+(-61+316*x-510*x^2+748*x^3-61*x^4)*f(x)+(-72+288*x-432*x^2+288*x^3-72*x^4)*f(x)^2 ogf A001093 8.29364 {(n+3)*a(n+4)+(-8-3*n)*a(n+3)+(1+9*n)*a(n+2)+(-14-7*n)*a(n+1),a(0)=0,a(1)=1,a(2)=2,a(3)=9} ogf A001094 24.0293 -(1-3*x+3*x^2+23*x^3)/(x-1)^5 ogf A001094 12.4437 -(x+3*x^3+23*x^4-3*x^2)/(-1+5*x-10*x^2+10*x^3-5*x^4+x^5) ogf A001094 13.4009 -2*(1-3*x+23*x^3+39*x^2)/(-1+x)/(23*x^3+3*x^2-3*x+1) lgdogf A001094 7.41328 {(6+5*n+n^2)*a(n+1)+(-6*n-2*n^2)*a(n+2)+(-2+n+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=28} ogf A001095 20.0023 (1-4*x+6*x^2-4*x^3+121*x^4)/(x-1)^6 ogf A001095 10.0011 -(x+121*x^5+6*x^3-4*x^4-4*x^2)/(-1+6*x-15*x^2+20*x^3-15*x^4+6*x^5-x^6) ogf A001095 10.4489 -2*(1-4*x+121*x^4+236*x^3+6*x^2)/(-1+x)/(121*x^4-4*x^3+6*x^2-4*x+1) lgdogf A001095 6.86352 {(-6-5*n-n^2)*a(n+1)+(-3+5*n+2*n^2)*a(n+2)+(4-n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=125} ogf A001096 15.9238 -(1-5*x+10*x^2-10*x^3+5*x^4+719*x^5)/(x-1)^7 ogf A001096 8.24291 -(x+719*x^6+5*x^5+10*x^3-10*x^4-5*x^2)/(-1+7*x-21*x^2+35*x^3-35*x^4+21*x^5-7*x^6+x^7) ogf A001096 8.34104 -2*(1-5*x+1805*x^4-10*x^3+719*x^5+10*x^2)/(-1+x)/(719*x^5+5*x^4-10*x^3+10*x^2-5*x+1) lgdogf A001096 6.36952 {(6+5*n+n^2)*a(n+1)+(6-4*n-2*n^2)*a(n+2)+(-6-n+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=5,a(6)=726} ogf A001105 25.5999 -(2*x+2*x^2)/(-1+3*x-3*x^2+x^3) ogf A001105 49.5998 -2*(x+1)/(x-1)^3 ogf A001105 37.7903 -2*(x+2)/(-1+x)/(1+x) lgdogf A001105 13.4508 2*x+2*x^2+(-1+7*x+x^2+x^3)*f(x)+(-6*x^2-2+6*x+2*x^3)*f(x)^2 ogf A001105 15.2615 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=2,a(2)=8} ogf A001106 25.0539 -(-x-6*x^2)/(1-3*x+3*x^2-x^3) ogf A001106 45.4103 -(1+6*x)/(x-1)^3 ogf A001106 29.0626 -3*(4*x+3)/(6*x+1)/(-1+x) lgdogf A001106 7.49036 9804*x+58824*x^2+(-9804+25051*x-55578*x^2+9804*x^3)*f(x)+(4361-13083*x+13083*x^2-4361*x^3)*f(x)^2 ogf A001106 13.9724 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=9} ogf A001107 50.2926 -(1+7*x)/(x-1)^3 ogf A001107 27.7476 -(x+7*x^2)/(-1+3*x-3*x^2+x^3) ogf A001107 32.1873 -2*(7*x+5)/(7*x+1)/(-1+x) lgdogf A001107 7.73732 37449*x+262143*x^2+(-37449+97819*x-214043*x^2+37449*x^3)*f(x)+(14528-43584*x+43584*x^2-14528*x^3)*f(x)^2 ogf A001107 15.1827 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=10} ogf A001108 27.4254 -(-x-x^2)/(1-7*x+7*x^2-x^3) ogf A001108 30.8536 -(x+1)/(x-1)/(1-6*x+x^2) ogf A001108 16.4552 -2*(4-7*x+x^3-2*x^2)/(-1+x)/(1+x)/(1-6*x+x^2) lgdogf A001108 12.767 x+x^2+(-1+15*x+x^2+x^3)*f(x)+(-56*x^2-8+56*x+8*x^3)*f(x)^2 ogf A001108 14.2401 {a(n+3)-7*a(n+2)+7*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=8} ogf A001109 16.9989 -1/2*(-6*x-1+(1+8*x)^(1/2)*(1+4*x)^(1/2))/x revogf A001109 34.8072 -2*(-3+x)/(1-6*x+x^2) lgdogf A001109 56.227 1/(1-6*x+x^2) ogf A001109 38.4711 x+(-1+6*x-x^2)*f(x) ogf A001109 56.227 x/(1-6*x+x^2) ogf A001109 20.3042 {a(n+2)-6*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A001110 17.6872 -(-x-x^2)/(1-35*x+35*x^2-x^3) ogf A001110 20.5172 -(x+1)/(x-1)/(x^2-34*x+1) ogf A001110 10.4679 -2*(18-35*x+x^3-16*x^2)/(-1+x)/(1+x)/(x^2-34*x+1) lgdogf A001110 8.01452 x+x^2+(-1+71*x+x^2+x^3)*f(x)+(-1260*x^2-36+1260*x+36*x^3)*f(x)^2 ogf A001110 9.32598 {a(n+3)-35*a(n+2)+35*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=36} ogf A001117 19.2917 -(-6*x+1+11*x^2)/(x-1)/(3*x-1)/(2*x-1) ogf A001117 20.3634 -(6*x-1-11*x^2)/(11*x^2+1-6*x-6*x^3) ogf A001117 18.797 -1+6*x-11*x^2+(11*x^2+1-6*x-6*x^3)*f(x) ogf A001117 12.0178 -6*x^2*(11*x^2-12*x+3)/(-1+x)/(3*x-1)/(-1+2*x)/(11*x^2-6*x+1) lgdogf A001117 13.3288 {a(n+3)-6*a(n+2)+11*a(n+1)-6*a(n),a(0)=1,a(1)=0,a(2)=0} ogf A001118 8.63334 -(-15*x+85*x^2-225*x^3+1+274*x^4)/(x-1)/(-1+4*x)/(3*x-1)/(2*x-1)/(-1+5*x) ogf A001118 8.75324 -(15*x-85*x^2+225*x^3-1-274*x^4)/(85*x^2+1-15*x+274*x^4-225*x^3-120*x^5) ogf A001118 5.48029 -120*x^4*(-450*x^3+5+274*x^4+255*x^2-60*x)/(-1+x)/(-1+4*x)/(3*x-1)/(-1+2*x)/(5*x-1)/(274*x^4-225*x^3+85*x^2-15*x+1) lgdogf A001120 6.46308 {(12+10*n+2*n^2)*a(n+1)+(28+18*n+3*n^2)*a(n+2)+(12+n^2+6*n)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=3,a(2)=8,a(3)=33} ogf A001147 37.3585 -1+(1-2*x)*f(x)^2 egf A001147 57.7359 -1/(-1+2*x) lgdegf A001147 48.8534 -1/2*x*(-2+x) revegf A001147 42.3397 1/(1-2*x)^(1/2) egf A001147 16.713 {(-2*n-3)*a(n+1)+a(n+2),a(0)=1,a(1)=1} ogf A001148 24.3968 -(-1-2*x-7*x^2)/(x^2+1-x-x^3) ogf A001148 25.2681 -(1+2*x+7*x^2)/(x^2+1)/(x-1) ogf A001148 12.634 -(3+12*x+7*x^4+4*x^3-6*x^2)/(-1+x)/(x^2+1)/(7*x^2+2*x+1) lgdogf A001148 10.7198 19+38*x+133*x^2+(-20+17*x-26*x^2+19*x^3)*f(x)+(x^2+1-x-x^3)*f(x)^2 ogf A001148 14.7397 {a(n+3)-a(n+2)+a(n+1)-a(n),a(0)=1,a(1)=3,a(2)=9} ogf A001167 3.40935 (1+20*x+20979*x^2-20899*x^3+20*x^4+980*x^5-980*x^6-20899020*x^8+20899020*x^9)/(x-1)/(-1+10*x^2)/(100*x^4+10*x^2+1) ogf A001169 18.6603 (2-4*x+5*x^2)/(-1+x)/(4*x^3-7*x^2+5*x-1) lgdogf A001169 26.6576 (x-1)^3/(-7*x^2-1+5*x+4*x^3) ogf A001169 19.1388 -(-1+3*x+x^3-3*x^2)/(7*x^2+1-5*x-4*x^3) ogf A001169 10.663 -1+3*x-3*x^2+x^3+(2-8*x+10*x^2-5*x^3)*f(x)+(-1+5*x-7*x^2+4*x^3)*f(x)^2 ogf A001169 11.6627 {a(n+4)-5*a(n+3)+7*a(n+2)-4*a(n+1),a(0)=1,a(1)=2,a(2)=6,a(3)=19} ogf A001181 8.46104 {(-8*n-8*n^2)*a(n)+(-7*n^2-35*n-40)*a(n+1)+(n^2+9*n+20)*a(n+2),a(0)=0,a(1)=1} ogf A001189 10.8084 -exp(x)+2*exp(1/2*x*(x+2))+2*x*exp(1/2*x*(x+2))+exp(1/2*x*(x+2))*x^2 egf A001189 7.49972 {(12+7*n+n^2)*a(n+1)+(-6*n-8-n^2)*a(n+2)+(-7-2*n)*a(n+3)+(n+3)*a(n+4),a(0)=0,a(1)=1,a(2)=3,a(3)=9} ogf A001193 34.3011 (-x+(1+x^2)^(1/2))*x revegf A001193 32.6677 -(-1+x)/(1-2*x)^(3/2) egf A001193 34.3011 -(x-1)/(1-2*x)^(3/2) egf A001193 31.1828 -(x-2)/(-1+2*x)/(-1+x) lgdegf A001193 18.0532 1-2*x+x^2+(-12*x^2-1+6*x+8*x^3)*f(x)^2 egf A001193 13.7204 {(-9-9*n-2*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=2} ogf A001194 14.0289 3/2*(3*x^2-4*x+2)/(1-2*x)^(1/2)/(2*x-1)^2 egf A001204 12.4408 (7+2*x+x^2+x^3+3*x^4+x^10+4*x^5+x^6-x^7-x^8)/(x-1)^2/(x^4+x^3+x^2+x+1)^2 ogf A001204 14.6842 -(7+2*x+x^6-x^7+x^10+x^3+4*x^5+3*x^4+x^2-x^8)/(-1+2*x^5-x^10) ogf A001205 38.741 -1/2*x^2/(-1+x) lgdegf A001205 34.1833 x^2+(-2+2*x)*f(x) lgdegf A001205 7.85291 {(-n^2-5*n-6)*a(n+1)+(-2*n-6)*a(n+3)+2*a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=1} ogf A001224 15.1695 -(-1-x+2*x^2+x^3+x^4+x^5)/(x^2-1+x)/(x^4+x^2-1) ogf A001224 14.2594 -(-1-x+x^3+x^5+x^4+2*x^2)/(-2*x^2+1-x+x^6+x^5+x^3) ogf A001224 6.92202 -(2+2*x^9+8*x^7-3*x^4-4*x^3+x^10+4*x^8+6*x^6-2*x^5-2*x^2)/(x^2+x-1)/(x^4+x^2-1)/(x^5+x^4+x^3+2*x^2-x-1) lgdogf A001240 11.5723 -(11-72*x+108*x^2)/(6*x-1)/(3*x-1)/(-1+2*x) lgdogf A001240 18.43 -1/(-1+6*x)/(3*x-1)/(2*x-1) ogf A001240 6.46247 -86+(247-946*x+3096*x^2-3096*x^3)*f(x)+(-5796*x^2+5796*x^3-161+1771*x)*f(x)^2 ogf A001240 20.7338 1/(1-11*x+36*x^2-36*x^3) ogf A001240 8.43407 {a(n+3)-11*a(n+2)+36*a(n+1)-36*a(n),a(0)=1,a(1)=11,a(2)=85} ogf A001241 14.0762 -1/(-1+50*x-840*x^2+5760*x^3-13824*x^4) ogf A001241 4.81555 -192+(-391-9600*x+161280*x^2-1105920*x^3+2654208*x^4)*f(x)+(583+8059392*x^4-29150*x+489720*x^2-3358080*x^3)*f(x)^2 ogf A001241 8.31777 -2*(48*x-5)*(576*x^2-120*x+5)/(6*x-1)/(-1+8*x)/(-1+12*x)/(-1+24*x) lgdogf A001241 14.4467 1/(-1+6*x)/(8*x-1)/(-1+12*x)/(-1+24*x) ogf A001242 8.21542 -1/(-1+24*x)/(30*x-1)/(40*x-1)/(60*x-1)/(120*x-1) ogf A001242 6.70926 1/(1-274*x+27000*x^2-1224000*x^3+25920000*x^4-207360000*x^5) ogf A001246 13.9237 {(16*n^2+48*n+36)*a(n+1)+(-n^2-6*n-9)*a(n+2),a(0)=1,a(1)=1} ogf A001249 11.7302 -(-1-9*x-x^3-9*x^2)/(21*x^2+1-7*x-x^7+35*x^4-21*x^5-35*x^3+7*x^6) ogf A001249 29.3255 -(x+1)*(x^2+8*x+1)/(x-1)^7 ogf A001249 16.2226 -4*(4+18*x+x^3+12*x^2)/(-1+x)/(1+x)/(x^2+8*x+1) lgdogf A001249 13.3765 {(25+10*n+n^2)*a(n+1)+(-n^2-4*n-4)*a(n+2),a(0)=1,a(1)=16} ogf A001254 30.4535 -(-4+7*x+x^2)/(x+1)/(x^2-3*x+1) ogf A001254 16.5624 -(1+14*x+x^4+14*x^3-24*x^2)/(1+x)/(x^2-3*x+1)/(x^2+7*x-4) lgdogf A001254 31.4686 -(4-7*x-x^2)/(2*x^2-1+2*x-x^3) ogf A001254 10.6074 -748+1309*x+187*x^2+(647-1179*x-489*x^2+187*x^3)*f(x)+(-115+230*x+230*x^2-115*x^3)*f(x)^2 ogf A001254 17.8124 {-a(n+3)+2*a(n+2)+2*a(n+1)-a(n),a(0)=4,a(1)=1,a(2)=9} ogf A001260 7.55153 {(42+13*n+n^2)*a(n+1)+(21+10*n+n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=5,a(2)=45} ogf A001261 6.23994 -1/120*exp(-x)*(120+1200*x^2-2000*x^3+2925*x^4-2636*x^5+1615*x^6-640*x^7+155*x^8-20*x^9+x^10)/(x-1)^7 egf A001261 7.97764 {(56+15*n+n^2)*a(n+1)+(24+11*n+n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=6,a(2)=63} ogf A001264 9.15302 -(1+3*x+12*x^2+48*x^3-8*x^4-31*x^5+75*x^6)/(x-1)/(x+1)/(x^4-x^3+x^2-x+1) ogf A001264 11.5617 -(1+3*x+75*x^6+48*x^3-31*x^5-8*x^4+12*x^2)/(-1+x-x^5+x^6) ogf A001277 4.49953 {(-n-5)*a(n+1)+(n+6)*a(n+3)-a(n+4),a(0)=1,a(1)=3,a(2)=12,a(3)=56} ogf A001281 29.8823 (2+x+4*x^2)/(x-1)^2/(x+1)^2 ogf A001281 12.8067 -(-2*x-4*x^3+67*x^30-61*x^29-72*x^28+66*x^27-x^2)/(1+x^4-2*x^2) ogf A001281 17.5396 -(1+16*x+8*x^3+3*x^2)/(-1+x)/(1+x)/(4*x^2+x+2) lgdogf A001281 7.33475 -28694*x-14347*x^2-57388*x^3+(14347+2240*x-27574*x^2+4480*x^3+14347*x^4)*f(x)+(-1120-1120*x^4+2240*x^2)*f(x)^2 ogf A001286 38.6703 (1+2*x)/(x-1)^4 egf A001286 17.5774 -(1+2*x)/(-6*x^2-1+4*x+4*x^3-x^4) egf A001286 4.79384 -26449-52898*x+(13300-132094*x+158694*x^2-105796*x^3+26449*x^4)*f(x)+(13149-52596*x^3-52596*x+78894*x^2+13149*x^4)*f(x)^2 egf A001286 25.2198 -6*(1+x)/(1+2*x)/(-1+x) lgdegf A001286 11.8379 {(-12-7*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=6} ogf A001287 62.0719 -1/(-1+x)^11 ogf A001287 67.7148 -1/(x-1)^11 ogf A001287 53.2045 -11+(1-x)*f(x) lgdogf A001287 74.4863 -11/(-1+x) lgdogf A001287 16.9287 {(-n-2)*a(n+2)+(12+n)*a(n+1),a(0)=1,a(1)=11} ogf A001287 43.8155 {-a(n+1),a(0)=11} ogf_with_Euler_Transform A001288 52.6742 -12+(1-x)*f(x) lgdogf A001288 73.7439 -12/(-1+x) lgdogf A001288 73.7439 1/(x-1)^12 ogf A001288 16.76 {(-n-2)*a(n+2)+(13+n)*a(n+1),a(0)=1,a(1)=12} ogf A001288 43.3787 {-a(n+1),a(0)=12} ogf_with_Euler_Transform A001296 49.5693 -(1+2*x)/(x-1)^5 ogf A001296 34.483 -(7+8*x)/(1+2*x)/(-1+x) lgdogf A001296 18.4444 -(x+2*x^2)/(-1+5*x-5*x^4-10*x^2+10*x^3+x^5) ogf A001296 12.2017 {(n+2)*a(n+3)+(-6+n)*a(n+2)+(-8-2*n)*a(n+1),a(0)=0,a(1)=1,a(2)=7} ogf A001297 11.0106 -(-x-6*x^3-8*x^2)/(1-7*x-x^7+21*x^2-21*x^5-35*x^3+35*x^4+7*x^6) ogf A001297 31.5303 -(1+8*x+6*x^2)/(x-1)^7 ogf A001297 18.2544 -15*(1+4*x+2*x^2)/(-1+x)/(6*x^2+8*x+1) lgdogf A001297 7.37943 {(n+3)*a(n+4)+(-1+7*n)*a(n+3)+(-62-2*n)*a(n+2)+(-30-6*n)*a(n+1),a(0)=0,a(1)=1,a(2)=15,a(3)=90} ogf A001298 8.59242 -(-1-22*x-24*x^3-58*x^2)/(-x^9+1-9*x-36*x^7+36*x^2-126*x^5-84*x^3+126*x^4+84*x^6+9*x^8) ogf A001298 24.1142 -(1+22*x+58*x^2+24*x^3)/(x-1)^9 ogf A001298 13.1147 -(31+292*x+144*x^3+478*x^2)/(-1+x)/(24*x^3+58*x^2+22*x+1) lgdogf A001298 7.47541 {(-364-129*n-11*n^2)*a(n+1)+(-149-14*n+7*n^2)*a(n+2)+(23*n+33+4*n^2)*a(n+3),a(0)=1,a(1)=31,a(2)=301} ogf A001299 8.44163 (1-2*x^15+4*x^20+3*x^10+2*x^5-x^25+5*x^30)/(x-1)/(x^30+x^25-5*x^20+6*x^15-x^5-1) ogf A001299 48.2379 1+x^4+x^9+x^24 ogf_with_Euler_Transform A001300 8.77052 (1-x^15+5*x^20+3*x^10+2*x^5+5*x^30)/(x-1)/(2*x^30+2*x^25-5*x^20+5*x^15-x^5-1) ogf A001300 6.25306 -(-1-2*x^5-5*x^20-3*x^10+x^15-5*x^30)/(-2*x^25+1-x+x^5+2*x^31-x^6+5*x^20-5*x^15-5*x^21+5*x^16+2*x^26-2*x^30) ogf A001301 50.9234 1+x+x^4+x^9+x^24 ogf_with_Euler_Transform A001303 12.8644 -(-6-8*x-x^2)/(1-7*x-x^7+21*x^2-21*x^5-35*x^3+35*x^4+7*x^6) ogf A001303 37.9499 -(6+8*x+x^2)/(x-1)^7 ogf A001303 21.6856 -5*(10+10*x+x^2)/(-1+x)/(x^2+8*x+6) lgdogf A001303 7.74487 {(6*n+24)*a(n+4)+(-44+2*n)*a(n+3)+(-64-7*n)*a(n+2)+(-6-n)*a(n+1),a(0)=6,a(1)=50,a(2)=225,a(3)=735} ogf A001304 12.6563 -(2+6*x+11*x^4+6*x^3+9*x^5+6*x^2)/(-1+x)/(1+x)/(x^4+x^3+x^2+x+1) lgdogf A001304 19.7562 -1/(-1+2*x-2*x^3+x^4+x^5-2*x^6+2*x^8-x^9) ogf A001304 24.5456 1/(x+1)/(x^4+x^3+x^2+x+1)/(x-1)^4 ogf A001304 115.715 2+x+x^4 ogf_with_Euler_Transform A001304 18.4092 {-a(n+5),a(0)=2,a(1)=1,a(2)=0,a(3)=0,a(4)=1} ogf_with_Euler_Transform A001305 38.7874 2+x+x^4+x^9+x^19 ogf_with_Euler_Transform A001307 38.0775 2+x+x^3+x^9+x^19 ogf_with_Euler_Transform A001310 17.091 (x^8-x^6+x^4-x^2+1)/(-1+2*x^20)/(x+1)^2/(x-1)^3 ogf A001310 9.02557 -(-1+x^6-x^4+x^2-x^8)/(4*x^22+1-x-2*x^2-x^5+2*x^3+x^4-2*x^20+2*x^21-4*x^23-2*x^24+2*x^25) ogf A001311 9.68937 -(1+6*x+36*x^2+16*x^3+96*x^4+75*x^5+50*x^6)/(x-1)/(x^4+x^3+x^2+x+1) ogf A001311 12.4844 -(1+6*x+50*x^6+16*x^3+75*x^5+96*x^4+36*x^2)/(-1+x^5) ogf A001318 21.6143 -(2+8*x+3*x^3+5*x^2)/(-1+x)/(1+x)/(x^2+x+1) lgdogf A001318 35.7467 -(x^2+x+1)/(x+1)^2/(x-1)^3 ogf A001318 103.268 2+2*x-x^2 ogf_with_Euler_Transform A001318 6.07461 {(9894+6475*n+1059*n^2)*a(n+1)+(34192+16037*n+1755*n^2)*a(n+2)+(3026-1543*n-1059*n^2)*a(n+3)+(-13344-9713*n-1755*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=2,a(3)=5} ogf A001319 8.96658 -(-2+2*x^15+2*x^10+4*x^5+3*x^25+3*x^30)/(x-1)/(x+1)/(2*x^30-3*x^25+2*x^20-6*x^15+6*x^5-2) ogf A001333 41.0171 (x-1)/(-1+2*x+x^2) ogf A001333 23.0721 -(-1-2*x+x^2)/(-1+x)/(x^2+2*x-1) lgdogf A001333 41.0171 -(1-x)/(x^2-1+2*x) ogf A001333 14.4766 -9+9*x+(19-28*x-9*x^2)*f(x)+(10*x^2-10+20*x)*f(x)^2 ogf A001333 19.9543 {-a(n+2)+2*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A001338 7.68367 {-a(n)+(2*n+4)*a(n+1)+(-n^2-6*n-8)*a(n+2)+(n^2+5*n+6)*a(n+3),a(0)=1,a(1)=0,a(2)=1,a(3)=7/6} egf A001339 44.2446 (-3+x)/(-1+x) lgdegf A001339 38.3453 -3+x+(1-x)*f(x) lgdegf A001339 41.0843 exp(x)/(x-1)^2 egf A001339 10.0909 {(-n-2)*a(n+1)+(n+5)*a(n+2)-a(n+3),a(0)=1,a(1)=3,a(2)=11} ogf A001340 59.3681 (x-4)/(-1+x) lgdegf A001340 41.9069 -2*exp(x)/(x-1)^3 egf A001340 12.4986 {(-n-2)*a(n+1)+(n+6)*a(n+2)-a(n+3),a(0)=2,a(1)=8,a(2)=38} ogf A001341 53.2318 (-5+x)/(-1+x) lgdegf A001341 43.2509 6*exp(x)/(x-1)^4 egf A001341 11.729 {(-n-2)*a(n+1)+(n+7)*a(n+2)-a(n+3),a(0)=6,a(1)=30,a(2)=174} ogf A001342 51.4145 (-6+x)/(-1+x) lgdegf A001342 37.1327 -24*exp(x)/(x-1)^5 egf A001342 10.9572 {(-n-2)*a(n+1)+(n+8)*a(n+2)-a(n+3),a(0)=24,a(1)=144,a(2)=984} ogf A001343 9.77383 -(1+x^20-x^10-x^30+x^40)/(x+1)^2/(x^4-x^3+x^2-x+1)^2/(x-1)^3/(x^4+x^3+x^2+x+1)^3 ogf A001344 7.59607 {(-23*n^2-13*n^3)*a(n)+(-66-154*n-97*n^2-19*n^3)*a(n+1)+(53*n+30+19*n^2)*a(n+2),a(0)=2,a(1)=5} ogf A001346 7.58918 -(-23+28*x-12*x^2+6*ln(1-x)*x^2+ln(1-x)-4*ln(1-x)*x+ln(1-x)*x^4-4*ln(1-x)*x^3+x^4)/(x-1)^4 egf A001347 5.88888 -(88-115*x+70*x^2-20*x^3+x^5-10*ln(1-x)*x^2+5*ln(1-x)*x-5*ln(1-x)*x^4+10*ln(1-x)*x^3+ln(1-x)*x^5-ln(1-x))/(x-1)^5 egf A001350 25.5886 (x^2+1)/(x-1)/(x+1)/(x^2-1+x) ogf A001350 11.9688 -(-1-6*x+x^4+4*x^3+2*x^5+4*x^2)/(-1+x)/(1+x)/(x^2+1)/(x^2+x-1) lgdogf A001350 25.5886 -(x+x^3)/(-1+x-x^4+2*x^2-x^3) ogf A001350 8.2452 -97*x-97*x^3+(97-22*x-194*x^2+172*x^3+97*x^4)*f(x)+(-75+75*x-75*x^4+150*x^2-75*x^3)*f(x)^2 ogf A001351 10.8074 (x^2+3*x+1)*(x^2-x+1)/(x^3-x^2-1)/(-1+x+x^3) ogf A001351 4.61675 -(-3+4*x+2*x^9-8*x^7+5*x^4-8*x^3+5*x^8+18*x^6-6*x^5-14*x^2)/(x^2+3*x+1)/(x^3-x^2-1)/(x^3+x-1)/(x^2-x+1) lgdogf A001351 8.97218 -(x-x^3+2*x^2+x^5+2*x^4)/(-1+x-x^2+3*x^3-x^4+x^5-x^6) ogf A001352 36.0853 (x+1)^2/(x^2+1-4*x) ogf A001352 27.4249 -(1+2*x+x^2)/(-x^2-1+4*x) ogf A001352 25.3934 -6*(-1+x)/(1+x)/(x^2-4*x+1) lgdogf A001352 25.3934 1+2*x+x^2+(-x^2-1+4*x)*f(x) ogf A001352 14.5877 {-a(n+3)+4*a(n+2)-a(n+1),a(0)=1,a(1)=6,a(2)=24} ogf A001353 14.747 -1/2*(-1-4*x+(2*x+1)^(1/2)*(6*x+1)^(1/2))/x revogf A001353 31.706 -2*(x-2)/(x^2-4*x+1) lgdogf A001353 48.7784 1/(x^2+1-4*x) ogf A001353 33.3747 x+(-x^2-1+4*x)*f(x) ogf A001353 48.7784 x/(1-4*x+x^2) ogf A001353 17.6144 {a(n+2)-4*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A001354 22.5227 (1+4*x+x^2)/(x^2-3*x+1) ogf A001354 20.7209 -(1+4*x+x^2)/(-x^2-1+3*x) ogf A001354 13.2826 -7*(-1+x)*(1+x)/(x^2+4*x+1)/(x^2-3*x+1) lgdogf A001354 19.186 1+4*x+x^2+(-x^2-1+3*x)*f(x) ogf A001354 11.0217 {-a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=7,a(2)=21} ogf A001360 17.0179 -(-1-4*x-x^2)/(4*x^2+1-4*x-x^3) ogf A001360 17.5852 -(1+4*x+x^2)/(x-1)/(x^2-3*x+1) ogf A001360 9.42065 -(8-6*x+x^4+8*x^3-17*x^2)/(-1+x)/(x^2+4*x+1)/(x^2-3*x+1) lgdogf A001360 5.38323 -1428-5712*x-1428*x^2+(2603-1012*x+6887*x^2-1428*x^3)*f(x)+(-4700*x^2-1175+4700*x+1175*x^3)*f(x)^2 ogf A001360 9.95389 {a(n+3)-4*a(n+2)+4*a(n+1)-a(n),a(0)=1,a(1)=8,a(2)=29} ogf A001361 8.98066 (-1-232*x-107224*x^3-24508*x^2-x^8-232*x^7-7228*x^6-55384*x^5-133510*x^4)/(x-1)^9 ogf A001361 8.98066 -(1+232*x+24508*x^2+107224*x^3+133510*x^4+55384*x^5+7228*x^6+232*x^7+x^8)/(x-1)^9 ogf A001362 6.33048 -(1+3*x+17*x^11+20*x^9+10*x^7+2*x^4+10*x^3+x^10+2*x^8+2*x^6+10*x^5+2*x^2)/(-1+x)/(1+x)/(1+x^2)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) lgdogf A001362 74.8148 1+x+x^3+x^9 ogf_with_Euler_Transform A001362 11.591 1/(1-x-x^2+x^3-x^4+x^5+x^6-x^7-x^10+x^11+x^12-x^13+x^14-x^15-x^16+x^17) ogf A001362 13.4912 1/(x^2+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x+1)^3/(x-1)^4 ogf A001365 36.9515 2+x+x^5+x^11+x^23 ogf_with_Euler_Transform A001382 3.57048 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A001386 21.1127 (1+6*x+x^2)*(x+1)^2/(x-1)^4 ogf A001386 11.4008 -(1+8*x+8*x^3+14*x^2+x^4)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A001386 4.38494 -1109-8872*x-15526*x^2-8872*x^3-1109*x^4+(849-6516*x+3014*x^2-6516*x^3+849*x^4)*f(x)+(1560*x^2+260-1040*x+260*x^4-1040*x^3)*f(x)^2 ogf A001386 13.9035 -4*(x+3)*(3*x+1)/(-1+x)/(1+x)/(x^2+6*x+1) lgdogf A001386 3.85164 {(-6439*n-1568*n^2)*a(n)+(-114501-65157*n-9108*n^2)*a(n+1)+(-225198-48209*n+1568*n^2)*a(n+2)+(55749*n+85275+9108*n^2)*a(n+3),a(0)=1,a(1)=12,a(2)=56} ogf A001392 6.86459 -(3*x-1)*(3*x^3-9*x^2+6*x-1)/(-81*x^8-1+18*x-1386*x^6-135*x^2+546*x^3-1287*x^4+1782*x^5+540*x^7+x^9) ogf A001392 20.19 18/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A001392 29.846 512/(1+(1-4*x)^(1/2))^9 ogf A001392 19.6131 81+(-9+36*x)*f(x)+(-x+4*x^2)*f(x)^2 lgdogf A001392 11.2534 {(-132-46*n-4*n^2)*a(n+1)+(13*n+22+n^2)*a(n+2),a(0)=1,a(1)=9} ogf A001392 11.2534 {(-132-46*n-4*n^2)*a(n+1)+(13*n+22+n^2)*a(n+2),a(0)=1,a(1)=9} ogf A001399 18.9848 -(1+2*x)*(3*x^2+2*x+1)/(-1+x)/(1+x)/(x^2+x+1) lgdogf A001399 34.1726 -1/(-1+x+x^2-x^4-x^5+x^6) ogf A001399 32.8583 -1/(x+1)/(x^2+x+1)/(x-1)^3 ogf A001399 122.045 1+x+x^2 ogf_with_Euler_Transform A001399 28.4772 {-a(n+3),a(0)=1,a(1)=1,a(2)=1} ogf_with_Euler_Transform A001400 13.0345 -(2*x^2+x+1)*(5*x^3+3*x^2+3*x+1)/(-1+x)/(1+x)/(1+x^2)/(x^2+x+1) lgdogf A001400 25.6616 -1/(-1+x+x^2-2*x^5+x^8+x^9-x^10) ogf A001400 74.6519 1+x+x^2+x^3 ogf_with_Euler_Transform A001400 23.462 1/(x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^4 ogf A001400 22.8103 {a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=1} ogf_with_Euler_Transform A001401 7.86496 -(3*x^4+2*x^3+3*x^2+x+1)*(5*x^5+7*x^4+7*x^3+6*x^2+4*x+1)/(-1+x)/(1+x)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(1+x^2) lgdogf A001401 15.293 -1/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x^2+1)/(x+1)^2/(x-1)^5 ogf A001401 55.0547 1+x+x^2+x^3+x^4 ogf_with_Euler_Transform A001401 16.1926 1/(1-x-x^2+x^5+x^6+x^7-x^8-x^9-x^10+x^13+x^14-x^15) ogf A001401 18.7686 {-a(n+5),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1} ogf_with_Euler_Transform A001402 11.6245 -1/(-1+x+x^2-x^5-2*x^7+x^9+x^10+x^11+x^12-2*x^14-x^16+x^19+x^20-x^21) ogf A001402 42.2154 1+x+x^3+x^5+x^2+x^4 ogf_with_Euler_Transform A001402 42.2154 1+x+x^5+x^2+x^3+x^4 ogf_with_Euler_Transform A001402 12.3399 1/(x^2-x+1)/(x^4+x^3+x^2+x+1)/(x^2+1)/(x^2+x+1)^2/(x+1)^3/(x-1)^6 ogf A001402 12.5327 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=0} ogf_with_Euler_Transform A001405 21.8194 -1+(1-2*x)*f(x)+(x-2*x^2)*f(x)^2 ogf A001405 11.0828 -1/2*(8*x^2+2*x-1+(-(-1+2*x)*(1+2*x))^(1/2))/x/(1+2*x)/(-1+2*x) lgdogf A001405 33.2485 x*(x+1)/(1+2*x+2*x^2) revogf A001405 11.637 {(-4*n-8)*a(n+1)-2*a(n+2)+(n+4)*a(n+3),a(0)=1,a(1)=1,a(2)=2} ogf A001407 1.6917 -1-8*x^3+(3+16*x^3)*f(x)+(-8*x^3-3)*f(x)^2+f(x)^3 ogf A001421 4.93853 {(5544+11472*n+7776*n^2+1728*n^3)*a(n+1)+(-n^3-6*n^2-12*n-8)*a(n+2),a(0)=1,a(1)=120} ogf A001438 1.64166 2-4*x^3+8*x^4-4*x^5 ogf_with_Euler_Transform A001444 16.3784 -(-1+x+3*x^2)/(-3*x^2+1-3*x+9*x^3) ogf A001444 10.1248 -(2+27*x^4+18*x^3-21*x^2)/(3*x-1)/(3*x^2-1)/(3*x^2+x-1) lgdogf A001444 18.5622 -(x+3*x^2-1)/(3*x-1)/(3*x^2-1) ogf A001444 8.43737 3-3*x-9*x^2+(-2+8*x+6*x^2-27*x^3)*f(x)+(-1+3*x+3*x^2-9*x^3)*f(x)^2 ogf A001444 10.3123 {a(n+3)-3*a(n+2)-3*a(n+1)+9*a(n),a(0)=1,a(1)=2,a(2)=6} ogf A001445 16.171 -(-3+x+6*x^2)/(-2*x^2+1-2*x+4*x^3) ogf A001445 17.7359 -(-3+x+6*x^2)/(2*x-1)/(2*x^2-1) ogf A001445 9.9966 -(5+24*x^4+8*x^3-26*x^2)/(-1+2*x)/(2*x^2-1)/(6*x^2+x-3) lgdogf A001445 7.23438 123-41*x-246*x^2+(-32+79*x+64*x^2-164*x^3)*f(x)+(-3+6*x+6*x^2-12*x^3)*f(x)^2 ogf A001445 9.9966 {a(n+3)-2*a(n+2)-2*a(n+1)+4*a(n),a(0)=3,a(1)=5,a(2)=10} ogf A001446 13.7394 -(-10+6*x+40*x^2)/(-4*x^2+1-4*x+16*x^3) ogf A001446 7.76573 -(17+320*x^4+96*x^3-172*x^2)/(-1+4*x)/(1+2*x)/(-1+2*x)/(20*x^2+3*x-5) lgdogf A001446 12.4613 -2*(-5+3*x+20*x^2)/(2*x+1)/(2*x-1)/(-1+4*x) ogf A001446 5.70038 7060-4236*x-28240*x^2+(-256+2554*x+1024*x^2-11296*x^3)*f(x)+(-45+180*x+180*x^2-720*x^3)*f(x)^2 ogf A001446 9.08196 {a(n+3)-4*a(n+2)-4*a(n+1)+16*a(n),a(0)=10,a(1)=34,a(2)=136} ogf A001447 14.0706 -(-1+2*x+5*x^2)/(-5*x^2+1-5*x+25*x^3) ogf A001447 15.7761 -(-1+2*x+5*x^2)/(5*x-1)/(5*x^2-1) ogf A001447 8.2637 -(5*x+1)*(25*x^3+15*x^2-15*x+3)/(5*x-1)/(5*x^2-1)/(5*x^2+2*x-1) lgdogf A001447 7.03531 5-10*x-25*x^2+(-1+17*x+5*x^2-125*x^3)*f(x)+(-4+20*x+20*x^2-100*x^3)*f(x)^2 ogf A001447 9.29666 {a(n+3)-5*a(n+2)-5*a(n+1)+25*a(n),a(0)=1,a(1)=3,a(2)=15} ogf A001448 9.7218 1/2*2^(1/2)/(1-16*x)^(1/2)*(1+(1-16*x)^(1/2))^(1/2) ogf A001448 9.53484 6+32*x+(-1+256*x^2)*f(x)+(512*x^3+2*x-64*x^2)*f(x)^2 lgdogf A001448 8.12806 {(70+96*n+32*n^2)*a(n+1)+(-7*n-6-2*n^2)*a(n+2),a(0)=1,a(1)=6} ogf A001449 3.94186 {(15120+41250*n+41875*n^2+18750*n^3+3125*n^4)*a(n+1)+(-4264*n-1680-4016*n^2-1664*n^3-256*n^4)*a(n+2),a(0)=1,a(1)=5} ogf A001450 4.54802 {(15120+41250*n+41875*n^2+18750*n^3+3125*n^4)*a(n+1)+(-1812*n-720-1698*n^2-702*n^3-108*n^4)*a(n+2),a(0)=1,a(1)=10} ogf A001451 5.26972 {(-15120-41250*n-41875*n^2-18750*n^3-3125*n^4)*a(n+1)+(492*n^2+564*n+240+189*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=20} ogf A001453 10.5742 12-34*x+25*x^2+(-3+20*x+20*x^3-37*x^2)*f(x)+(6*x^2+4*x^4-9*x^3-x)*f(x)^2 lgdogf A001453 8.36636 {(-56-30*n-4*n^2)*a(n+1)+(74+39*n+5*n^2)*a(n+2)+(-9*n-18-n^2)*a(n+3),a(0)=1,a(1)=4,a(2)=13} ogf A001459 4.13627 {(15120+41250*n+41875*n^2+18750*n^3+3125*n^4)*a(n+1)+(-292*n^2-336*n-144-112*n^3-16*n^4)*a(n+2),a(0)=1,a(1)=30} ogf A001460 4.29634 {(-15120-41250*n-41875*n^2-18750*n^3-3125*n^4)*a(n+1)+(30*n^3+84*n^2+104*n+48+4*n^4)*a(n+2),a(0)=1,a(1)=60} ogf A001464 83.4342 -1-x-f(x) lgdegf A001464 150.182 -1-x] lgdegf A001464 44.1711 exp(-1/2*x*(x+2)) egf A001464 15.0182 {(n+2)*a(n+1)+a(n+2)+a(n+3),a(0)=1,a(1)=-1,a(2)=0} ogf A001470 58.7939 1+x^2-f(x) lgdegf A001470 97.9899 1+x^2] lgdegf A001470 32.6633 exp(1/3*x*(x^2+3)) egf A001470 9.33237 {(-n^2-5*n-6)*a(n+1)-a(n+3)+a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=3} ogf A001471 32.6633 1+1/2*x^2+1/36*x^5 lgdegf A001472 51.3377 -1-x-x^3+f(x) lgdegf A001472 83.4238 1+x+x^3] lgdegf A001472 30.3359 exp(1/4*x*(4+2*x+x^3)) egf A001472 8.89854 {(-n-5)*a(n+5)+a(n+4)+a(n+3)+a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=2/3,a(4)=2/3} egf A001475 24.3796 (1+x)*(x^2+2*x+4)/(x^2+2+2*x) lgdegf A001475 22.094 1/2*exp(1/2*x*(x+2))*(2+2*x+x^2) egf A001475 21.4245 4+6*x+x^3+3*x^2+(-x^2-2-2*x)*f(x) lgdegf A001475 7.60223 {(8+6*n+n^2)*a(n+1)+(22+10*n+n^2)*a(n+2)+2*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=2,a(2)=5,a(3)=13} ogf A001477 107.95 -2/(-1+x) lgdogf A001477 107.95 1/(x-1)^2 ogf A001477 42.2411 4*x/(1+(1+4*x)^(1/2))^2 revogf A001477 51.134 x+(-1+2*x-x^2)*f(x) ogf A001477 26.9874 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A001478 16.0553 -(-5+6*x^18-25*x^20+25*x^21)/(6*x^18-5+10*x-5*x^2-12*x^19+6*x^20) ogf A001478 104.36 -1/(x-1)^2 ogf A001478 115.955 -2/(-1+x) lgdogf A001478 43.4832 -4*x/(1+(1-4*x)^(1/2))^2 revogf A001478 28.2053 1+(-2*x+x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A001478 65.2248 {-a(n+1),a(0)=2} ogf_with_Euler_Transform A001478 26.7589 {-a(n+2)+2*a(n+1)-a(n),a(0)=-1,a(1)=-2} ogf A001489 105.579 -1/(x-1)^2 ogf A001489 117.31 -2/(-1+x) lgdogf A001489 43.9913 -4*x/(1+(1-4*x)^(1/2))^2 revogf A001489 52.7896 -x+(-1+2*x-x^2)*f(x) ogf A001489 28.5349 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=-1} ogf A001496 14.1904 (x^4+12*x^3+62*x^2+12*x+1)*(x+1)^2/(x-1)^10 ogf A001496 5.17106 -(1+14*x+148*x^3+14*x^5+x^6+87*x^2+87*x^4)/(-45*x^2-1+10*x+10*x^9-210*x^4-x^10+120*x^3-45*x^8-210*x^6+252*x^5+120*x^7) ogf A001496 7.82289 -4*(6+69*x+18*x^4+130*x^3+x^5+216*x^2)/(-1+x)/(1+x)/(x^4+12*x^3+62*x^2+12*x+1) lgdogf A001499 7.76569 {(-n^3-7*n^2-16*n-12)*a(n+1)+(-2*n^2-10*n-12)*a(n+2)+2*a(n+3),a(0)=1,a(1)=0,a(2)=1} ogf A001499 10.5664 {(n+2)*a(n+1)+(2*n+4)*a(n+2)-2*a(n+3),a(0)=1,a(1)=0,a(2)=1/2} egf A001504 23.9294 -(-2-14*x-2*x^2)/(3*x^2+1-3*x-x^3) ogf A001504 24.6546 -(10+16*x+x^2)/(-1+x)/(x^2+7*x+1) lgdogf A001504 36.9819 -2*(1+7*x+x^2)/(x-1)^3 ogf A001504 9.68572 -200-1400*x-200*x^2+(122-146*x+322*x^2-100*x^3)*f(x)+(-33*x^2-11+33*x+11*x^3)*f(x)^2 ogf A001504 15.0667 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=2,a(1)=20,a(2)=56} ogf A001505 16.4563 -(35+155*x+x^3+65*x^2)/(-1+x)/(1+x)/(x^2+30*x+1) lgdogf A001505 16.1205 -(6+186*x+6*x^3+186*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A001505 28.2109 6*(x+1)*(x^2+30*x+1)/(x-1)^4 ogf A001505 7.74416 {(-78-67*n-14*n^2)*a(n+1)+(273+140*n+28*n^2)*a(n+2)+(-73*n-93-14*n^2)*a(n+3),a(0)=6,a(1)=210,a(2)=990} ogf A001509 15.8042 -(6+312*x+24*x^3+408*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A001509 15.1964 -4*(14+73*x+x^3+37*x^2)/(-1+x)/(4*x^3+68*x^2+52*x+1) lgdogf A001509 25.4907 6*(1+52*x+68*x^2+4*x^3)/(x-1)^4 ogf A001509 6.81217 {(-1782-1561*n-335*n^2)*a(n+1)+(4680+2472*n+570*n^2)*a(n+2)+(-1211*n-1518-235*n^2)*a(n+3),a(0)=6,a(1)=336,a(2)=1716} ogf A001512 10.5467 -(-24-2904*x-2904*x^3-9144*x^2-24*x^4)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A001512 10.3981 -(126+1246*x+x^4+246*x^3+1506*x^2)/(-1+x)/(x^4+121*x^3+381*x^2+121*x+1) lgdogf A001512 18.0065 -24*(1+121*x+381*x^2+121*x^3+x^4)/(x-1)^5 ogf A001513 23.2182 -(-5-62*x-5*x^2)/(3*x^2+1-3*x-x^3) ogf A001513 34.3226 -(5+62*x+5*x^2)/(x-1)^3 ogf A001513 20.2415 -(77+134*x+5*x^2)/(-1+x)/(5*x^2+62*x+5) lgdogf A001513 7.59058 -69010-855724*x-69010*x^2+(15577-19396*x+43181*x^2-13802*x^3)*f(x)+(-1065*x^2-355+1065*x+355*x^3)*f(x)^2 ogf A001513 14.3531 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=5,a(1)=77,a(2)=221} ogf A001514 5.8328 {(-3-n)*a(n+1)+(-17-10*n-2*n^2)*a(n+2)+(-29-14*n-2*n^2)*a(n+3)+(n+3)*a(n+4),a(0)=0,a(1)=1,a(2)=9,a(3)=81} ogf A001515 18.4127 -(1+(1-2*x)^(1/2))/(-1+2*x) lgdegf A001515 20.7143 -1/2*ln(1+x)*(ln(1+x)-2) revegf A001515 13.0827 2*x+(-2+4*x)*f(x)+(1-4*x+4*x^2)*f(x)^2 lgdegf A001515 4.7347 {(-2-n)*a(n+1)+(-14-10*n-2*n^2)*a(n+2)+(-26-14*n-2*n^2)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=2,a(2)=7,a(3)=37} ogf A001516 6.252 {(12+7*n+n^2)*a(n+1)+(40+41*n+15*n^2+2*n^3)*a(n+2)+(-2-3*n-n^2)*a(n+3),a(0)=0,a(1)=0,a(2)=6} ogf A001517 20.0423 -(2+(1-4*x)^(1/2))/(-1+4*x) lgdegf A001517 27.0572 -ln(1+x)*(ln(1+x)-1) revegf A001517 12.8844 3+4*x+(-4+16*x)*f(x)+(16*x^2+1-8*x)*f(x)^2 lgdegf A001517 5.15374 {(n+2)*a(n+1)+(24+19*n+4*n^2)*a(n+2)+(54+29*n+4*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=3,a(2)=19,a(3)=193} ogf A001518 22.4558 -(3+(-6*x+1)^(1/2))/(6*x-1) lgdegf A001518 23.3195 -1/2*ln(1+x)*(3*ln(1+x)-2) revegf A001518 14.1002 8+6*x+(-6+36*x)*f(x)+(1-12*x+36*x^2)*f(x)^2 lgdegf A001518 5.77435 {(n+2)*a(n+1)+(34+28*n+6*n^2)*a(n+2)+(82+44*n+6*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=4,a(2)=37,a(3)=559} ogf A001519 36.6292 -(-1+2*x)/(x^2+1-3*x) ogf A001519 21.9775 -(1-2*x+2*x^2)/(-1+2*x)/(x^2-3*x+1) lgdogf A001519 36.6292 -(2*x-1)/(-3*x+1+x^2) ogf A001519 19.7234 -1/2*(-1-3*x+(1-2*x+5*x^2)^(1/2))/(2+x) revogf A001519 16.0253 -2+4*x+(5-12*x+2*x^2)*f(x)+(-3*x^2-3+9*x)*f(x)^2 ogf A001519 21.367 {a(n+2)-3*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A001520 15.1541 -(15+633*x+15*x^3+633*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A001520 13.8011 -(231+1055*x+5*x^3+437*x^2)/(-1+x)/(1+x)/(5*x^2+206*x+5) lgdogf A001520 24.931 3*(x+1)*(5*x^2+206*x+5)/(x-1)^4 ogf A001520 7.09046 {(558+475*n+98*n^2)*a(n+1)+(-1869-980*n-196*n^2)*a(n+2)+(505*n+633+98*n^2)*a(n+3),a(0)=15,a(1)=693,a(2)=3315} ogf A001525 12.0919 {(27*n^2+135*n+168)*a(n+1)-a(n+2),a(0)=1,a(1)=60} ogf A001526 23.6522 -(-6-86*x-6*x^2)/(3*x^2+1-3*x-x^3) ogf A001526 21.1625 -(52+92*x+3*x^2)/(-1+x)/(3*x^2+43*x+3) lgdogf A001526 32.167 -2*(3+43*x+3*x^2)/(x-1)^3 ogf A001526 8.12299 -38916-557796*x-38916*x^2+(7212-9052*x+20184*x^2-6486*x^3)*f(x)+(-363*x^2-121+363*x+121*x^3)*f(x)^2 ogf A001526 14.3603 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=6,a(1)=104,a(2)=300} ogf A001533 22.4001 -(-7-114*x-7*x^2)/(3*x^2+1-3*x-x^3) ogf A001533 19.122 -(135+242*x+7*x^2)/(-1+x)/(7*x^2+114*x+7) lgdogf A001533 32.6667 -(7+114*x+7*x^2)/(x-1)^3 ogf A001533 7.25928 -313390-5103780*x-313390*x^2+(49201-62148*x+138741*x^2-44770*x^3)*f(x)+(-1899*x^2-633+1899*x+633*x^3)*f(x)^2 ogf A001533 14 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=7,a(1)=135,a(2)=391} ogf A001534 23.0281 -(-8-146*x-8*x^2)/(3*x^2+1-3*x-x^3) ogf A001534 20.6662 -(85+154*x+4*x^2)/(-1+x)/(4*x^2+73*x+4) lgdogf A001534 32.2393 -2*(4+73*x+4*x^2)/(x-1)^3 ogf A001534 7.46281 -289520-5283740*x-289520*x^2+(39398-50024*x+111778*x^2-36190*x^3)*f(x)+(-1203*x^2-401+1203*x+401*x^3)*f(x)^2 ogf A001534 14.3926 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=8,a(1)=170,a(2)=494} ogf A001535 22.657 -(-9-182*x-9*x^2)/(3*x^2+1-3*x-x^3) ogf A001535 19.3413 -(209+382*x+9*x^2)/(-1+x)/(9*x^2+182*x+9) lgdogf A001535 33.0414 -(9+182*x+9*x^2)/(x-1)^3 ogf A001535 6.95609 -1000458-20231484*x-1000458*x^2+(120081-153124*x+342405*x^2-111162*x^3)*f(x)+(-2973*x^2-991+2973*x+991*x^3)*f(x)^2 ogf A001535 14.1606 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=9,a(1)=209,a(2)=609} ogf A001536 21.08 -(-10-222*x-10*x^2)/(3*x^2+1-3*x-x^3) ogf A001536 19.0234 -(126+232*x+5*x^2)/(-1+x)/(5*x^2+111*x+5) lgdogf A001536 7.57241 -102370-2272614*x-102370*x^2+(10987-14061*x+31461*x^2-10237*x^3)*f(x)+(-225*x^2-75+225*x+75*x^3)*f(x)^2 ogf A001536 29.9984 -2*(5+111*x+5*x^2)/(x-1)^3 ogf A001536 13.6835 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=10,a(1)=252,a(2)=736} ogf A001538 21.4703 -(-11-266*x-11*x^2)/(3*x^2+1-3*x-x^3) ogf A001538 30.5539 -(11+266*x+11*x^2)/(x-1)^3 ogf A001538 18.0546 -(299+554*x+11*x^2)/(-1+x)/(11*x^2+266*x+11) lgdogf A001538 6.8483 -2565574-62040244*x-2565574*x^2+(248953-319588*x+715421*x^2-233234*x^3)*f(x)+(-4287*x^2-1429+4287*x+1429*x^3)*f(x)^2 ogf A001538 13.9369 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=11,a(1)=299,a(2)=875} ogf A001539 23.5253 -(-3-26*x-3*x^2)/(3*x^2+1-3*x-x^3) ogf A001539 34.7766 -(3+26*x+3*x^2)/(x-1)^3 ogf A001539 21.049 -(35+58*x+3*x^2)/(-1+x)/(3*x^2+26*x+3) lgdogf A001539 8.41959 -7830-67860*x-7830*x^2+(3081-3748*x+8301*x^2-2610*x^3)*f(x)+(-471*x^2-157+471*x+157*x^3)*f(x)^2 ogf A001539 14.8122 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=3,a(1)=35,a(2)=99} ogf A001540 6.59061 {(-12-7*n-n^2)*a(n+1)+(16+8*n+n^2)*a(n+3)+(-n-3)*a(n+4),a(0)=0,a(1)=2,a(2)=8,a(3)=36} ogf A001540 6.59061 {(-12-7*n-n^2)*a(n+1)+(n^2+8*n+16)*a(n+3)+(-3-n)*a(n+4),a(0)=0,a(1)=2,a(2)=8,a(3)=36} ogf A001541 32.9973 -(-1+3*x)/(x^2+1-6*x) ogf A001541 34.6472 -(3*x-1)/(1-6*x+x^2) ogf A001541 20.3807 -(3-2*x+3*x^2)/(3*x-1)/(1-6*x+x^2) lgdogf A001541 13.0744 -7+21*x+(23-90*x+7*x^2)*f(x)+(-16+96*x-16*x^2)*f(x)^2 ogf A001541 19.2484 {a(n+2)-6*a(n+1)+a(n),a(0)=1,a(1)=3} ogf A001542 14.2858 -(-1-3*x+(2*x+1)^(1/2)*(1+4*x)^(1/2))/x revogf A001542 26.5308 -2*(-3+x)/(1-6*x+x^2) lgdogf A001542 26.5308 2*x+(-1+6*x-x^2)*f(x) ogf A001542 37.1431 2*x/(x^2+1-6*x) ogf A001542 42.8575 2/(1-6*x+x^2) ogf A001542 15.4763 {a(n+2)-6*a(n+1)+a(n),a(0)=0,a(1)=2} ogf A001545 23.5921 -(-4-42*x-4*x^2)/(3*x^2+1-3*x-x^3) ogf A001545 21.1087 -(27+46*x+2*x^2)/(-1+x)/(2*x^2+21*x+2) lgdogf A001545 8.10233 -13064-137172*x-13064*x^2+(3758-4632*x+10290*x^2-3266*x^3)*f(x)+(-369*x^2-123+369*x+123*x^3)*f(x)^2 ogf A001545 32.0852 -2*(2+21*x+2*x^2)/(x-1)^3 ogf A001545 14.5842 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=4,a(1)=54,a(2)=154} ogf A001546 6.83026 -(-105-18780*x-18780*x^3-60534*x^2-105*x^4)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A001546 5.88816 -(6435+65396*x+35*x^4+12660*x^3+79314*x^2)/(-1+x)/(35*x^4+6260*x^3+20178*x^2+6260*x+35) lgdogf A001546 10.6723 -3*(35+6260*x+20178*x^2+6260*x^3+35*x^4)/(x-1)^5 ogf A001547 14.746 -(-8-760*x-90*x^3-1200*x^2)/(6*x^2+1-4*x+x^4-4*x^3) ogf A001547 12.3286 -3*(132+780*x+15*x^3+445*x^2)/(-1+x)/(45*x^3+600*x^2+380*x+4) lgdogf A001547 22.1189 2*(4+380*x+600*x^2+45*x^3)/(x-1)^4 ogf A001547 6.65525 {(-1050-927*n-201*n^2)*a(n+1)+(2090+1158*n+304*n^2)*a(n+2)+(-525*n-648-103*n^2)*a(n+3),a(0)=8,a(1)=792,a(2)=4320} ogf A001550 16.6335 -(3-12*x+11*x^2)/(-11*x^2-1+6*x+6*x^3) ogf A001550 16.6335 -(3-12*x+11*x^2)/(x-1)/(3*x-1)/(2*x-1) ogf A001550 8.77877 -2*(3-22*x+33*x^4-72*x^3+60*x^2)/(-1+x)/(3*x-1)/(-1+2*x)/(11*x^2-12*x+3) lgdogf A001550 8.20872 33-132*x+121*x^2+(-17+90*x-143*x^2+66*x^3)*f(x)+(22*x^2+2-12*x-12*x^3)*f(x)^2 ogf A001550 11.089 {-a(n+3)+6*a(n+2)-11*a(n+1)+6*a(n),a(0)=3,a(1)=6,a(2)=14} ogf A001551 13.1736 -(4-30*x-50*x^3+70*x^2)/(-35*x^2-1+10*x-24*x^4+50*x^3) ogf A001551 6.64834 -(5-70*x+1955*x^4-1192*x^3+600*x^6-1680*x^5+400*x^2)/(-1+x)/(-1+4*x)/(3*x-1)/(-1+2*x)/(5*x-2)/(5*x^2-5*x+1) lgdogf A001551 12.934 -2*(5*x-2)*(5*x^2-5*x+1)/(x-1)/(3*x-1)/(2*x-1)/(-1+4*x) ogf A001551 5.83092 1268-9510*x+22190*x^2-15850*x^3+(-209+2360*x-9205*x^2+14500*x^3-7608*x^4)*f(x)+(-945*x^2-27+270*x-648*x^4+1350*x^3)*f(x)^2 ogf A001552 10.1521 -(5-60*x+255*x^2-450*x^3+274*x^4)/(x-1)/(-1+4*x)/(3*x-1)/(2*x-1)/(5*x-1) ogf A001552 9.87772 -(5-60*x-450*x^3+255*x^2+274*x^4)/(-85*x^2-1+15*x-274*x^4+225*x^3+120*x^5) ogf A001553 7.56397 -(6-105*x-2205*x^3-1764*x^5+700*x^2+3248*x^4)/(-175*x^2-1+21*x-1624*x^4+735*x^3-720*x^6+1764*x^5) ogf A001553 8.33755 -(7*x-2)*(252*x^4-392*x^3+203*x^2-42*x+3)/(x-1)/(6*x-1)/(-1+4*x)/(3*x-1)/(2*x-1)/(5*x-1) ogf A001554 6.31885 -(7-168*x+1610*x^2-7840*x^3+20307*x^4-26264*x^5+13068*x^6)/(x-1)/(6*x-1)/(-1+4*x)/(3*x-1)/(2*x-1)/(7*x-1)/(5*x-1) ogf A001558 11.8221 -24-25*x+(8-27*x-20*x^2)*f(x)+(-7*x^2-4*x^3+2*x)*f(x)^2 lgdogf A001558 4.85234 {(56+30*n+4*n^2)*a(n+1)+(954+387*n+39*n^2)*a(n+2)+(1428+558*n+54*n^2)*a(n+3)+(-192*n-512-16*n^2)*a(n+4),a(0)=1,a(1)=3,a(2)=10,a(3)=33} ogf A001559 12.9742 -40-36*x+(10-34*x-24*x^2)*f(x)+(-7*x^2-4*x^3+2*x)*f(x)^2 lgdogf A001559 5.34233 {(-72-34*n-4*n^2)*a(n+1)+(-768-288*n-27*n^2)*a(n+2)+(-1068-375*n-33*n^2)*a(n+3)+(130*n+360+10*n^2)*a(n+4),a(0)=1,a(1)=4,a(2)=15,a(3)=54} ogf A001561 14.948 -(90+1200*x+8*x^3+760*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A001561 13.1439 -4*(195+640*x+x^3+193*x^2)/(-1+x)/(4*x^3+380*x^2+600*x+45) lgdogf A001561 22.4219 2*(4*x^3+380*x^2+600*x+45)/(x-1)^4 ogf A001561 6.57195 {(-598-505*n-103*n^2)*a(n+1)+(3900+1882*n+304*n^2)*a(n+2)+(-1083*n-1440-201*n^2)*a(n+3),a(0)=90,a(1)=1560,a(2)=6460} ogf A001563 50.3398 -(x+1)/(x-1)^3 egf A001563 78.3063 -2/(-1+x) lgdegf A001563 30.6416 4*x/(1+(1+4*x)^(1/2))^2 revegf A001563 37.0925 x+(-1+2*x-x^2)*f(x) egf A001563 54.2121 x/(1-2*x+x^2) egf A001563 14.6824 {(-4-4*n-n^2)*a(n+1)+(n+1)*a(n+2),a(0)=0,a(1)=1} ogf A001564 25.4838 -(-1-x^2)/(1-3*x+3*x^2-x^3) egf A001564 43.0038 -(1+x^2)/(x-1)^3 egf A001564 25.4838 -(3+2*x+x^2)/(-1+x)/(1+x^2) lgdegf A001564 10.4252 -4-4*x^2+(13-12*x+21*x^2-4*x^3)*f(x)+(-27*x^2+9*x^3-9+27*x)*f(x)^2 egf A001564 6.31249 {(n^2+4*n+4)*a(n+1)+(-24-15*n-2*n^2)*a(n+2)+(30+12*n+n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=3,a(2)=14,a(3)=78} ogf A001565 35.1604 (3*x+x^3+2)/(x-1)^4 egf A001565 17.5802 -(11+9*x+x^3+3*x^2)/(-1+x)/(2+3*x+x^3) lgdegf A001565 18.0553 -(2+3*x+x^3)/(-6*x^2-1+4*x-x^4+4*x^3) egf A001565 6.01845 -1138-1707*x-569*x^3+(-599-4028*x+3414*x^2-2860*x^3+569*x^4)*f(x)+(584-2336*x^3-2336*x+584*x^4+3504*x^2)*f(x)^2 egf A001565 6.01845 {(n^2+4*n+4)*a(n+1)+(10+5*n+n^2)*a(n+2)+(-62-23*n-2*n^2)*a(n+3)+(2*n+8)*a(n+4),a(0)=2,a(1)=11,a(2)=64,a(3)=426} ogf A001570 32.8305 -(-1+x)/(x^2+1-14*x) ogf A001570 19.8973 -(13-2*x+x^2)/(-1+x)/(x^2-14*x+1) lgdogf A001570 34.5584 -(x-1)/(x^2+1-14*x) ogf A001570 15.27 -1/2*(-1-14*x+(1+24*x+192*x^2)^(1/2))/(x+1) revogf A001570 10.7641 -11+11*x+(191-334*x+11*x^2)*f(x)+(-180+2520*x-180*x^2)*f(x)^2 ogf A001570 17.2792 {a(n+2)-14*a(n+1)+a(n),a(0)=1,a(1)=13} ogf A001571 31.0228 (x-2)/(x-1)/(x^2-4*x+1) ogf A001571 24.6043 -(-2*x+x^2)/(1-5*x+5*x^2-x^3) ogf A001571 14.8651 -(-9+20*x+2*x^3-11*x^2)/(-1+x)/(x-2)/(x^2-4*x+1) lgdogf A001571 9.51365 -22*x+11*x^2+(11+35*x+10*x^2-11*x^3)*f(x)+(-45+225*x-225*x^2+45*x^3)*f(x)^2 ogf A001571 13.4627 {-a(n+3)+5*a(n+2)-5*a(n+1)+a(n),a(0)=0,a(1)=2,a(2)=9} ogf A001576 15.5124 -(3-14*x+14*x^2)/(-14*x^2-1+7*x+8*x^3) ogf A001576 15.1147 -(3-14*x+14*x^2)/(x-1)/(2*x-1)/(-1+4*x) ogf A001576 7.96584 -(7-56*x+112*x^4-224*x^3+170*x^2)/(-1+x)/(-1+2*x)/(-1+4*x)/(14*x^2-14*x+3) lgdogf A001576 6.62328 1389-6482*x+6482*x^2+(-436+3115*x-6356*x^2+3704*x^3)*f(x)+(-9+63*x-126*x^2+72*x^3)*f(x)^2 ogf A001576 10.3416 {-a(n+3)+7*a(n+2)-14*a(n+1)+8*a(n),a(0)=3,a(1)=7,a(2)=21} ogf A001579 13.4808 -(3-28*x+63*x^2)/(-63*x^2-1+14*x+90*x^3) ogf A001579 13.4808 -(3-28*x+63*x^2)/(6*x-1)/(3*x-1)/(5*x-1) ogf A001579 6.91322 -2*(7-126*x+2835*x^4-2520*x^3+846*x^2)/(6*x-1)/(3*x-1)/(5*x-1)/(63*x^2-28*x+3) lgdogf A001579 6.19806 129-1204*x+2709*x^2+(-37+546*x-2583*x^2+3870*x^3)*f(x)+(-2+28*x-126*x^2+180*x^3)*f(x)^2 ogf A001579 8.98719 {-a(n+3)+14*a(n+2)-63*a(n+1)+90*a(n),a(0)=3,a(1)=14,a(2)=70} ogf A001580 12.0363 -(-1+2*x+3*x^3-2*x^2)/(9*x^2+1-5*x+2*x^4-7*x^3) ogf A001580 15.2894 -(-1+2*x-2*x^2+3*x^3)/(2*x-1)/(x-1)^3 ogf A001580 9.42844 -(3-8*x+6*x^4+4*x^3+x^2)/(-1+x)/(-1+2*x)/(3*x^3-2*x^2+2*x-1) lgdogf A001580 4.91919 -751+1502*x-1502*x^2+2253*x^3+(723-3699*x+6703*x^2-5173*x^3+1502*x^4)*f(x)+(28-140*x+252*x^2-196*x^3+56*x^4)*f(x)^2 ogf A001580 4.25343 {(-228-182*n-34*n^2)*a(n+1)+(362+339*n+69*n^2)*a(n+2)+(-228-222*n-44*n^2)*a(n+3)+(49*n+52+9*n^2)*a(n+4),a(0)=1,a(1)=3,a(2)=8,a(3)=17} ogf A001582 18.7794 -(1-x^2)/(-1+2*x+7*x^2+2*x^3-x^4) ogf A001582 17.2144 -(x-1)*(x+1)/(1-2*x-7*x^2-2*x^3+x^4) ogf A001582 8.48931 -1+x^2+(10-2*x-16*x^2-2*x^3+x^4)*f(x)+(63*x^2+18*x^3-9+18*x-9*x^4)*f(x)^2 ogf A001582 9.24955 -2*(1+6*x-x^4-2*x^3+x^5+4*x^2)/(-1+x)/(1+x)/(x^4-2*x^3-7*x^2-2*x+1) lgdogf A001584 22.1694 (x-1)*(x^2+x+1)^2/(x^4-x^3+1)/(x^4+x^3-1) ogf A001584 9.98839 -(-1-x+x^9-9*x^7+2*x^4+2*x^3+3*x^10-x^6+2*x^5-x^2)/(-1+x)/(x^2+x+1)/(x^4+x^3-1)/(x^4-x^3+1) lgdogf A001585 14.7751 (-1+3*x-7*x^2+15*x^3+2*x^4)/(3*x-1)/(x-1)^4 ogf A001585 10.0846 -(-1+3*x+15*x^3-7*x^2+2*x^4)/(18*x^2+1-7*x+13*x^4-22*x^3-3*x^5) ogf A001585 8.25103 -2*(2-5*x+54*x^4+2*x^3+3*x^5-8*x^2)/(-1+x)/(3*x-1)/(2*x^4+15*x^3-7*x^2+3*x-1) lgdogf A001588 29.5372 -(-1-x+3*x^2)/(1-2*x+x^3) ogf A001588 25.4631 -(-1-x+3*x^2)/(x-1)/(x-1+x^2) ogf A001588 13.426 -(3-6*x+3*x^4-2*x^3+3*x^2)/(-1+x)/(3*x^2-x-1)/(x^2+x-1) lgdogf A001588 12.5158 8+8*x-24*x^2+(-7+17*x-3*x^2-8*x^3)*f(x)+(-1+2*x-x^3)*f(x)^2 ogf A001588 17.1728 {a(n+3)-2*a(n+2)+a(n),a(0)=1,a(1)=3,a(2)=3} ogf A001589 7.59753 -(-1+4*x+43*x^3+5*x^5-17*x^2+38*x^4)/(30*x^2+1-9*x+45*x^4-50*x^3+4*x^6-21*x^5) ogf A001589 11.1813 -(-1+4*x-17*x^2+43*x^3+38*x^4+5*x^5)/(-1+4*x)/(x-1)^5 ogf A001589 6.10936 -(5-6*x+909*x^4-166*x^3+20*x^6+384*x^5-66*x^2)/(-1+x)/(-1+4*x)/(5*x^5+38*x^4+43*x^3-17*x^2+4*x-1) lgdogf A001590 41.1622 (x-1)/(x^2-1+x+x^3) ogf A001590 34.0036 -(x-x^2)/(-1+x+x^2+x^3) ogf A001590 21.7245 -2*x*(-1+x^2-x)/(-1+x)/(x^3+x^2+x-1) lgdogf A001590 31.2833 -x+x^2+(1-x-x^2-x^3)*f(x) ogf A001590 15.9609 {-a(n+3)+a(n+2)+a(n+1)+a(n),a(0)=0,a(1)=1,a(2)=0} ogf A001591 16.2934 -(1+2*x+5*x^4+4*x^3+3*x^2)/(x^2-1+x+x^4+x^3+x^5) lgdogf A001591 31.2833 -1/(-1+x+x^2+x^3+x^4+x^5) ogf A001591 25.2284 -x^4+(1-x-x^2-x^3-x^4-x^5)*f(x) ogf A001591 28.966 -x^4/(-1+x+x^2+x^3+x^4+x^5) ogf A001592 13.7699 -(1+2*x+5*x^4+4*x^3+6*x^5+3*x^2)/(x^2-1+x+x^4+x^3+x^6+x^5) lgdogf A001592 27.5399 -1/(-1+x+x^2+x^3+x^4+x^5+x^6) ogf A001592 25.7631 -x^5/(-1+x+x^2+x^3+x^4+x^5+x^6) ogf A001593 12.1296 (-1+5*x-36*x^2+84*x^3+289*x^4+135*x^5+4*x^6)/(5*x-1)/(x-1)^6 ogf A001593 7.58097 -(-1+5*x+84*x^3+135*x^5+4*x^6-36*x^2+289*x^4)/(45*x^2+1-11*x+115*x^4-95*x^3+31*x^6-81*x^5-5*x^7) ogf A001593 6.22029 -2*(3+6*x+10*x^7+2381*x^4-734*x^3+725*x^6+3438*x^5-69*x^2)/(-1+x)/(5*x-1)/(4*x^6+135*x^5+289*x^4+84*x^3-36*x^2+5*x-1) lgdogf A001594 7.59481 -(-1+6*x-72*x^2+75*x^3+1475*x^4+1776*x^5+334*x^6+7*x^7)/(6*x-1)/(x-1)^7 ogf A001594 4.64855 -(1-6*x-75*x^3-1776*x^5-7*x^7-334*x^6+72*x^2-1475*x^4)/(-63*x^2-1+13*x-6*x^8-245*x^4+161*x^3-133*x^6+231*x^5+43*x^7) ogf A001595 30.4103 (x^2-x+1)/(x-1)/(x-1+x^2) ogf A001595 33.0546 -(-1+x-x^2)/(1-2*x+x^3) ogf A001595 14.6203 -(-1-2*x+x^4-2*x^3+5*x^2)/(-1+x)/(x^2-x+1)/(x^2+x-1) lgdogf A001595 13.1079 -5+5*x-5*x^2+(2-7*x-3*x^2+5*x^3)*f(x)+(3+3*x^3-6*x)*f(x)^2 ogf A001595 17.6804 {a(n+3)-2*a(n+2)+a(n),a(0)=1,a(1)=1,a(2)=3} ogf A001596 6.31977 (-1+7*x-141*x^2-295*x^3+5851*x^4+15777*x^5+8189*x^6+847*x^7+6*x^8)/(7*x-1)/(x-1)^8 ogf A001596 5.95657 -1/7*(1-7*x+295*x^3-15777*x^5-6*x^8-847*x^7-8189*x^6+141*x^2-5851*x^4)/(x-1/7)/(-1+x)^8 ogf A001603 7.06739 -(-1-13*x^2-x^4)/(-x^5+1-11*x+33*x^2-33*x^3+11*x^4) ogf A001603 7.83558 -(1+13*x^2+x^4)/(x-1)/(x^2-7*x+1)/(-3*x+1+x^2) ogf A001604 5.02924 -(11-90*x+173*x^2-90*x^3+11*x^4)/(x-1)/(x^2-7*x+1)/(-3*x+1+x^2) ogf A001604 4.72898 -(11-90*x-90*x^3+173*x^2+11*x^4)/(-33*x^2-1+11*x-11*x^4+33*x^3+x^5) ogf A001607 36.4423 -(1+4*x)/(2*x^2+1+x) lgdogf A001607 38.3603 -x+(1+x+2*x^2)*f(x) ogf A001607 48.5897 -x/(-1-x-2*x^2) ogf A001607 56.065 1/(x+1+2*x^2) ogf A001607 19.6985 {-a(n+2)-a(n+1)-2*a(n),a(0)=0,a(1)=1} ogf A001608 35.9163 (-3+x^2)/(-1+x^3+x^2) ogf A001608 34.2837 -(-3+x^2)/(-x^3+1-x^2) ogf A001608 11.6037 -813+271*x^2+(478-340*x^2-271*x^3)*f(x)+(69*x^3-69+69*x^2)*f(x)^2 ogf A001608 21.5498 -x*(-4+x^3-9*x)/(x^3+x^2-1)/(x^2-3) lgdogf A001608 18.3961 {a(n+3)-a(n+1)-a(n),a(0)=3,a(1)=0,a(2)=2} ogf A001609 37.3767 -(-1-3*x^2)/(1-x-x^3) ogf A001609 37.3767 -(1+3*x^2)/(-1+x+x^3) ogf A001609 23.0856 -(1+6*x+3*x^4)/(3*x^2+1)/(x^3+x-1) lgdogf A001609 34.1266 -1-3*x^2+(1-x-x^3)*f(x) ogf A001609 19.1442 {a(n+3)-a(n+2)-a(n),a(0)=1,a(1)=1,a(2)=4} ogf A001610 31.7133 -(2*x-x^2)/(-1+2*x-x^3) ogf A001610 18.7027 -(3+2*x^3-6*x^2)/(x-2)/(-1+x)/(x^2+x-1) lgdogf A001610 33.1548 -(x-2)/(x-1)/(x-1+x^2) ogf A001610 11.0516 -78*x+39*x^2+(39-118*x+20*x^2+39*x^3)*f(x)+(20+20*x^3-40*x)*f(x)^2 ogf A001610 16.5774 {-a(n+3)+2*a(n+2)-a(n),a(0)=0,a(1)=2,a(2)=3} ogf A001611 30.2078 -(-1+2*x^2)/(1-2*x+x^3) ogf A001611 26.7223 -(2*x^2-1)/(x-1)/(x-1+x^2) ogf A001611 15.4395 -(2-4*x+2*x^4+x^2)/(-1+x)/(2*x^2-1)/(x^2+x-1) lgdogf A001611 27.7912 1-2*x^2+(-1+2*x-x^3)*f(x) ogf A001611 16.1577 {a(n+3)-2*a(n+2)+a(n),a(0)=1,a(1)=2,a(2)=2} ogf A001612 35.3366 -(-3+4*x)/(1-2*x+x^3) ogf A001612 18.0992 -(2+8*x^3-9*x^2)/(-1+x)/(4*x-3)/(x^2+x-1) lgdogf A001612 30.9195 -(4*x-3)/(x-1)/(x-1+x^2) ogf A001612 13.742 99-132*x+(-18+46*x-33*x^3)*f(x)+(-5+10*x-5*x^3)*f(x)^2 ogf A001612 16.8652 {-a(n+3)+2*a(n+2)-a(n),a(0)=3,a(1)=2,a(2)=4} ogf A001621 15.7318 -(-2*x-2*x^3-2*x^2)/(1-5*x+10*x^2-x^5-10*x^3+5*x^4) ogf A001621 40.116 -2*(x^2+x+1)/(x-1)^5 ogf A001621 25.8813 -3*(2+2*x+x^2)/(-1+x)/(x^2+x+1) lgdogf A001621 10.5568 {(-3-n)*a(n+4)+6*a(n+3)+6*a(n+2)+(n+3)*a(n+1),a(0)=0,a(1)=2,a(2)=12,a(3)=42} ogf A001628 56.4218 -1/(x-1+x^2)^3 ogf A001628 39.4952 -3*(1+2*x)/(x^2-1+x) lgdogf A001628 31.5962 1/(1-3*x+5*x^3-3*x^5-x^6) ogf A001628 12.5382 {(n+3)*a(n+3)+(-5-n)*a(n+2)+(-7-n)*a(n+1),a(0)=1,a(1)=3,a(2)=9} ogf A001629 40.5591 -2*(1+2*x)/(x^2-1+x) lgdogf A001629 30.0438 -x^2/(-1+2*x+x^2-2*x^3-x^4) ogf A001629 62.3987 1/(x-1+x^2)^2 ogf A001629 12.8759 x^2+(-1+2*x+2*x^2-2*x^3-x^4)*f(x)+(-1+2*x+x^2-2*x^3-x^4)*f(x)^2 ogf A001629 13.0836 {(-1-n)*a(n+3)+(n+2)*a(n+2)+(n+3)*a(n+1),a(0)=0,a(1)=0,a(2)=1} ogf A001630 19.0822 (x^2+x^3)*f(x)+(-1+x+x^2+x^3+x^4)*f(x)^2 ogf A001630 26.3203 -(-x^3-x^2)/(1-x-x^2-x^3-x^4) ogf A001630 15.2658 -(2+2*x+3*x^4+6*x^3+4*x^2)/(1+x)/(x^4+x^3+x^2+x-1) lgdogf A001630 31.8037 -(x+1)/(x^2-1+x+x^3+x^4) ogf A001631 34.478 (x-1)/(x^2-1+x+x^3+x^4) ogf A001631 26.4332 -(-x^3+x^2)/(-1+x+x^2+x^3+x^4) ogf A001631 16.5207 -x*(-2+3*x^3-2*x^2-2*x)/(-1+x)/(x^4+x^3+x^2+x-1) lgdogf A001631 11.4927 5*x^2-5*x^3+(-5+5*x+6*x^2+4*x^3+5*x^4)*f(x)+(-1+x+x^2+x^3+x^4)*f(x)^2 ogf A001633 29.1838 -(-1-90*x^9+90*x^10)/(x-1)^2 ogf A001633 24.762 -(x+90*x^10-90*x^11)/(-1+2*x-x^2) ogf A001633 14.5919 2*(1-765*x^9+360*x^10+405*x^8)/(-1+x)/(90*x^10-90*x^9-1) lgdogf A001633 7.10562 {-a(n+3)+2*a(n+2)-a(n+1),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=5,a(6)=6,a(7)=7,a(8)=8,a(9)=9,a(10)=100,a(11)=101} ogf A001634 22.426 -(2*x+4*x^3+3*x^2)/(-1+x^2+x^3+x^4) ogf A001634 25.3197 -(2+3*x+4*x^2)/(x+1)/(-1+x+x^3) ogf A001634 12.0755 -(3+12*x+13*x^4+14*x^3+8*x^5+9*x^2)/(1+x)/(4*x^2+3*x+2)/(x^3+x-1) lgdogf A001634 6.27929 39176*x+58764*x^2+78352*x^3+(-19588+20646*x+50557*x^2+60880*x^3+19588*x^4)*f(x)+(-10323+10323*x^2+10323*x^3+10323*x^4)*f(x)^2 ogf A001635 17.4607 -(2*x+4*x^3+3*x^2+5*x^4)/(-1+x^2+x^3+x^4+x^5) ogf A001635 19.6433 -(2+3*x+4*x^2+5*x^3)/(x^5-1+x^2+x^3+x^4) ogf A001635 8.63441 -(3+12*x+10*x^7+18*x^4+14*x^3+17*x^6+20*x^5+24*x^2)/(x^5+x^4+x^3+x^2-1)/(5*x^3+4*x^2+3*x+2) lgdogf A001636 14.0547 -(2*x+4*x^3+3*x^2+6*x^5+5*x^4)/(-1+x^2+x^3+x^4+x^5+x^6) ogf A001636 16.8046 -(2+3*x+4*x^2+5*x^3+6*x^4)/(x+1)/(x^5+x^3+x-1) ogf A001636 6.96406 -(3+12*x+12*x^9+26*x^7+18*x^4+38*x^3+21*x^8+26*x^6+20*x^5+24*x^2)/(1+x)/(6*x^4+5*x^3+4*x^2+3*x+2)/(x^5+x^3+x-1) lgdogf A001637 16.5997 -(10+21*x-27*x^2+99000*x^87+900*x^88)/(5*x^2-1-x-9900*x^87+10800*x^88-3*x^3) ogf A001637 10.3408 -(9900+30521*x-31599*x^2+81000000*x^87+5890500000*x^86)/(58609*x^2-9000-18010*x-5355000000*x^86+5719500000*x^87-31599*x^3) lgdogf A001638 23.6466 (x-1)*(x^2+x+4)/(1+x^2)/(x-1+x^2) ogf A001638 12.3863 -(-1+9*x^4-12*x^3+x^6-9*x^2)/(-1+x)/(1+x^2)/(x^2+x+4)/(x^2-1+x) lgdogf A001638 27.8692 -(-4+3*x+x^3)/(-x^3+1-x-x^4) ogf A001638 10.1343 -148+111*x+37*x^3+(81-70*x-48*x^3-37*x^4)*f(x)+(11*x^3-11+11*x+11*x^4)*f(x)^2 ogf A001639 18.3985 -(-1-4*x^3-3*x^2-5*x^4)/(-x^3+1-x-x^5-x^4) ogf A001639 19.3184 -(1+3*x^2+4*x^3+5*x^4)/(x^3-1+x+x^5+x^4) ogf A001639 8.39931 -(1+6*x+8*x^7-7*x^4+16*x^3+5*x^8+8*x^6+6*x^5+12*x^2)/(5*x^4+4*x^3+3*x^2+1)/(x^5+x^4+x^3+x-1) lgdogf A001640 15.2075 -(-1-4*x^3-3*x^2-6*x^5-5*x^4)/(-x^3+1-x-x^5-x^4-x^6) ogf A001640 15.8158 -(1+3*x^2+4*x^3+5*x^4+6*x^5)/(x^3-1+x+x^5+x^4+x^6) ogf A001640 6.64531 -(1+6*x+10*x^9+8*x^7+23*x^4+16*x^3+6*x^10+11*x^8+8*x^6-12*x^5+12*x^2)/(6*x^5+5*x^4+4*x^3+3*x^2+1)/(x^6+x^5+x^4+x^3+x-1) lgdogf A001641 21.5011 -(1+2*x+4*x^3)/(x+1)/(x^3-x^2+2*x-1) ogf A001641 27.6443 -(1+2*x+4*x^3)/(x^2-1+x+x^4) ogf A001641 11.218 -(3+2*x+2*x^4-4*x^3+4*x^6+14*x^2)/(1+x)/(4*x^3+2*x+1)/(x^3-x^2+2*x-1) lgdogf A001641 6.67276 77216+154432*x+308864*x^3+(-82391+66866*x+77216*x^2-20700*x^3+77216*x^4)*f(x)+(5175-5175*x^4-5175*x-5175*x^2)*f(x)^2 ogf A001642 19.11 -(-1-2*x-4*x^3-5*x^4)/(-x^2+1-x-x^5-x^4) ogf A001642 8.3087 -(3+2*x+8*x^7-8*x^4+16*x^3+5*x^8+4*x^6-2*x^5+14*x^2)/(1+x)/(5*x^3-x^2+x+1)/(x^5+x^4+x^2+x-1) lgdogf A001642 19.11 -(x+1)*(5*x^3-x^2+x+1)/(x^2-1+x+x^5+x^4) ogf A001643 15.5013 -(-1-2*x-4*x^3-6*x^5-5*x^4)/(-x^2+1-x-x^5-x^4-x^6) ogf A001643 13.8405 -(1+2*x+4*x^3+5*x^4+6*x^5)/(x+1)/(x^2-x+1)/(x^2-1+x+x^3) ogf A001643 6.20053 -(3+2*x+10*x^9+8*x^7+22*x^4+16*x^3+6*x^10+11*x^8-4*x^6-20*x^5+14*x^2)/(1+x)/(x^2-x+1)/(x^3+x^2+x-1)/(6*x^5+5*x^4+4*x^3+2*x+1) lgdogf A001644 31.535 (x+3)*(x-1)/(x^2-1+x+x^3) ogf A001644 15.161 -(-1-4*x+x^4+4*x^3-8*x^2)/(-1+x)/(x+3)/(x^3+x^2+x-1) lgdogf A001644 28.1562 -(-3+2*x+x^2)/(-x^2+1-x-x^3) ogf A001644 10.5117 -93+62*x+31*x^2+(64-53*x-42*x^2-31*x^3)*f(x)+(11*x^2-11+11*x+11*x^3)*f(x)^2 ogf A001644 16.4245 {a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=3,a(1)=1,a(2)=3} ogf A001645 18.9542 -(-1-2*x-3*x^2-5*x^4)/(-x^2+1-x-x^5-x^3) ogf A001645 19.9518 -(1+2*x+3*x^2+5*x^4)/(x^2-1+x+x^5+x^3) ogf A001645 9.13455 -(3+8*x-7*x^4+24*x^3+5*x^8+4*x^6-2*x^5+2*x^2)/(x^5+x^3+x^2+x-1)/(5*x^4+3*x^2+2*x+1) lgdogf A001648 19.2187 -(-1-2*x-4*x^3-3*x^2)/(-x^2+1-x-x^4-x^3) ogf A001648 20.2302 -(1+2*x+3*x^2+4*x^3)/(x^2-1+x+x^3+x^4) ogf A001648 10.8274 -(3+8*x+5*x^4+4*x^6+6*x^5+14*x^2)/(4*x^3+3*x^2+2*x+1)/(x^4+x^3+x^2+x-1) lgdogf A001649 15.657 -(-1-2*x-4*x^3-3*x^2-6*x^5)/(-x^2+1-x-x^4-x^3-x^6) ogf A001649 13.4974 -(1+2*x+3*x^2+4*x^3+6*x^5)/(x+1)/(x^5-x^4+2*x^3-x^2+2*x-1) ogf A001649 7.3854 -(3+8*x+35*x^4+6*x^10+6*x^8-4*x^6-12*x^5+14*x^2)/(1+x)/(x^5-x^4+2*x^3-x^2+2*x-1)/(6*x^5+4*x^3+3*x^2+2*x+1) lgdogf A001650 30.7062 -(3+2*x^2+x^3)/(-1-x-x^2-x^3) ogf_with_Euler_Transform A001650 30.7062 -(3+x^3+2*x^2)/(-1-x-x^2-x^3) ogf_with_Euler_Transform A001650 14.8414 {-a(n+4)-a(n+3)-a(n+2)-a(n+1),a(0)=3,a(1)=-3,a(2)=2,a(3)=-1} ogf_with_Euler_Transform A001651 38.2365 (x^2+x+1)/(x+1)/(x-1)^2 ogf A001651 33.8246 -(-1-x-x^2)/(-x^2+1-x+x^3) ogf A001651 21.4497 -(2+6*x+x^3+3*x^2)/(-1+x)/(1+x)/(x^2+x+1) lgdogf A001651 12.3865 -43-43*x-43*x^2+(38-48*x-48*x^2+43*x^3)*f(x)+(5-5*x-5*x^2+5*x^3)*f(x)^2 ogf A001651 109.93 -x^2+x+2 ogf_with_Euler_Transform A001651 29.3147 {a(n+3),a(0)=2,a(1)=1,a(2)=-1} ogf_with_Euler_Transform A001651 18.3217 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=1,a(1)=2,a(2)=4} ogf A001652 14.3092 (-3*x+x^2)*f(x)+(1-7*x+7*x^2-x^3)*f(x)^2 ogf A001652 24.8856 (x-3)/(x-1)/(1-6*x+x^2) ogf A001652 19.7369 -(-3*x+x^2)/(1-7*x+7*x^2-x^3) ogf A001652 11.9244 -2*(-10+21*x+x^3-8*x^2)/(-1+x)/(x-3)/(1-6*x+x^2) lgdogf A001652 10.5994 {-a(n+3)+7*a(n+2)-7*a(n+1)+a(n),a(0)=0,a(1)=3,a(2)=20} ogf A001653 37.2958 -(-1+x)/(x^2+1-6*x) ogf A001653 22.8587 -(5-2*x+x^2)/(-1+x)/(1-6*x+x^2) lgdogf A001653 39.3678 -(x-1)/(1-6*x+x^2) ogf A001653 17.7155 -1/2*(-6*x-1+(32*x^2+8*x+1)^(1/2))/(x+1) revogf A001653 13.3702 -3+3*x+(31-46*x+3*x^2)*f(x)+(-28+168*x-28*x^2)*f(x)^2 ogf A001653 19.6839 {a(n+2)-6*a(n+1)+a(n),a(0)=1,a(1)=5} ogf A001654 20.4079 -(-2-4*x+3*x^2)/(1+x)/(x^2-3*x+1) lgdogf A001654 32.0695 -x/(-1+2*x+2*x^2-x^3) ogf A001654 33.673 1/(x+1)/(-3*x+1+x^2) ogf A001654 12.9512 x+(-1+4*x+2*x^2-x^3)*f(x)+(4*x^2-2+4*x-2*x^3)*f(x)^2 ogf A001654 12.7068 {-a(n+3)+2*a(n+2)+2*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=2} ogf A001655 16.3139 -(-3-12*x+4*x^3+9*x^2)/(x^2+4*x-1)/(x^2-x-1) lgdogf A001655 28.7124 1/(1-3*x-6*x^2+3*x^3+x^4) ogf A001655 31.2091 1/(x^2+4*x-1)/(x^2-x-1) ogf A001655 9.08621 2+(185+6*x+12*x^2-6*x^3-2*x^4)*f(x)+(1122*x^2-561*x^3-187+561*x-187*x^4)*f(x)^2 ogf A001656 17.4127 -1/(x-1)/(x^2+3*x+1)/(x^2-7*x+1) ogf A001656 9.77554 -5*(1+6*x+x^4-4*x^3-9*x^2)/(-1+x)/(x^2+3*x+1)/(x^2-7*x+1) lgdogf A001656 16.885 1/(1-5*x-15*x^2+15*x^3+5*x^4-x^5) ogf A001657 18.4602 -1/(x-1+x^2)/(x^2+11*x-1)/(x^2-4*x-1) ogf A001657 9.35653 -2*(4+40*x+20*x^4-80*x^3+3*x^5-90*x^2)/(x^2+x-1)/(x^2-1+11*x)/(x^2-4*x-1) lgdogf A001657 17.0757 1/(1-8*x-40*x^2+60*x^3+40*x^4-8*x^5-x^6) ogf A001658 7.59855 -(-13-208*x-520*x^4+1040*x^3+7*x^6-78*x^5+780*x^2)/(1+x)/(x^2+7*x+1)/(x^2-3*x+1)/(x^2-18*x+1) lgdogf A001658 12.8485 -1/(-1+13*x+104*x^2-260*x^3-260*x^4+104*x^5+13*x^6-x^7) ogf A001658 15.7037 1/(x+1)/(1+7*x+x^2)/(-3*x+1+x^2)/(x^2-18*x+1) ogf A001670 17.6693 {a(n+3)+a(n+1),a(0)=1,a(1)=1,a(2)=0} ogf_with_Euler_Transform A001676 24.53 -1+(3-3*x)*f(x)+(-3+6*x-3*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 ogf A001680 28.4457 (-2-2*x-x^2)*f(x)+2*f(x)^2 lgdegf A001680 67.2353 1+x+1/2*x^2 lgdegf A001680 33.6177 exp(1/6*x*(x^2+3*x+6)) egf A001680 9.13072 {(n^2+5*n+6)*a(n+1)+(2*n+6)*a(n+2)-2*a(n+4)+2*a(n+3),a(0)=1,a(1)=1,a(2)=2,a(3)=5} ogf A001681 13.1792 -6-6*x-x^3-3*x^2+(-6-6*x^2-12*x-2*x^3)*f(x)+12*f(x)^2 lgdegf A001681 36.763 1+x+1/2*x^2+1/6*x^3 lgdegf A001681 22.5322 exp(1/24*x*(24+12*x+4*x^2+x^3)) egf A001681 17.4624 {a(n+4),a(0)=1,a(1)=1,a(2)=1/2,a(3)=1/6} lgdegf A001682 8.89559 (21+21*x+23*x^2+21*x^3+23*x^4+21*x^5+21*x^6+2*x^7)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A001682 10.6747 -(21*x+21*x^6+21*x^7+23*x^3+21*x^2+23*x^5+2*x^8+21*x^4)/(-1+x-x^8+x^7) ogf A001687 53.9397 -1/(-1+x^2+x^5) ogf A001687 32.3638 -x*(2+5*x^3)/(-1+x^2+x^5) lgdogf A001687 53.9397 -x/(-1+x^2+x^5) ogf A001687 10.7879 x+(-1+6*x+x^2+x^5)*f(x)+(-6+2*x+6*x^2+6*x^5)*f(x)^2+(-2+2*x^2+2*x^5)*f(x)^3 ogf A001700 18.4905 1+(-1+4*x)*f(x)+(-x+4*x^2)*f(x)^2 ogf A001700 17.4339 2/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2)) ogf A001700 18.4905 2/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) ogf A001700 35.8933 x*(x+1)/(2*x+1)^2 revogf A001700 13.5597 {(-4*n-10)*a(n+1)+(n+3)*a(n+2),a(0)=1,a(1)=3} ogf A001701 21.8796 (-1-x-6*x^2+9*x^3-5*x^4+x^5)/(x-1)^5 ogf A001701 14.3212 (6+16*x+2*x^3-9*x^2)/(-1+x)/(x^5-5*x^4+9*x^3-6*x^2-x-1) lgdogf A001701 12.9125 -(-1-x+9*x^3-6*x^2+x^5-5*x^4)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A001702 14.0555 (-1-17*x-7*x^2+29*x^3-34*x^4+21*x^5-7*x^6+x^7)/(x-1)^7 ogf A001702 8.92938 -(-24-116*x+3*x^4-20*x^3+52*x^2)/(-1+x)/(x^7-7*x^6+21*x^5-34*x^4+29*x^3-7*x^2-17*x-1) lgdogf A001703 15.3483 -(123-12*x+8010*x^7-72000*x^9+73980*x^8)/(-x^2-1+2*x) ogf A001703 16.6012 -3*(-41+4*x-2670*x^7-24660*x^8+24000*x^9)/(x-1)^2 ogf A001703 8.56273 2*(39-2*x+84000*x^9+91965*x^7-181980*x^8+9345*x^6)/(-1+x)/(24000*x^9-24660*x^8-2670*x^7+4*x-41) lgdogf A001704 12.3122 (23-x+5040*x^9+6480*x^7-11340*x^8)/(-1+x)/(720*x^9-810*x^8+x-12) lgdogf A001704 21.8883 -(-12+x+720*x^9-810*x^8)/(x^2+1-2*x) ogf A001704 24.6243 -(-12+x-810*x^8+720*x^9)/(x-1)^2 ogf A001705 11.3499 {(n^2+6*n+9)*a(n+1)+(-2*n-7)*a(n+2)+a(n+3),a(0)=0,a(1)=1,a(2)=5} ogf A001706 4.30399 {(-125-75*n-15*n^2-n^3)*a(n+1)+(157*n+182+39*n^2+3*n^3)*a(n+2)+(-108*n-108-33*n^2-3*n^3)*a(n+3)+(26*n+24+9*n^2+n^3)*a(n+4),a(0)=1,a(1)=9,a(2)=71/2,a(3)=290/3} egf A001710 21.5458 (2-2*x+x^2)/(-1+x)/(x^2-2) lgdegf A001710 32.9525 -(2-x^2)/(-2+2*x) egf A001710 31.1218 1/2*(-2+x^2)/(x-1) egf A001710 29.4838 2-x^2+(-2+2*x)*f(x) egf A001710 6.22435 {(-n^2-2*n)*a(n+1)+a(n+2)*n+(16+8*n+n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=3} ogf A001710 6.22435 {(-n^2-2*n)*a(n+1)+a(n+2)*n+(n^2+8*n+16)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=3} ogf A001711 9.82423 {(-10*n-n^2-25)*a(n+1)+(11+2*n)*a(n+2)-a(n+3),a(0)=1,a(1)=7,a(2)=47} ogf A001715 22.1679 (-1+(1+3*x)^(1/3))/(1+3*x)^(1/3) revegf A001715 26.2731 -1/(-1+4*x-6*x^2+4*x^3-x^4) egf A001715 78.8192 -4/(-1+x) lgdegf A001715 11.8229 1+(4*x-6*x^2+4*x^3-x^4)*f(x)+(-1-x^4+4*x-6*x^2+4*x^3)*f(x)^2 egf A001715 78.8192 1/(x-1)^4 egf A001715 19.7048 {(-n-5)*a(n+1)+a(n+2),a(0)=1,a(1)=4} ogf A001716 10.1767 {(-12*n-n^2-36)*a(n+1)+(13+2*n)*a(n+2)-a(n+3),a(0)=1,a(1)=9,a(2)=74} ogf A001717 4.2037 {(-343-147*n-21*n^2-n^3)*a(n+1)+(259*n+338+51*n^2+3*n^3)*a(n+2)+(-138*n-144-39*n^2-3*n^3)*a(n+3)+(26*n+24+9*n^2+n^3)*a(n+4),a(0)=1,a(1)=15,a(2)=179/2,a(3)=345} egf A001720 16.0777 (-1+(1+4*x)^(1/4))/(1+4*x)^(1/4) revegf A001720 14.6996 -1/(-1+5*x-10*x^2+10*x^3-5*x^4+x^5) egf A001720 51.4486 -1/(x-1)^5 egf A001720 57.1651 -5/(-1+x) lgdegf A001720 14.2913 {(-n-6)*a(n+1)+a(n+2),a(0)=1,a(1)=5} ogf A001721 9.29602 {(-14*n-n^2-49)*a(n+1)+(15+2*n)*a(n+2)-a(n+3),a(0)=1,a(1)=11,a(2)=107} ogf A001725 10.6629 (-1+(1+5*x)^(1/5))/(1+5*x)^(1/5) revegf A001725 8.12415 -1/(-1+6*x-15*x^2+20*x^3-15*x^4+6*x^5-x^6) egf A001725 37.9127 -6/(-1+x) lgdegf A001725 37.9127 1/(x-1)^6 egf A001725 9.47818 {(-n-7)*a(n+1)+a(n+2),a(0)=1,a(1)=6} ogf A001730 16.9809 (-1+(1+6*x)^(1/6))/(1+6*x)^(1/6) revegf A001730 54.339 -1/(x-1)^7 egf A001730 60.3766 -7/(-1+x) lgdegf A001730 11.5615 1/(1-7*x+21*x^2-35*x^3+35*x^4-21*x^5+7*x^6-x^7) egf A001730 15.0942 {(-n-8)*a(n+1)+a(n+2),a(0)=1,a(1)=7} ogf A001735 1.7425 25+(-10+10*x)*f(x)+(x^2+1-2*x)*f(x)^2 ogf A001736 1.7105 16+(-8+8*x)*f(x)+(x^2+1-2*x)*f(x)^2 ogf A001752 21.7979 -1/(-1+4*x-5*x^2+5*x^4-4*x^5+x^6) ogf A001752 44.9582 -1/(x+1)/(x-1)^5 ogf A001752 31.2753 -2*(2+3*x)/(-1+x)/(1+x) lgdogf A001752 239.777 4+x ogf_with_Euler_Transform A001752 12.1921 {(n+3)*a(n+3)-4*a(n+2)+(-7-n)*a(n+1),a(0)=1,a(1)=4,a(2)=11} ogf A001752 32.6969 {a(n+2),a(0)=4,a(1)=1} ogf_with_Euler_Transform A001753 28.4716 -(7*x+5)/(-1+x)/(1+x) lgdogf A001753 13.9047 1/(1-5*x+9*x^2-5*x^3-5*x^4+9*x^5-5*x^6+x^7) ogf A001753 39.8602 1/(x+1)/(x-1)^6 ogf A001753 199.301 x+5 ogf_with_Euler_Transform A001753 10.134 {(n+3)*a(n+3)-5*a(n+2)+(-8-n)*a(n+1),a(0)=1,a(1)=5,a(2)=16} ogf A001753 27.1774 {a(n+2),a(0)=5,a(1)=1} ogf_with_Euler_Transform A001754 32.6199 (1+6*x+3*x^2)/(x-1)^6 egf A001754 76.113 -4/(-1+x) lgdegf A001754 21.4068 -x^2/(-2+8*x-12*x^2+8*x^3-2*x^4) egf A001754 19.0282 x^2+(-2+8*x-12*x^2+8*x^3-2*x^4)*f(x) egf A001754 13.4317 {(-6-5*n-n^2)*a(n+1)+a(n+2)*n,a(0)=0,a(1)=0,a(2)=1} ogf A001755 24.0632 (1+12*x+18*x^2+4*x^3)/(x-1)^8 egf A001755 9.182 -(1+12*x+4*x^3+18*x^2)/(-28*x^2-1+8*x+8*x^7-70*x^4+56*x^5+56*x^3-x^8-28*x^6) egf A001755 13.9566 -20*(1+x)*(x^2+5*x+1)/(-1+x)/(4*x^3+18*x^2+12*x+1) lgdegf A001755 13.683 {(-30-11*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=20} ogf A001761 35.2264 -1+f(x)-x*f(x)^2 egf A001761 28.1811 2/(1+(-4*x+1)^(1/2)) egf A001761 29.6643 2/(1+(1-4*x)^(1/2)) egf A001761 17.0795 2/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdegf A001761 10.8389 {(4*n^2+14*n+12)*a(n+1)+(-n-3)*a(n+2),a(0)=1,a(1)=1} ogf A001762 4.72945 {(-144*n-684*n^2-810*n^3-162*n^4)*a(n)+(600+1302*n+981*n^2+294*n^3+27*n^4)*a(n+1)+(-74*n-60-30*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=1} ogf A001763 41.0071 -1+f(x)-x*f(x)^3 egf A001763 18.7461 1/27+2/3*x-1/27*(-(-1+6*x)^3)^(1/2) revegf A001763 19.8822 hypergeom([1/3,2/3],[3/2],27/4*x) egf A001763 11.7163 {(27*n^2+81*n+60)*a(n+1)+(-4*n-10)*a(n+2),a(0)=1,a(1)=1} ogf A001764 47.4785 -1+f(x)-x*f(x)^3 ogf A001764 33.0285 1/2*(1+(1-4*x)^(1/2))*x revogf A001764 23.0199 hypergeom([1/3,2/3],[3/2],27/4*x) ogf A001764 12.058 {(-60-81*n-27*n^2)*a(n+1)+(18*n+20+4*n^2)*a(n+2),a(0)=1,a(1)=1} ogf A001769 12.1241 -1/(-1+6*x-14*x^2+14*x^3-14*x^5+14*x^6-6*x^7+x^8) ogf A001769 37.13 -1/(x+1)/(x-1)^7 ogf A001769 25.8296 -2*(4*x+3)/(-1+x)/(1+x) lgdogf A001769 198.027 6+x ogf_with_Euler_Transform A001769 10.0692 {(n+3)*a(n+3)-6*a(n+2)+(-9-n)*a(n+1),a(0)=1,a(1)=6,a(2)=22} ogf A001769 27.0036 {a(n+2),a(0)=6,a(1)=1} ogf_with_Euler_Transform A001777 7.43702 (5*x^4+40*x^3+60*x^2+20*x+1)/(-1+x)/(x^2-2*x+1)/(x^3-3*x^2+3*x-1)/(x^4-4*x^3+6*x^2-4*x+1) egf A001777 17.889 (5*x^4+40*x^3+60*x^2+20*x+1)/(x-1)^10 egf A001777 10.0287 -30*(1+10*x+x^4+10*x^3+20*x^2)/(-1+x)/(5*x^4+40*x^3+60*x^2+20*x+1) lgdegf A001777 12.9783 {(-42-13*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=30} ogf A001778 13.3654 (6*x^5+75*x^4+200*x^3+150*x^2+30*x+1)/(x-1)^12 egf A001778 5.5388 (6*x^5+75*x^4+200*x^3+150*x^2+30*x+1)/(x^5-5*x^4+10*x^3-10*x^2+5*x-1)/(x^4-4*x^3+6*x^2-4*x+1)/(x^3-3*x^2+3*x-1) egf A001778 7.5902 -42*(1+x)*(x^4+14*x^3+36*x^2+14*x+1)/(-1+x)/(6*x^5+75*x^4+200*x^3+150*x^2+30*x+1) lgdegf A001778 12.055 {(-56-15*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=42} ogf A001779 25.8642 -(7+9*x)/(-1+x)/(1+x) lgdogf A001779 8.62141 -1/(-1+7*x-20*x^2+28*x^3-14*x^4-14*x^5+28*x^6-20*x^7+7*x^8-x^9) ogf A001779 36.2099 1/(x+1)/(x-1)^8 ogf A001779 181.05 x+7 ogf_with_Euler_Transform A001779 9.05248 {(n+3)*a(n+3)-7*a(n+2)+(-10-n)*a(n+1),a(0)=1,a(1)=7,a(2)=29} ogf A001779 24.6886 {a(n+2),a(0)=7,a(1)=1} ogf_with_Euler_Transform A001780 9.00735 -1/(-1+8*x-27*x^2+48*x^3-42*x^4+42*x^6-48*x^7+27*x^8-8*x^9+x^10) ogf A001780 36.0294 -1/(x+1)/(x-1)^9 ogf A001780 25.0639 -2*(5*x+4)/(-1+x)/(1+x) lgdogf A001780 192.157 8+x ogf_with_Euler_Transform A001780 9.60784 {(n+3)*a(n+3)-8*a(n+2)+(-11-n)*a(n+1),a(0)=1,a(1)=8,a(2)=37} ogf A001780 26.2032 {a(n+2),a(0)=8,a(1)=1} ogf_with_Euler_Transform A001781 26.2169 -(9+11*x)/(-1+x)/(1+x) lgdogf A001781 7.49055 1/(1-9*x+35*x^2-75*x^3+90*x^4-42*x^5-42*x^6+90*x^7-75*x^8+35*x^9-9*x^10+x^11) ogf A001781 36.0483 1/(x+1)/(x-1)^10 ogf A001781 192.257 9+x ogf_with_Euler_Transform A001781 9.61287 {(n+3)*a(n+3)-9*a(n+2)+(-12-n)*a(n+1),a(0)=1,a(1)=9,a(2)=46} ogf A001781 26.2169 {a(n+2),a(0)=9,a(1)=1} ogf_with_Euler_Transform A001786 31.2421 -1/(x+1)/(x-1)^11 ogf A001786 23.092 -2*(5+6*x)/(-1+x)/(1+x) lgdogf A001786 6.17576 1/(1-10*x+44*x^2-110*x^3+165*x^4-132*x^5+132*x^7-165*x^8+110*x^9-44*x^10+10*x^11-x^12) ogf A001786 132.779 10+x ogf_with_Euler_Transform A001786 8.56637 {(n+3)*a(n+3)-10*a(n+2)+(-13-n)*a(n+1),a(0)=1,a(1)=10,a(2)=56} ogf A001786 23.092 {a(n+2),a(0)=10,a(1)=1} ogf_with_Euler_Transform A001787 61.5308 -4/(-1+2*x) lgdogf A001787 61.5308 1/(2*x-1)^2 ogf A001787 29.4278 4*x/(1+(1+8*x)^(1/2))^2 revogf A001787 32.2304 x+(-1+4*x-4*x^2)*f(x) ogf A001787 45.1226 x/(1-4*x+4*x^2) ogf A001787 17.8115 {a(n+2)-4*a(n+1)+4*a(n),a(0)=0,a(1)=1} ogf A001788 51.0855 -1/(2*x-1)^3 ogf A001788 55.7297 -6/(-1+2*x) lgdogf A001788 21.8938 x+(-1+6*x-12*x^2+8*x^3)*f(x) ogf A001788 27.8648 x/(1-6*x+12*x^2-8*x^3) ogf A001788 11.1459 {a(n+3)-6*a(n+2)+12*a(n+1)-8*a(n),a(0)=0,a(1)=1,a(2)=6} ogf A001789 20.3631 -1/(-1+8*x-24*x^2+32*x^3-16*x^4) ogf A001789 59.2382 -8/(-1+2*x) lgdogf A001789 9.30886 1+(8*x-24*x^2+32*x^3-16*x^4)*f(x)+(-1-16*x^4+8*x-24*x^2+32*x^3)*f(x)^2 ogf A001789 59.2382 1/(2*x-1)^4 ogf A001789 14.4804 {(-n-2)*a(n+2)+(10+2*n)*a(n+1),a(0)=1,a(1)=8} ogf A001791 19.9168 -x+(1-4*x)*f(x)+(x-4*x^2)*f(x)^2 ogf A001791 11.1814 1/8*((1+6*x+x^2)^(1/2)*x+(1+6*x+x^2)^(1/2)-1-4*x+x^2)/x^2 revogf A001791 17.2254 4*x/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^2 ogf A001791 17.2254 4/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^2 ogf A001791 10.9886 {(-12-14*n-4*n^2)*a(n+1)+(3+n^2+4*n)*a(n+2),a(0)=0,a(1)=1} ogf A001792 37.1329 -(1-x)/(-4*x^2-1+4*x) ogf A001792 32.4913 -(2*x-3)/(-1+2*x)/(-1+x) lgdogf A001792 48.737 -(x-1)/(2*x-1)^2 ogf A001792 15.5958 -5+5*x+(1-16*x+20*x^2)*f(x)+(4-16*x+16*x^2)*f(x)^2 ogf A001792 22.2798 2*x/(1+4*x)^(1/2)/(1+(1+4*x)^(1/2)) revogf A001792 19.9947 {-a(n+2)+4*a(n+1)-4*a(n),a(0)=1,a(1)=3} ogf A001793 44.8736 (x-1)/(2*x-1)^3 ogf A001793 26.9242 -(-5+4*x)/(-1+2*x)/(-1+x) lgdogf A001793 24.9298 -(x-1)/(12*x^2+1-6*x-8*x^3) ogf A001793 8.97473 -30+30*x+(49-199*x+360*x^2-240*x^3)*f(x)+(-228*x^2-19+114*x+152*x^3)*f(x)^2 ogf A001793 12.0197 {a(n+3)-6*a(n+2)+12*a(n+1)-8*a(n),a(0)=1,a(1)=5,a(2)=18} ogf A001794 25.4132 -(-7+6*x)/(-1+2*x)/(-1+x) lgdogf A001794 17.648 -(1-x)/(-1+8*x-24*x^2+32*x^3-16*x^4) ogf A001794 39.7081 -(x-1)/(2*x-1)^4 ogf A001794 6.54979 -121+121*x+(60-907*x+2904*x^2-3872*x^3+1936*x^4)*f(x)+(61-1952*x^3-488*x+1464*x^2+976*x^4)*f(x)^2 ogf A001794 9.34308 {(n+3)*a(n+3)+(-13-3*n)*a(n+2)+(8+2*n)*a(n+1),a(0)=1,a(1)=7,a(2)=32} ogf A001804 13.5319 -(-2-8*x-2*x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) egf A001804 28.909 -2*(x^2+4*x+1)/(x-1)^5 egf A001804 19.2727 -3*(3+6*x+x^2)/(-1+x)/(x^2+4*x+1) lgdegf A001804 12.72 {(-16-8*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=2,a(1)=18} ogf A001805 9.21567 -(-6-54*x-54*x^2-6*x^3)/(21*x^2+1-7*x-x^7+35*x^4-21*x^5-35*x^3+7*x^6) egf A001805 13.5294 -4*(4+18*x+x^3+12*x^2)/(-1+x)/(1+x)/(x^2+8*x+1) lgdegf A001805 22.71 -6*(x+1)*(x^2+8*x+1)/(x-1)^7 egf A001805 12.4683 {(-25-10*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=6,a(1)=96} ogf A001806 7.36635 -24*(x^4+16*x^3+36*x^2+16*x+1)/(6*x^2-4*x+1-4*x^3+x^4)/(x^2-2*x+1)/(-3*x^2+3*x-1+x^3) egf A001806 16.4774 -24*(x^4+16*x^3+36*x^2+16*x+1)/(x-1)^9 egf A001806 9.93872 -5*(5+40*x+x^4+20*x^3+60*x^2)/(-1+x)/(x^4+16*x^3+36*x^2+16*x+1) lgdegf A001806 11.814 {(-36-12*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=24,a(1)=600} ogf A001807 13.2602 -120*(x+1)*(x^4+24*x^3+76*x^2+24*x+1)/(x-1)^11 egf A001807 5.59605 -120*(x^5+25*x^4+100*x^3+100*x^2+25*x+1)/(-5*x^4+10*x^3-10*x^2+x^5+5*x-1)/(x^2-2*x+1)/(6*x^2-4*x+1-4*x^3+x^4) egf A001807 7.82013 -6*(6+75*x+30*x^4+150*x^3+x^5+200*x^2)/(-1+x)/(1+x)/(x^4+24*x^3+76*x^2+24*x+1) lgdegf A001807 11.0904 {(-49-14*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=120,a(1)=4320} ogf A001808 33.1247 -(11+13*x)/(-1+x)/(1+x) lgdogf A001808 14.1087 -803-949*x+(315+286*x-73*x^2)*f(x)+(-22+22*x^2)*f(x)^2 lgdogf A001808 47.6168 1/(x-1)^12/(x+1) ogf A001808 190.467 x+11 ogf_with_Euler_Transform A001808 12.2882 {(n+3)*a(n+3)-11*a(n+2)+(-14-n)*a(n+1),a(0)=1,a(1)=11,a(2)=67} ogf A001808 33.1247 {a(n+2),a(0)=11,a(1)=1} ogf_with_Euler_Transform A001809 28.3096 -(x^2+4*x+1)/(x-1)^5 egf A001809 62.9103 -3/(-1+x) lgdegf A001809 9.13214 -x^2+(2-6*x+12*x^2-2*x^3)*f(x)+(-36*x^2-12+36*x+12*x^3)*f(x)^2 egf A001809 24.6171 x^2/(2-6*x+6*x^2-2*x^3) egf A001809 11.1018 {(-4-4*n-n^2)*a(n+1)+a(n+2)*n,a(0)=0,a(1)=0,a(2)=1} ogf A001809 11.1018 {(-4-4*n-n^2)*a(n+1)+n*a(n+2),a(0)=0,a(1)=0,a(2)=1} ogf A001810 27.9382 -(x+1)*(x^2+8*x+1)/(x-1)^7 egf A001810 80.7105 -4/(-1+x) lgdegf A001810 8.85847 x^3+(-6+24*x-36*x^2+48*x^3-6*x^4)*f(x)+(-864*x^2-144+576*x-144*x^4+576*x^3)*f(x)^2 egf A001810 22.6998 x^3/(6-24*x+36*x^2-24*x^3+6*x^4) egf A001810 11.5301 {(-4-4*n-n^2)*a(n+1)+(-1+n)*a(n+2),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A001810 11.716 {(-4-4*n-n^2)*a(n+1)+(n-1)*a(n+2),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A001812 14.766 (-100*x^2-25*x^4-x^5-25*x-100*x^3-1)/(-1+x)^11 egf A001812 16.1723 -(x+1)*(x^4+24*x^3+76*x^2+24*x+1)/(x-1)^11 egf A001812 8.70817 -6*(6+75*x+30*x^4+150*x^3+x^5+200*x^2)/(-1+x)/(1+x)/(x^4+24*x^3+76*x^2+24*x+1) lgdegf A001812 13.3184 {(-49-14*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=36} ogf A001813 31.332 -1+(1-4*x)*f(x)^2 egf A001813 48.4221 -2/(-1+4*x) lgdegf A001813 59.1826 -x*(-1+x) revegf A001813 33.2902 1/(-4*x+1)^(1/2) egf A001813 35.5096 1/(1-4*x)^(1/2) egf A001813 14.0169 {(-4*n-6)*a(n+1)+a(n+2),a(0)=1,a(1)=2} ogf A001814 24.4492 (2*x+1)/(-4*x+1)^(5/2) egf A001814 25.6135 (2*x+1)/(1-4*x)^(5/2) egf A001814 20.6878 -12*(1+x)/(1+2*x)/(-1+4*x) lgdegf A001814 8.27511 -6732-6732*x+(1365-318*x-4488*x^2)*f(x)+(536*x^2-67+134*x)*f(x)^2 lgdegf A001814 10.1487 {(-30-22*n-4*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=12} ogf A001815 58.0859 -2/(2*x-1)^3 ogf A001815 63.3665 -6/(-1+2*x) lgdogf A001815 21.7822 2*x^2+(-1+6*x-12*x^2+8*x^3)*f(x) ogf A001815 26.8089 2*x^2/(1-6*x+12*x^2-8*x^3) ogf A001815 12.6733 {a(n+3)-6*a(n+2)+12*a(n+1)-8*a(n),a(0)=0,a(1)=0,a(2)=2} ogf A001816 61.1587 -10/(-1+2*x) lgdogf A001816 56.4542 -12/(2*x-1)^5 ogf A001816 18.8181 12/(1-10*x+40*x^2-80*x^3+80*x^4-32*x^5) ogf A001816 15.2897 {(-n-2)*a(n+2)+(12+2*n)*a(n+1),a(0)=12,a(1)=120} ogf A001818 10.0764 {(4*n^2+12*n+9)*a(n+1)-a(n+2),a(0)=1,a(1)=1} ogf A001819 5.73639 {(n^3+6*n^2+12*n+8)*a(n+1)+(-2*n^2-10*n-13)*a(n+2)+(n+3)*a(n+3),a(0)=0,a(1)=1,a(2)=5/2} egf A001823 9.88037 -(-9-196*x-350*x^2-84*x^3-x^4)/(21*x^2+1-7*x+7*x^6+35*x^4-35*x^3-x^7-21*x^5) ogf A001823 10.4293 -(259+1876*x+3*x^4+340*x^3+2002*x^2)/(-1+x)/(x^4+84*x^3+350*x^2+196*x+9) lgdogf A001823 20.2948 -(9+196*x+350*x^2+84*x^3+x^4)/(x-1)^7 ogf A001823 7.36184 {(-21-13*n-2*n^2)*a(n+1)+(1647+685*n+74*n^2)*a(n+2)+(-216-252*n-72*n^2)*a(n+3),a(0)=0,a(1)=9,a(2)=259} ogf A001834 43.5052 (x+1)/(x^2-4*x+1) ogf A001834 23.8577 -(-5+2*x+x^2)/(1+x)/(x^2-4*x+1) lgdogf A001834 38.9257 -(1+x)/(-x^2-1+4*x) ogf A001834 17.6093 -1/2*(-1-4*x+(1+12*x+12*x^2)^(1/2))/(-1+x) revogf A001834 14.2229 -7-7*x+(-11-46*x+7*x^2)*f(x)+(18-72*x+18*x^2)*f(x)^2 ogf A001834 19.9889 {-a(n+2)+4*a(n+1)-a(n),a(0)=1,a(1)=5} ogf A001835 29.7363 -(-1+3*x)/(x^2+1-4*x) ogf A001835 18.3666 -(1-2*x+3*x^2)/(3*x-1)/(x^2-4*x+1) lgdogf A001835 31.2231 -(3*x-1)/(x^2-4*x+1) ogf A001835 15.6116 -1/2*(-1-4*x+(1-4*x+12*x^2)^(1/2))/(3+x) revogf A001835 12.2444 -7+21*x+(15-52*x+7*x^2)*f(x)+(-8*x^2-8+32*x)*f(x)^2 ogf A001835 17.3462 {a(n+2)-4*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A001839 18.7389 (-1-2*x^3-2*x^4+x^5)/(x^2+x+1)/(x^2-x+1)/(x+1)^2/(x-1)^3 ogf A001839 8.74483 -(-1-3*x-9*x^9-7*x^7-4*x^4-13*x^3+4*x^10-11*x^8-5*x^6-16*x^5-7*x^2)/(-1+x)/(1+x)/(x^2+x+1)/(x^2-x+1)/(x^5-2*x^4-2*x^3-1) lgdogf A001839 19.7996 -(-2*x^6+x^7-x^2-2*x^5)/(1-x-x^2-x^9+x^3-x^6+x^7+x^8) ogf A001840 26.9644 -(2+2*x+5*x^2)/(-1+x)/(x^2+x+1) lgdogf A001840 41.7948 -1/(x^2+x+1)/(x-1)^3 ogf A001840 167.179 2+x^2 ogf_with_Euler_Transform A001840 30.9591 x/(1-2*x-x^5+x^2-x^3+2*x^4) ogf A001840 11.2959 {(n+3)*a(n+4)-2*a(n+3)-2*a(n+2)+(-5-n)*a(n+1),a(0)=0,a(1)=1,a(2)=2,a(3)=3} ogf A001841 7.87299 -(-3-2*x-2*x^2-2*x^3-x^5-2*x^4)/(1-x-x^2-x^9+x^3-x^6+x^7+x^8) ogf A001841 7.27655 -(3+2*x+2*x^2+2*x^3+2*x^4+x^5)/(x^2+x+1)/(x^2-x+1)/(x+1)^2/(x-1)^3 ogf A001844 25.2123 -(-1-2*x-x^2)/(3*x^2+1-3*x-x^3) ogf A001844 48.8488 -(x+1)^2/(x-1)^3 ogf A001844 41.1358 -(x+5)/(-1+x)/(1+x) lgdogf A001844 10.1504 -30-60*x-30*x^2+(49-52*x+109*x^2-30*x^3)*f(x)+(-19+57*x-57*x^2+19*x^3)*f(x)^2 ogf A001844 156.316 5-2*x ogf_with_Euler_Transform A001844 33.9818 {a(n+2),a(0)=5,a(1)=-2} ogf_with_Euler_Transform A001844 14.7468 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=5,a(2)=13} ogf A001845 50.1688 (x+1)^3/(x-1)^4 ogf A001845 17.5007 -(1+3*x+3*x^2+x^3)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A001845 39.6069 -(7+x)/(-1+x)/(1+x) lgdogf A001845 7.033 -121-363*x-363*x^2-121*x^3+(60-667*x+543*x^2-545*x^3+121*x^4)*f(x)+(61-244*x+366*x^2-244*x^3+61*x^4)*f(x)^2 ogf A001845 150.506 7-3*x ogf_with_Euler_Transform A001845 12.7548 {(-n-3)*a(n+3)+7*a(n+2)+(n+2)*a(n+1),a(0)=1,a(1)=7,a(2)=25} ogf A001845 32.7188 {a(n+2),a(0)=7,a(1)=-3} ogf_with_Euler_Transform A001846 13.8102 -(-1-4*x-6*x^2-4*x^3-x^4)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A001846 49.1988 -(x+1)^4/(x-1)^5 ogf A001846 41.4306 -(x+9)/(-1+x)/(1+x) lgdogf A001846 157.436 9-4*x ogf_with_Euler_Transform A001846 13.342 {(-n-3)*a(n+3)+9*a(n+2)+(n+2)*a(n+1),a(0)=1,a(1)=9,a(2)=41} ogf A001846 34.2252 {a(n+2),a(0)=9,a(1)=-4} ogf_with_Euler_Transform A001847 51.955 (x+1)^5/(x-1)^6 ogf A001847 10.824 -(1+5*x+10*x^2+10*x^3+x^5+5*x^4)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A001847 38.9663 -(x+11)/(-1+x)/(1+x) lgdogf A001847 129.888 11-5*x ogf_with_Euler_Transform A001847 12.7758 {(-n-3)*a(n+3)+11*a(n+2)+(n+2)*a(n+1),a(0)=1,a(1)=11,a(2)=61} ogf A001847 32.4719 {a(n+2),a(0)=11,a(1)=-5} ogf_with_Euler_Transform A001848 9.06734 -(-1-6*x-x^6-15*x^2-20*x^3-6*x^5-15*x^4)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A001848 38.9896 -(13+x)/(-1+x)/(1+x) lgdogf A001848 48.737 -(x+1)^6/(x-1)^7 ogf A001848 129.965 13-6*x ogf_with_Euler_Transform A001848 12.7835 {(-n-3)*a(n+3)+13*a(n+2)+(n+2)*a(n+1),a(0)=1,a(1)=13,a(2)=85} ogf A001848 32.4913 {a(n+2),a(0)=13,a(1)=-6} ogf_with_Euler_Transform A001849 51.2447 (x+1)^7/(x-1)^8 ogf A001849 7.68671 -(1+7*x+7*x^6+x^7+21*x^2+35*x^3+21*x^5+35*x^4)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A001849 38.4336 -(15+x)/(-1+x)/(1+x) lgdogf A001849 128.112 15-7*x ogf_with_Euler_Transform A001849 12.3979 {(-n-3)*a(n+3)+15*a(n+2)+(n+2)*a(n+1),a(0)=1,a(1)=15,a(2)=113} ogf A001849 32.028 {a(n+2),a(0)=15,a(1)=-7} ogf_with_Euler_Transform A001850 34.8204 -(-3+x)/(1-6*x+x^2) lgdogf A001850 31.5042 -1+(1-6*x+x^2)*f(x)^2 ogf A001850 34.8204 1/(1-6*x+x^2)^(1/2) ogf A001850 9.87445 {(-n-3)*a(n+3)+(15+6*n)*a(n+2)+(-2-n)*a(n+1),a(0)=1,a(1)=3,a(2)=13} ogf A001859 27.6584 -(-2*x-x^2)/(1-2*x+2*x^3-x^4) ogf A001859 23.591 -(5+10*x+3*x^2)/(-1+x)/(x+2)/(1+x) lgdogf A001859 40.1047 -(x+2)/(x+1)/(x-1)^3 ogf A001859 8.53291 1970*x+985*x^2+(-985+1268*x-351*x^2-1970*x^3+985*x^4)*f(x)+(-351*x^4+351-702*x+702*x^3)*f(x)^2 ogf A001859 9.1147 {(-6-2*n)*a(n+4)+(3-n)*a(n+3)+(12+2*n)*a(n+2)+(n+3)*a(n+1),a(0)=0,a(1)=2,a(2)=5,a(3)=10} ogf A001860 26.1231 (3+3*x+2*x^2)/(x^2+x+1)/(x-1)^4 ogf A001860 14.7239 -(-3*x-3*x^2-2*x^3)/(1-3*x+3*x^2-3*x^5-2*x^3+3*x^4+x^6) ogf A001860 13.2757 -(12+22*x+8*x^4+21*x^3+33*x^2)/(-1+x)/(x^2+x+1)/(2*x^2+3*x+3) lgdogf A001860 5.39878 {(-588-415*n-99*n^2-8*n^3)*a(n+1)+(-324-174*n-24*n^2)*a(n+2)+(-324-174*n-24*n^2)*a(n+3)+(264+241*n+75*n^2+8*n^3)*a(n+4),a(0)=0,a(1)=3,a(2)=12,a(3)=29} ogf A001861 77.6624 2*exp(x) lgdegf A001861 17.2583 {(-n-2)*a(n+2)+a(n+1),a(0)=2,a(1)=2} lgdegf A001862 31.366 -exp(x)*(x*exp(-x)-1-x) lgdegf A001862 7.28704 {-n*a(n+1)+(-1+n^2)*a(n+2)+(5*n+6+n^2)*a(n+3)+(-7*n-12-n^2)*a(n+4),a(0)=1,a(1)=1,a(2)=3/2,a(3)=2/3} lgdegf A001870 18.7097 -(-1+x)/(11*x^2+1-6*x-6*x^3+x^4) ogf A001870 18.1428 -(5-7*x+3*x^2)/(-1+x)/(x^2-3*x+1) lgdogf A001870 28.5101 -(x-1)/(-3*x+1+x^2)^2 ogf A001870 6.17229 49-49*x+(-1025+1270*x-539*x^2+294*x^3-49*x^4)*f(x)+(976-5856*x^3-5856*x+10736*x^2+976*x^4)*f(x)^2 ogf A001870 6.57925 {(-4-n)*a(4+n)+(17+4*n)*a(n+3)+(-15-4*n)*a(n+2)+(4+n)*a(n+1),a(0)=1,a(1)=5,a(2)=19,a(3)=65} ogf A001871 23.5049 -1/(-1+6*x-11*x^2+6*x^3-x^4) ogf A001871 7.47882 -16+(-279-96*x+176*x^2-96*x^3+16*x^4)*f(x)+(295+295*x^4-1770*x+3245*x^2-1770*x^3)*f(x)^2 ogf A001871 29.9153 -2*(2*x-3)/(x^2-3*x+1) lgdogf A001871 41.1335 1/(-3*x+1+x^2)^2 ogf A001871 9.82293 {(-n-3)*a(n+3)+(12+3*n)*a(n+2)+(-5-n)*a(n+1),a(0)=1,a(1)=6,a(2)=25} ogf A001872 14.2073 -1/(-1+4*x-2*x^2-8*x^3+5*x^4+8*x^5-2*x^6-4*x^7-x^8) ogf A001872 36.2286 -4*(1+2*x)/(x^2-1+x) lgdogf A001872 55.7363 1/(x-1+x^2)^4 ogf A001872 11.3214 {(n+3)*a(n+3)+(-6-n)*a(n+2)+(-9-n)*a(n+1),a(0)=1,a(1)=4,a(2)=14} ogf A001873 55.925 -1/(x-1+x^2)^5 ogf A001873 14.2354 -280-560*x+(31-106*x-56*x^2)*f(x)+(-5*x^2+5-5*x)*f(x)^2 lgdogf A001873 39.1475 -5*(1+2*x)/(x^2-1+x) lgdogf A001873 12.0454 {(n+3)*a(n+3)+(-7-n)*a(n+2)+(-11-n)*a(n+1),a(0)=1,a(1)=5,a(2)=20} ogf A001874 12.5076 -2016-4032*x+(186-636*x-336*x^2)*f(x)+(-25*x^2+25-25*x)*f(x)^2 lgdogf A001874 38.7737 -6*(1+2*x)/(x^2-1+x) lgdogf A001874 59.6518 1/(x-1+x^2)^6 ogf A001874 11.9304 {(n+3)*a(n+3)+(-8-n)*a(n+2)+(-13-n)*a(n+1),a(0)=1,a(1)=6,a(2)=27} ogf A001875 55.3199 -1/(x-1+x^2)^7 ogf A001875 12.4916 -2744-5488*x+(217-742*x-392*x^2)*f(x)+(-25*x^2+25-25*x)*f(x)^2 lgdogf A001875 38.724 -7*(1+2*x)/(x^2-1+x) lgdogf A001875 11.9151 {(n+3)*a(n+3)+(-9-n)*a(n+2)+(-15-n)*a(n+1),a(0)=1,a(1)=7,a(2)=35} ogf A001879 33.2722 (x+1)/(-2*x+1)^(5/2) egf A001879 35.0233 (x+1)/(1-2*x)^(5/2) egf A001879 28.9323 -3*(x+2)/(1+x)/(-1+2*x) lgdegf A001879 10.0825 -3366-1683*x+(1365-159*x-1122*x^2)*f(x)+(268*x^2-134+134*x)*f(x)^2 lgdegf A001879 12.797 {(-15-11*n-2*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=6} ogf A001880 16.7493 -15*(2+6*x+x^2)/(-1+2*x)/(3*x^2+12*x+2) lgdegf A001880 15.1912 1/2*(3*x^2+12*x+2)/(-2*x+1)^(5/2)/(2*x-1)^2 egf A001880 14.2005 1/2*(3*x^2+12*x+2)/(1-2*x)^(5/2)/(4*x^2-4*x+1) egf A001880 12.325 {(-28-15*n-2*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=15} ogf A001881 15.9979 -21*(2+10*x+5*x^2)/(-1+2*x)/(15*x^2+20*x+2) lgdegf A001881 15.6343 1/2*(15*x^2+20*x+2)/(-2*x+1)^(7/2)/(2*x-1)^2 egf A001881 14.6363 1/2*(15*x^2+20*x+2)/(1-2*x)^(7/2)/(4*x^2-4*x+1) egf A001881 12.9794 {(-36-17*n-2*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=21} ogf A001882 22.0432 -(-2-3*x+3*x^2+x^3)/(1+2*x^4-4*x^2) ogf A001882 22.0432 -(-2-3*x+x^3+3*x^2)/(1+2*x^4-4*x^2) ogf A001882 10.1515 -(3+10*x-14*x^4-16*x^3+2*x^6+12*x^5+9*x^2)/(x^3+3*x^2-3*x-2)/(2*x^4-4*x^2+1) lgdogf A001882 7.95372 -318-477*x+477*x^2+159*x^3+(-185-516*x-120*x^2+172*x^3+318*x^4)*f(x)+(172+344*x^4-688*x^2)*f(x)^2 ogf A001891 19.6795 -(-4+3*x^3+5*x^2)/(-1+x)/(1+x)/(x^2+x-1) lgdogf A001891 25.3929 -(-x-x^2)/(1-3*x-x^4+2*x^2+x^3) ogf A001891 32.7992 -(x+1)/(x-1+x^2)/(x-1)^2 ogf A001891 8.46431 17*x+17*x^2+(-17+163*x+78*x^2-17*x^3+17*x^4)*f(x)+(-112+336*x+112*x^4-224*x^2-112*x^3)*f(x)^2 ogf A001891 9.15326 {(2*n+7)*a(n+1)+2*a(n+2)+(-4*n-12)*a(n+3)+(2*n+5)*a(n+4),a(0)=0,a(1)=1,a(2)=4,a(3)=10} ogf A001900 4.94708 {(-12-16*n-7*n^2-n^3)*a(n+1)+(-50-41*n-11*n^2-n^3)*a(n+2)-2*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=2,a(2)=4,a(3)=16} ogf A001903 24.3968 -(-1-6*x-3*x^2)/(x^2+1-x-x^3) ogf A001903 25.2681 -(1+6*x+3*x^2)/(x-1)/(1+x^2) ogf A001903 12.634 -(7+4*x+3*x^4+12*x^3-6*x^2)/(-1+x)/(1+x^2)/(3*x^2+6*x+1) lgdogf A001903 9.5609 -97-582*x-291*x^2+(92-127*x+82*x^2-97*x^3)*f(x)+(5*x^2+5-5*x-5*x^3)*f(x)^2 ogf A001903 14.7397 {a(n+3)-a(n+2)+a(n+1)-a(n),a(0)=1,a(1)=7,a(2)=9} ogf A001906 39.4909 -(2*x-3)/(x^2+1-3*x) lgdogf A001906 19.2638 -1/2*(-1-3*x+(x+1)^(1/2)*(1+5*x)^(1/2))/x revogf A001906 56.4155 1/(-3*x+1+x^2) ogf A001906 41.5694 x+(-1+3*x-x^2)*f(x) ogf A001906 60.7552 x/(1-3*x+x^2) ogf A001906 21.9394 {a(n+2)-3*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A001907 32.4986 -(4*x+3)/(-1+4*x) lgdegf A001907 29.0777 -3-4*x+(1-4*x)*f(x) lgdegf A001907 32.4986 -exp(-x)/(-1+4*x) egf A001907 8.76946 {(-4*n-8)*a(n+1)+(-4*n-11)*a(n+2)+a(n+3),a(0)=1,a(1)=3,a(2)=25} ogf A001908 40.1251 -(5*x+4)/(-1+5*x) lgdegf A001908 35.9014 -4-5*x+(1-5*x)*f(x) lgdegf A001908 42.633 -exp(-x)/(5*x-1) egf A001908 10.6582 {(-5*n-10)*a(n+1)+(-5*n-14)*a(n+2)+a(n+3),a(0)=1,a(1)=4,a(2)=41} ogf A001909 41.2913 -exp(-x)/(x-1)^5 egf A001909 15.73 {a(n)*n+(n+4)*a(n+1)-a(n+2),a(0)=0,a(1)=1} ogf A001910 45.6678 exp(-x)/(x-1)^6 egf A001910 16.3099 {a(n)*n+(n+5)*a(n+1)-a(n+2),a(0)=0,a(1)=1} ogf A001911 34.9056 (x+1)/(x-1)/(x-1+x^2) ogf A001911 18.3254 -(-3+2*x^3+3*x^2)/(-1+x)/(1+x)/(x^2+x-1) lgdogf A001911 34.9056 -(x+x^2)/(-1+2*x-x^3) ogf A001911 31.8703 -x-x^2+(1-2*x+x^3)*f(x) ogf A001911 16.6595 {-a(n+3)+2*a(n+2)-a(n),a(0)=0,a(1)=1,a(2)=3} ogf A001919 36.9631 (6-8*x+3*x^2)/(x-1)^8 ogf A001919 11.4151 -(6-8*x+3*x^2)/(-28*x^2-1+8*x-70*x^4+56*x^5-28*x^6+56*x^3-x^8+8*x^7) ogf A001919 19.9032 -2*(20-25*x+9*x^2)/(-1+x)/(3*x^2-8*x+6) lgdogf A001919 7.61005 {(-6*n-24)*a(n+4)+(82+14*n)*a(n+3)+(-72-11*n)*a(n+2)+(21+3*n)*a(n+1),a(0)=6,a(1)=40,a(2)=155,a(3)=456} ogf A001920 15.4033 -1/(-1-759*x^2-2576*x^3-759*x^4-x^6) ogf A001920 8.94384 -6*x*(253+506*x^2+x^4+1288*x)/(1+759*x^2+2576*x^3+759*x^4+x^6) lgdogf A001920 16.3094 1/(1+759*x^2+2576*x^3+759*x^4+x^6) ogf A001921 15.4233 (-7*x+x^2)*f(x)+(1-15*x+15*x^2-x^3)*f(x)^2 ogf A001921 26.9907 (x-7)/(x-1)/(x^2+1-14*x) ogf A001921 20.896 -(-7*x+x^2)/(1-15*x+15*x^2-x^3) ogf A001921 12.7015 -2*(-52+105*x+x^3-18*x^2)/(-1+x)/(x-7)/(x^2-14*x+1) lgdogf A001921 11.3645 {-a(n+3)+15*a(n+2)-15*a(n+1)+a(n),a(0)=0,a(1)=7,a(2)=104} ogf A001922 19.2876 (7*x-1)/(x-1)/(x^2+1-14*x) ogf A001922 17.2924 -(-1+7*x)/(1-15*x+15*x^2-x^3) ogf A001922 9.46185 -2*(-4+15*x+7*x^3-54*x^2)/(-1+x)/(7*x-1)/(x^2-14*x+1) lgdogf A001922 4.17898 -357167+2500169*x+(-4698913+30035055*x+5357505*x^2-357167*x^3)*f(x)+(75841200*x^2+5056080-75841200*x-5056080*x^3)*f(x)^2 ogf A001922 8.95497 {a(n+3)-15*a(n+2)+15*a(n+1)-a(n),a(0)=1,a(1)=8,a(2)=105} ogf A001924 25.8152 -(1+x)*(4*x-3)/(-1+x)/(x^2+x-1) lgdogf A001924 40.0135 -1/(x-1+x^2)/(x-1)^2 ogf A001924 12.9076 -x+(1-6*x+2*x^2+x^3-x^4)*f(x)+(3-9*x+6*x^2+3*x^3-3*x^4)*f(x)^2 ogf A001924 34.7943 x/(1-3*x+2*x^2+x^3-x^4) ogf A001924 10.13 {(-3-n)*a(n+4)+(7+2*n)*a(n+3)-a(n+2)+(-n-4)*a(n+1),a(0)=0,a(1)=1,a(2)=3,a(3)=7} ogf A001925 15.9277 -(-1-x)/(8*x^2+1-5*x+4*x^5+x^6-2*x^3-6*x^4-x^7) ogf A001925 28.7923 -(x+1)/(x-1+x^2)^2/(x-1)^3 ogf A001925 17.0136 -2*(-3-x+3*x^3+4*x^2)/(-1+x)/(1+x)/(x^2+x-1) lgdogf A001925 7.06226 {(-28-11*n-n^2)*a(n+1)-a(n+2)*n+(17*n+33+2*n^2)*a(n+3)+(-7*n-12-n^2)*a(n+4),a(0)=1,a(1)=6,a(2)=22,a(3)=64} ogf A001926 17.0816 -(-9-2*x+8*x^3+11*x^2)/(-1+x)/(1+x)/(x^2+x-1) lgdogf A001926 10.3874 -(1+2*x+x^2)/(x^10-1+7*x+7*x^4-18*x^2+9*x^6+17*x^3-6*x^8-24*x^5+9*x^7-x^9) ogf A001926 27.4525 -(x+1)^2/(x-1+x^2)^3/(x-1)^4 ogf A001932 23.63 -(2-3*x-2*x^2)/(-1+3*x-3*x^3-x^4) ogf A001932 10.8304 -(3-4*x+15*x^4+10*x^3+4*x^5-12*x^2)/(-1+2*x)/(x+2)/(x^2+x-1)/(x^2+2*x-1) lgdogf A001932 21.0754 -(x+2)*(2*x-1)/(x-1+x^2)/(-1+2*x+x^2) ogf A001932 8.66435 -134+201*x+134*x^2+(-37-45*x+104*x^2+201*x^3+67*x^4)*f(x)+(52-156*x+156*x^3+52*x^4)*f(x)^2 ogf A001934 42.1638 -(4+2*x)/(-1+x^2) ogf_with_Euler_Transform A001934 25.5994 {-a(n+2)+a(n),a(0)=4,a(1)=2} ogf_with_Euler_Transform A001935 43.6499 -(-1-x-x^2)/(1-x^4) ogf_with_Euler_Transform A001935 20.228 {a(n+4)-a(n),a(0)=1,a(1)=1,a(2)=1,a(3)=0} ogf_with_Euler_Transform A001936 32.1756 -(-2-2*x-2*x^2)/(1-x^4) ogf_with_Euler_Transform A001936 18.0497 {a(n+4)-a(n),a(0)=2,a(1)=2,a(2)=2,a(3)=0} ogf_with_Euler_Transform A001937 35.1672 -(-3-3*x-3*x^2)/(1-x^4) ogf_with_Euler_Transform A001937 19.728 {a(n+4)-a(n),a(0)=3,a(1)=3,a(2)=3,a(3)=0} ogf_with_Euler_Transform A001938 34.6574 -(4-4*x)/(1+x+x^2+x^3) ogf_with_Euler_Transform A001938 34.6574 -(4-4*x)/(1+x+x^3+x^2) ogf_with_Euler_Transform A001938 34.6574 -(4-4*x)/(x^2+1+x+x^3) ogf_with_Euler_Transform A001938 14.9503 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-4,a(1)=8,a(2)=-4} ogf_with_Euler_Transform A001939 33.7533 -(-5-5*x-5*x^2)/(1-x^4) ogf_with_Euler_Transform A001939 18.9348 {a(n+4)-a(n),a(0)=5,a(1)=5,a(2)=5,a(3)=0} ogf_with_Euler_Transform A001940 32.2375 -(-6-6*x-6*x^2)/(1-x^4) ogf_with_Euler_Transform A001940 18.0844 {a(n+4)-a(n),a(0)=6,a(1)=6,a(2)=6,a(3)=0} ogf_with_Euler_Transform A001941 32.209 -(-7-7*x-7*x^2)/(1-x^4) ogf_with_Euler_Transform A001941 18.0684 {a(n+4)-a(n),a(0)=7,a(1)=7,a(2)=7,a(3)=0} ogf_with_Euler_Transform A001945 17.3685 (1+2*x+x^2+2*x^3+x^4)/(-1+x^3+x^2)/(-x-1+x^3) ogf A001945 7.44362 -(-1-4*x+2*x^9+8*x^7-5*x^4-24*x^3+7*x^8+14*x^6+14*x^5-18*x^2)/(x^3+x^2-1)/(x^3-x-1)/(x^4+2*x^3+x^2+2*x+1) lgdogf A001945 14.7468 -(x+x^5+2*x^4+2*x^2+x^3)/(-1-x+x^2+3*x^3+x^4-x^5-x^6) ogf A001946 31.1828 (-2+11*x)/(x^2+11*x-1) ogf A001946 17.1506 -(-11-4*x+11*x^2)/(-2+11*x)/(x^2-1+11*x) lgdogf A001946 31.1828 -(2-11*x)/(x^2-1+11*x) ogf A001946 10.5542 258-1419*x+(-379+2794*x+129*x^2)*f(x)+(125-1375*x-125*x^2)*f(x)^2 ogf A001946 17.5903 {-a(n+2)+11*a(n+1)+a(n),a(0)=2,a(1)=11} ogf A001947 35.3496 (4*x-3)/(x^2+11*x-1) ogf A001947 19.1079 -(-29-6*x+4*x^2)/(4*x-3)/(x^2-1+11*x) lgdogf A001947 33.6663 -(3-4*x)/(x^2-1+11*x) ogf A001947 16.4417 1/2/(-4+x)*(-3-11*x+(9+50*x+125*x^2)^(1/2)) revogf A001947 10.8768 402-536*x+(-1109+2774*x+134*x^2)*f(x)+(325-3575*x-325*x^2)*f(x)^2 ogf A001947 18.128 {-a(n+2)+11*a(n+1)+a(n),a(0)=3,a(1)=29} ogf A001949 18.621 -2*(-1+3*x^5)/(-1+x)/(x^5+x^4+x^3+x^2+x-1) lgdogf A001949 26.0694 1/(x-1)/(-1+x+x^2+x^3+x^4+x^5) ogf A001949 52.1388 x^5/(1-2*x+x^6) ogf A001954 7.95904 -(-1-4*x-4*x^8-4*x^11-3*x^10-3*x^9-2*x^12-4*x^6-3*x^5-3*x^7-4*x^4-3*x^2-3*x^3+x^20-x^21)/(1-x+x^13-x^12) ogf A001955 8.89273 (1+x+x^2+2*x^3+x^4+x^5+2*x^6+x^7+x^8+2*x^9)/(x+1)/(1+x+x^2+x^3+x^4)/(x^4-x^3+x^2-x+1)/(x-1)^2 ogf A001955 13.5578 -(1+x+x^8+2*x^9+2*x^6+x^5+x^7+x^4+x^2+2*x^3)/(-x^11-1+x+x^10) ogf A001956 11.4582 -(-4-4*x-4*x^8-5*x^9-5*x^6-4*x^5-4*x^7-4*x^4-4*x^2-5*x^3)/(x^11+1-x-x^10) ogf A001957 7.83623 -(-1-2*x-x^2-x^3-x^4-x^24+x^25-2*x^5-x^6-x^7-2*x^8-x^9)/(x+1)/(1+x+x^2+x^3+x^4)/(x^4-x^3+x^2-x+1)/(x-1)^2 ogf A001971 13.3766 -(1+2*x-3*x^4+6*x^3+4*x^5+2*x^2)/(-1+x)/(1+x)/(1+x^2)/(x^2-x+1) lgdogf A001971 26.3353 -(x^2-x+1)/(1+x^2)/(x+1)/(x-1)^3 ogf A001971 20.5543 -(x^4+x^2-x^3)/(-1+2*x-x^2-2*x^5+x^6+x^4) ogf A001971 56.1819 1+x+x^2+x^3-x^5 ogf_with_Euler_Transform A001972 28.5428 -1/(-1+2*x-x^2-2*x^5+x^6+x^4) ogf A001972 34.4892 -1/(1+x^2)/(x+1)/(x-1)^3 ogf A001972 21.2241 -2*(1+x+x^2+3*x^3)/(1+x^2)/(-1+x)/(1+x) lgdogf A001972 165.548 2+x^3 ogf_with_Euler_Transform A001972 19.7081 {-a(n+4)+a(n),a(0)=2,a(1)=2,a(2)=2,a(3)=6} lgdogf A001972 22.9928 {a(n+4),a(0)=2,a(1)=0,a(2)=0,a(3)=1} ogf_with_Euler_Transform A001973 16.7676 (x^2-x+1)/(x+1)/(x^2+x+1)/(x-1)^4 ogf A001973 8.78305 -(1+5*x+7*x^2+5*x^3+x^4+5*x^5)/(-1+x)/(1+x)/(x^2+x+1)/(x^2-x+1) lgdogf A001973 36.8888 1+2*x+2*x^2-x^5 ogf_with_Euler_Transform A001977 7.78046 (1+3*x^7+x^10+x^2+3*x^3+4*x^4+4*x^5+4*x^6+x^8)/(x^2+x+1)/(1+x+x^2+x^3+x^4)/(1+x^2)/(x+1)^3/(x-1)^6 ogf A001978 9.74209 (1+2*x+2*x^2+x^3+2*x^4+2*x^5+x^6)/(x^2+x+1)/(1+x+x^2+x^3+x^4)/(x+1)^3/(x-1)^6 ogf A001978 6.35713 -(1+2*x+x^6+2*x^5+2*x^4+2*x^2+x^3)/(3*x^2-1+x+3*x^9-4*x^4-4*x^11-2*x^3+3*x^13+3*x^6-x^15+x^5-x^8+x^10-x^7-2*x^12+x^14) ogf A001993 12.202 -(3*x^2+2*x+1)*(5*x^3+2*x^2+4*x+1)/(-1+x)/(1+x)/(1+x^2)/(x^2+x+1) lgdogf A001993 52.8754 1+2*x+2*x^2+x^3 ogf_with_Euler_Transform A001993 21.436 1/(1+x^2)/(x^2+x+1)^2/(x+1)^3/(x-1)^6 ogf A001993 10.4359 1/(1-x-2*x^2+2*x^4+4*x^5-x^6-3*x^7-3*x^8-x^9+4*x^10+2*x^11-2*x^13-x^14+x^15) ogf A001993 22.0314 {a(n+4),a(0)=1,a(1)=2,a(2)=2,a(3)=1} ogf_with_Euler_Transform A001994 7.30147 -(1+7*x+17*x^9+58*x^7+53*x^4+35*x^3+35*x^8+68*x^6+69*x^5+17*x^2)/(-1+x)/(1+x)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(1+x^2) lgdogf A001994 48.5333 1+2*x+x^2+x^3+x^4 ogf_with_Euler_Transform A001994 10.5778 1/(1-x-2*x^2+x^3+x^4+x^5+x^6-2*x^8-2*x^9+x^11+x^12+x^13+x^14-2*x^15-x^16+x^17) ogf A001994 15.5673 1/(x^2+x+1)/(1+x+x^2+x^3+x^4)/(1+x^2)/(x+1)^3/(x-1)^6 ogf A001994 18.7515 {-a(n+5),a(0)=1,a(1)=2,a(2)=1,a(3)=1,a(4)=1} ogf_with_Euler_Transform A001996 35.1781 (1+x+x^2+x^3+x^4+x^5)*x ogf_with_Euler_Transform A001996 35.1781 (1+x+x^3+x^5+x^2+x^4)*x ogf_with_Euler_Transform A001996 7.35541 1/(1-x^2-x^3-x^4+x^7+2*x^8+2*x^9+x^10-2*x^12-2*x^13-2*x^14-2*x^15+x^17+2*x^18+2*x^19+x^20-x^23-x^24-x^25+x^27) ogf A001996 8.89116 1/(x^2-x+1)/(1+x+x^2+x^3+x^4)/(x^6+x^5+x^4+x^3+x^2+x+1)/(1+x^2)/(x^2+x+1)^2/(x+1)^3/(x-1)^6 ogf A001996 11.5585 {-a(n+1)+a(n),a(0)=0,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=0} ogf_with_Euler_Transform A001998 16.423 -(1-2*x-4*x^2+6*x^3)/(-1+4*x+9*x^4-12*x^3) ogf A001998 15.6765 -(1-2*x-4*x^2+6*x^3)/(3*x-1)/(x-1)/(3*x^2-1) ogf A001998 8.02053 -2*(1-4*x-3*x^4+18*x^3+27*x^6-36*x^5-x^2)/(-1+x)/(3*x-1)/(3*x^2-1)/(6*x^3-4*x^2-2*x+1) lgdogf A001998 7.18506 -33+66*x+132*x^2-198*x^3+(20-106*x+52*x^2+318*x^3-297*x^4)*f(x)+(13-52*x-117*x^4+156*x^3)*f(x)^2 ogf A001998 10.7776 {-a(n+4)+4*a(n+3)-12*a(n+1)+9*a(n),a(0)=1,a(1)=2,a(2)=4,a(3)=10} ogf A002001 53.7587 (x-1)/(-1+4*x) ogf A002001 50.1747 -(-1+x)/(1-4*x) ogf A002001 23.5194 1/2+2*x-1/2*(1+4*x+16*x^2)^(1/2) revogf A002001 44.2718 3/(-1+4*x)/(-1+x) lgdogf A002001 47.0388 x-1+(1-4*x)*f(x) ogf A002001 24.2781 {a(n+2)-4*a(n+1),a(0)=1,a(1)=3} ogf A002002 8.30165 -1/2*(2*(8*x^2+8*x+1)^(1/2)*x+(8*x^2+8*x+1)^(1/2)-1-6*x-6*x^2)/x/(x+1) revogf A002002 12.1066 -1/2*(x-1+(1-6*x+x^2)^(1/2))/(1-6*x+x^2)^(1/2)/x ogf A002002 14.9004 x+(-1+6*x-x^2)*f(x)+(-1+6*x-x^2)*f(x)^2 ogf A002002 5.92975 {(n+n^2)*a(n)+(-5*n-5*n^2)*a(n+1)+(-25*n-30-5*n^2)*a(n+2)+(5*n+6+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=5} ogf A002002 5.92975 {(n+n^2)*a(n)+(-5*n-5*n^2)*a(n+1)+(-25*n-30-5*n^2)*a(n+2)+(6+5*n+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=5} ogf A002003 10.7861 -(2*(2*x^2+2*x+1)^(1/2)*x+(2*x^2+2*x+1)^(1/2)-1-3*x-3*x^2)/x/(x+1) revogf A002003 14.5282 -1/2*(-x-1+(1-6*x+x^2)^(1/2))/(1-6*x+x^2)^(1/2)/x ogf A002003 17.7971 -2*x+(1-6*x+x^2)*f(x)+(1-6*x+x^2)*f(x)^2 ogf A002003 7.04835 {(n+n^2)*a(n)+(-13*n-6-7*n^2)*a(n+1)+(29*n+30+7*n^2)*a(n+2)+(-5*n-6-n^2)*a(n+3),a(0)=0,a(1)=2,a(2)=8} ogf A002011 20.1431 -16+(1-12*x+48*x^2-64*x^3)*f(x)^2 ogf A002011 60.4294 -6/(-1+4*x) lgdogf A002011 41.5452 4/(-4*x+1)^(3/2) ogf A002011 44.3149 4/(1-4*x)^(3/2) ogf A002011 14.4505 {(-n-2)*a(n+2)+(10+4*n)*a(n+1),a(0)=4,a(1)=24} ogf A002012 2.08011 -4*(-2+3*x)/(-1+4*x)/(-1+2*x) lgdogf A002012 2.41293 -4*(2*x-1)/(-4*x+1)^(5/2) ogf A002017 108.603 cos(x) lgdegf A002017 12.7769 {a(n+1)+(5*n+6+n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=-1/2} lgdegf A002018 10.0516 {(-n^3-2*n-3*n^2)*a(n)+(2*n^2+8+8*n)*a(n+1)-2*a(n+2),a(0)=1,a(1)=1} ogf A002018 14.3289 {a(n)*n+(-2*n-4)*a(n+1)+2*a(n+2),a(0)=1,a(1)=1} egf A002019 40.1835 -1+(1+x^2)*f(x) lgdegf A002019 66.9725 1/(1+x^2) lgdegf A002019 43.0538 exp(arctan(x)) egf A002019 14.3513 {(n^2+n)*a(n)+a(n+2)-a(n+1),a(0)=1,a(1)=1} ogf A002020 12.038 {(n^2+n)*a(n)+a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1} ogf A002020 10.8731 {-a(n)*n+a(n+1)+(-n-2)*a(n+2),a(0)=1,a(1)=1,a(2)=1/2,a(3)=1/6} egf A002023 29.1321 -1/4*ln(3)+1/4*ln(2*x+3) revegf A002023 63.561 -4/(-1+4*x) lgdogf A002023 46.6114 -6+(1-4*x)*f(x) ogf A002023 63.561 -6/(-1+4*x) ogf A002023 53.7824 1/2*x/(3+2*x) revogf A002023 77.6857 6/(1-4*x) ogf A002023 31.7805 {a(n+1)-4*a(n),a(0)=6} ogf A002024 70.2115 -(2+x)/(-1-x) ogf_with_Euler_Transform A002024 70.2115 -(x+2)/(-1-x) ogf_with_Euler_Transform A002024 29.4435 {-a(n+2)-a(n+1),a(0)=2,a(1)=-1} ogf_with_Euler_Transform A002026 19.1159 x+(-1+2*x+x^2)*f(x)+x^3*f(x)^2 ogf A002026 6.44355 {(18+15*n+3*n^2)*a(n+1)+(21+13*n+2*n^2)*a(n+2)+(-12-8*n-n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=2} ogf A002041 27.749 -1/(-1+6*x-x^2-24*x^3+20*x^4) ogf A002041 25.1475 -1/(x-1)/(2*x+1)/(2*x-1)/(5*x-1) ogf A002041 14.9022 -2*(3-x+40*x^3-36*x^2)/(-1+x)/(1+2*x)/(-1+2*x)/(5*x-1) lgdogf A002042 29.397 -1/4*ln(7)+1/4*ln(7+4*x) revegf A002042 64.1388 -4/(-1+4*x) lgdogf A002042 47.0351 -7+(1-4*x)*f(x) ogf A002042 64.1388 -7/(-1+4*x) ogf A002042 78.3919 7/(1-4*x) ogf A002042 78.3919 x/(7+4*x) revogf A002042 32.0694 {a(n+1)-4*a(n),a(0)=7} ogf A002050 4.23999 {(n^2+n^3)*a(n)+(10*n^2+5*n+5*n^3)*a(n+1)+(-35*n^2-80*n-60-5*n^3)*a(n+2)+(-8*n^2-21*n-18-n^3)*a(n+3),a(0)=0,a(1)=1,a(2)=-5/2} revegf A002054 14.6584 -1+(1-5*x+4*x^2)*f(x)+(x^3-4*x^4)*f(x)^2 ogf A002054 15.8469 8/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^3 ogf A002054 16.7525 8/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^3 ogf A002054 9.93791 {(-42-26*n-4*n^2)*a(n+1)+(7*n+10+n^2)*a(n+2),a(0)=1,a(1)=5} ogf A002055 6.31361 {(56+30*n+4*n^2)*a(n+1)+(216+77*n+7*n^2)*a(n+2)+(-20*n-42-2*n^2)*a(n+3),a(0)=1,a(1)=9,a(2)=56} ogf A002056 5.58152 {(180+76*n+8*n^2)*a(n+1)+(144+34*n+2*n^2)*a(n+2)+(-11*n-24-n^2)*a(n+3),a(0)=1,a(1)=14,a(2)=120} ogf A002057 18.7704 1+(-1+4*x-2*x^2)*f(x)+x^4*f(x)^2 ogf A002057 26.1153 16/(1+(-4*x+1)^(1/2))^4 ogf A002057 27.3023 16/(1+(1-4*x)^(1/2))^4 ogf A002057 18.2016 8/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A002057 10.1805 {(-42-26*n-4*n^2)*a(n+1)+(8*n+12+n^2)*a(n+2),a(0)=1,a(1)=4} ogf A002058 16.8326 64/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^5 ogf A002058 17.7678 64/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^5 ogf A002058 10.6607 {(-72-34*n-4*n^2)*a(n+1)+(9*n+14+n^2)*a(n+2),a(0)=2,a(1)=14} ogf A002059 5.70478 {(-180-76*n-8*n^2)*a(n+1)+(-1400-432*n-34*n^2)*a(n+2)+(108*n+243+9*n^2)*a(n+3),a(0)=3,a(1)=32,a(2)=225} ogf A002061 37.2862 -(-2*x+1+3*x^2)/(x-1)^3 ogf A002061 24.5024 -(1+2*x+3*x^2)/(-1+x)/(3*x^2-2*x+1) lgdogf A002061 12.6115 3-6*x+9*x^2+(-7+17*x+3*x^3-21*x^2)*f(x)+(12*x^2+4-12*x-4*x^3)*f(x)^2 ogf A002061 12.6115 3-6*x+9*x^2+(-7+17*x-21*x^2+3*x^3)*f(x)+(12*x^2+4-12*x-4*x^3)*f(x)^2 ogf A002061 16.492 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=1,a(2)=3} ogf A002062 31.4293 (3*x-2)/(x-1+x^2)/(x-1)^2 ogf A002062 22.4495 -(2*x-3*x^2)/(-1+3*x+x^4-2*x^2-x^3) ogf A002062 17.4607 -(3-5*x+9*x^3-5*x^2)/(3*x-2)/(-1+x)/(x^2+x-1) lgdogf A002062 10.0735 56*x-84*x^2+(-28+82*x-53*x^2-28*x^3+28*x^4)*f(x)+(-x^4+1-3*x+x^3+2*x^2)*f(x)^2 ogf A002062 9.82164 {-a(n)*n-a(n+1)+(2*n-1)*a(n+2)+(-n+1)*a(n+3),a(0)=0,a(1)=2,a(2)=3,a(3)=5,a(4)=7} ogf A002063 29.397 -1/2*ln(3)+1/4*ln(4*x+9) revegf A002063 64.1388 -4/(-1+4*x) lgdogf A002063 47.0351 -9+(1-4*x)*f(x) ogf A002063 64.1388 -9/(-1+4*x) ogf A002063 78.3919 9/(1-4*x) ogf A002063 78.3919 x/(9+4*x) revogf A002063 32.0694 {a(n+1)-4*a(n),a(0)=9} ogf A002064 21.3889 -(-1+2*x-2*x^2)/(8*x^2+1-5*x-4*x^3) ogf A002064 14.6786 -(-3+6*x+4*x^3-6*x^2)/(-1+x)/(-1+2*x)/(1+2*x^2-2*x) lgdogf A002064 24.9537 -(1-2*x+2*x^2)/(x-1)/(2*x-1)^2 ogf A002064 11.009 1-2*x+2*x^2+(7-11*x+8*x^2+4*x^3)*f(x)+(-64*x^2-8+40*x+32*x^3)*f(x)^2 ogf A002064 13.8631 {a(n+3)-5*a(n+2)+8*a(n+1)-4*a(n),a(0)=1,a(1)=3,a(2)=9} ogf A002066 30.0591 -1/4*ln(5)+1/4*ln(5+2*x) revegf A002066 45.0886 -10+(1-4*x)*f(x) ogf A002066 60.1181 -10/(-1+4*x) ogf A002066 65.5834 -4/(-1+4*x) lgdogf A002066 55.4936 1/2*x/(5+2*x) revogf A002066 72.1417 10/(1-4*x) ogf A002066 31.366 {a(n+1)-4*a(n),a(0)=10} ogf A002081 15.8612 (2+4*x^2+4*x^3)*f(x)+(-1+2*x^3+2*x-2*x^2-x^4)*f(x)^2 ogf A002081 20.1166 -(-2-4*x^2-4*x^3)/(1-2*x+2*x^2-2*x^3+x^4) ogf A002081 13.9794 -2*(1+x+3*x^4-x^3+x^5+5*x^2)/(-1+x)/(1+x^2)/(1+2*x^3+2*x^2) lgdogf A002081 24.9934 2*(1+2*x^2+2*x^3)/(1+x^2)/(x-1)^2 ogf A002081 9.81884 {(-n-3)*a(n+1)+(n+2)*a(n+2)+(-n-3)*a(n+3)+(n+2)*a(n+4),a(0)=2,a(1)=4,a(2)=8,a(3)=16} ogf A002082 5.14466 -2*(1-2*x+3*x^2-x^3+x^4+2*x^10+2*x^5+2*x^6+2*x^7+x^8-x^9)/(1+x+x^2+x^3+x^4)/(x^4-x^3+x^2-x+1)/(x-1)^3 ogf A002089 27.7468 -1/4*ln(11)+1/4*ln(11+4*x) revegf A002089 45.0886 -11+(1-4*x)*f(x) ogf A002089 60.1181 -11/(-1+4*x) ogf A002089 65.5834 -4/(-1+4*x) lgdogf A002089 72.1417 11/(1-4*x) ogf A002089 72.1417 x/(11+4*x) revogf A002089 31.366 {a(n+1)-4*a(n),a(0)=11} ogf A002104 6.88823 {(-n-3)*a(n+1)+(2*n+8)*a(n+2)+(-n-6)*a(n+3)+a(n+4),a(0)=1,a(1)=3,a(2)=8,a(3)=24} ogf A002107 111.407 2/(x-1) ogf_with_Euler_Transform A002107 35.4478 {-a(n+1)+a(n),a(0)=-2} ogf_with_Euler_Transform A002119 24.2346 (-2+(1+4*x)^(1/2))/(1+4*x) lgdegf A002119 15.3683 3-4*x+(4+16*x)*f(x)+(1+8*x+16*x^2)*f(x)^2 lgdegf A002119 33.1632 ln(1+x)*(ln(1+x)+1) revegf A002119 5.88879 {(n+2)*a(n+1)+(-17*n-4*n^2-16)*a(n+2)+(-58-31*n-4*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=-1,a(2)=7,a(3)=-71} ogf A002135 33.0253 1/2*(-2+x^2)/(-1+x) lgdegf A002135 33.0253 2-x^2+(-2+2*x)*f(x) lgdegf A002135 8.59563 {(n^2+5*n+6)*a(n+1)+(-2*n-8)*a(n+3)+2*a(n+4),a(0)=1,a(1)=1,a(2)=2,a(3)=5} ogf A002136 35.6306 1/2*(x-2)*(x+2)/(-1+x) lgdegf A002137 22.3665 (-2*x+x^2)*f(x)+(2-2*x)*f(x)^2 lgdegf A002137 37.2775 1/2*x*(x-2)/(-1+x) lgdegf A002137 7.53927 {(n^2+5*n+6)*a(n+1)+(-2*n-6)*a(n+2)+(-2*n-6)*a(n+3)+2*a(n+4),a(0)=1,a(1)=0,a(2)=1,a(3)=1} ogf A002171 65.4233 -(2+4*x)/(1-x^2) ogf_with_Euler_Transform A002171 36.0956 {a(n+2)-a(n),a(0)=-2,a(1)=-4} ogf_with_Euler_Transform A002175 26.2886 -(2+2*x+2*x^4)/(-x^2-1-x-x^5-x^3-x^4) ogf_with_Euler_Transform A002203 24.0379 -(-1-2*x+x^2)/(-1+x)/(x^2+2*x-1) lgdogf A002203 38.4607 -(2-2*x)/(x^2-1+2*x) ogf A002203 15.0826 -18+18*x+(19-28*x-9*x^2)*f(x)+(5*x^2-5+10*x)*f(x)^2 ogf A002203 38.4607 2*(x-1)/(-1+2*x+x^2) ogf A002203 20.7896 {-a(n+2)+2*a(n+1)+a(n),a(0)=2,a(1)=2} ogf A002212 25.0271 -1+x+(1-x)*f(x)-x*f(x)^2 ogf A002212 9.24079 1/2*((5*x-1)^(1/2)*(-1+x)^(1/2)+1-x)/x/(-1+x)^(3/2)/(5*x-1)^(1/2) lgdogf A002212 15.8066 1/2*(-x+1+(x-1)^(1/2)*(5*x-1)^(1/2))/x ogf A002212 18.2016 1/2+1/2*x-1/2*(1-2*x+5*x^2)^(1/2) revogf A002212 5.56159 {(5*n+5*n^2)*a(n)+(-35*n-24-11*n^2)*a(n+1)+(48+37*n+7*n^2)*a(n+2)+(-7*n-12-n^2)*a(n+3),a(0)=1,a(1)=1,a(2)=3} ogf A002215 13.6364 -1-3*x+x^3-x^2+(1+2*x-4*x^3-3*x^2)*f(x)-x^3*f(x)^2 ogf A002215 13.6364 -1-3*x-x^2+x^3+(1+2*x-3*x^2-4*x^3)*f(x)-x^3*f(x)^2 ogf A002248 15.8354 -(-2+4*x^2)/(1-4*x+7*x^2-8*x^3+4*x^4) ogf A002248 15.4187 -2*(2*x^2-1)/(2*x-1)/(x-1)/(2*x^2-x+1) ogf A002248 8.02617 -2*(2-9*x-8*x^4-8*x^3+8*x^5+16*x^2)/(-1+x)/(-1+2*x)/(2*x^2-1)/(2*x^2-x+1) lgdogf A002248 6.10323 254-508*x^2+(69+508*x-1281*x^2+1016*x^3-508*x^4)*f(x)+(-686*x^2+784*x^3-98+392*x-392*x^4)*f(x)^2 ogf A002249 38.2479 -(-2+x)/(2*x^2+1-x) ogf A002249 22.7097 -(1-8*x+2*x^2)/(x-2)/(2*x^2-x+1) lgdogf A002249 40.3727 -(x-2)/(2*x^2-x+1) ogf A002249 34.6052 -2+x+(1-x+2*x^2)*f(x) ogf A002249 20.1864 {a(n+2)-a(n+1)+2*a(n),a(0)=2,a(1)=1} ogf A002250 24.4307 (5*x-1)/(-1+4*x)/(3*x-1) ogf A002250 15.4299 -(1-5*x+48*x^4+20*x^3)/(-12*x^2-1+7*x) ogf A002250 24.4307 -(5*x-1)/(-12*x^2-1+7*x) ogf A002250 11.4968 -1+5*x+(-2+12*x-12*x^2)*f(x)+(-12*x^2-1+7*x)*f(x)^2 ogf A002250 13.6357 -2*(1-12*x+30*x^2)/(-1+4*x)/(3*x-1)/(5*x-1) lgdogf A002250 14.6584 1/2/(-5+12*x)*(-1+7*x+(1+6*x+x^2)^(1/2)) revogf A002250 13.9604 {-a(n+2)+7*a(n+1)-12*a(n),a(0)=-1,a(1)=-2} ogf A002264 29.4191 -(1+x+4*x^2)/(-1+x)/(x^2+x+1) lgdogf A002264 37.0936 -x^3+(1-x-x^3+x^4)*f(x) ogf A002264 44.9028 1/(x^2+x+1)/(x-1)^2 ogf A002264 170.631 x^2+1 ogf_with_Euler_Transform A002264 50.1855 x^3/(1-x-x^3+x^4) ogf A002264 6.66526 {(-n-2)*a(n+1)-a(n+2)-a(n+3)+(n+1)*a(n+4),a(0)=0,a(1)=0,a(2)=0,a(3)=1,a(4)=1,a(5)=1,a(6)=2,a(7)=2,a(8)=2,a(9)=3,a(10)=3,a(11)=3} ogf A002265 23.5682 -(1+x+x^2+5*x^3)/(-1+x)/(1+x)/(1+x^2) lgdogf A002265 174.405 1+x^3 ogf_with_Euler_Transform A002265 37.9141 1/(1+x^2)/(x+1)/(x-1)^2 ogf A002265 51.2955 x^4/(1-x-x^4+x^5) ogf A002265 20.7625 {-a(n+4)+a(n),a(0)=1,a(1)=1,a(2)=1,a(3)=5} lgdogf A002266 19.4429 -(1+x+x^2+x^3+6*x^4)/(-1+x)/(x^4+x^3+x^2+x+1) lgdogf A002266 174.986 1+x^4 ogf_with_Euler_Transform A002266 32.4048 1/(1+x+x^2+x^3+x^4)/(x-1)^2 ogf A002266 51.4665 x^5/(1-x-x^5+x^6) ogf A002271 1.65528 4-4*x+x^2+(-4+10*x-8*x^2+2*x^3)*f(x)+(1+6*x^2-4*x-4*x^3+x^4)*f(x)^2 ogf A002275 26.0476 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A002275 18.0329 -1/20*(-11*x-1+(81*x^2+22*x+1)^(1/2))/x revogf A002275 43.9553 1/(10*x-1)/(x-1) ogf A002275 30.5776 x+(-1+11*x-10*x^2)*f(x) ogf A002275 41.3697 x/(1-11*x+10*x^2) ogf A002275 17.5821 {a(n+2)-11*a(n+1)+10*a(n),a(0)=0,a(1)=1} ogf A002276 18.3057 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A002276 12.6732 -1/20*(-2-11*x+(4+44*x+81*x^2)^(1/2))/x revogf A002276 19.7701 2*x+(-1+11*x-10*x^2)*f(x) ogf A002276 26.0133 2*x/(1-11*x+10*x^2) ogf A002276 30.8908 2/(10*x-1)/(x-1) ogf A002276 12.3563 {a(n+2)-11*a(n+1)+10*a(n),a(0)=0,a(1)=2} ogf A002277 18.3057 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A002277 10.516 -1/20*(-3-11*x+(3+22*x+27*x^2)^(1/2)*3^(1/2))/x revogf A002277 19.7701 3*x+(-1+11*x-10*x^2)*f(x) ogf A002277 26.0133 3*x/(1-11*x+10*x^2) ogf A002277 30.8908 3/(10*x-1)/(x-1) ogf A002277 12.3563 {a(n+2)-11*a(n+1)+10*a(n),a(0)=0,a(1)=3} ogf A002278 18.3057 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A002278 12.3563 -1/20*(-4-11*x+(16+88*x+81*x^2)^(1/2))/x revogf A002278 19.7701 4*x+(-1+11*x-10*x^2)*f(x) ogf A002278 26.0133 4*x/(1-11*x+10*x^2) ogf A002278 30.8908 4/(10*x-1)/(x-1) ogf A002278 12.3563 {a(n+2)-11*a(n+1)+10*a(n),a(0)=0,a(1)=4} ogf A002279 18.3057 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A002279 12.055 -1/20*(-5-11*x+(25+110*x+81*x^2)^(1/2))/x revogf A002279 19.7701 5*x+(-1+11*x-10*x^2)*f(x) ogf A002279 26.0133 5*x/(1-11*x+10*x^2) ogf A002279 30.8908 5/(10*x-1)/(x-1) ogf A002279 12.3563 {a(n+2)-11*a(n+1)+10*a(n),a(0)=0,a(1)=5} ogf A002280 18.3057 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A002280 10.2969 -1/20*(-6-11*x+(12+44*x+27*x^2)^(1/2)*3^(1/2))/x revogf A002280 19.7701 6*x+(-1+11*x-10*x^2)*f(x) ogf A002280 26.0133 6*x/(1-11*x+10*x^2) ogf A002280 30.8908 6/(10*x-1)/(x-1) ogf A002280 12.3563 {a(n+2)-11*a(n+1)+10*a(n),a(0)=0,a(1)=6} ogf A002281 23.3001 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A002281 15.344 -1/20*(-7-11*x+(49+154*x+81*x^2)^(1/2))/x revogf A002281 25.1641 7*x+(-1+11*x-10*x^2)*f(x) ogf A002281 33.1107 7*x/(1-11*x+10*x^2) ogf A002281 39.319 7/(10*x-1)/(x-1) ogf A002281 15.7276 {a(n+2)-11*a(n+1)+10*a(n),a(0)=0,a(1)=7} ogf A002282 23.3001 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A002282 15.344 -1/20*(-8-11*x+(64+176*x+81*x^2)^(1/2))/x revogf A002282 25.1641 8*x+(-1+11*x-10*x^2)*f(x) ogf A002282 33.1107 8*x/(1-11*x+10*x^2) ogf A002282 39.319 8/(10*x-1)/(x-1) ogf A002282 15.7276 {a(n+2)-11*a(n+1)+10*a(n),a(0)=0,a(1)=8} ogf A002283 23.3001 -(-11+20*x)/(10*x-1)/(-1+x) lgdogf A002283 15.7276 -1/20*(-9-11*x+3*(9+22*x+9*x^2)^(1/2))/x revogf A002283 25.1641 9*x+(-1+11*x-10*x^2)*f(x) ogf A002283 33.1107 9*x/(1-11*x+10*x^2) ogf A002283 39.319 9/(10*x-1)/(x-1) ogf A002283 15.7276 {a(n+2)-11*a(n+1)+10*a(n),a(0)=0,a(1)=9} ogf A002284 17.2396 -(2-3*x+2*x^2-x^3+2*x^4-3*x^5+2*x^6-13*x^7)/(-1+x^8) ogf_with_Euler_Transform A002288 47.8418 -(8+16*x)/(1-x^2) ogf_with_Euler_Transform A002293 7.46113 {(-840-1712*n-1152*n^2-256*n^3)*a(n+1)+(321*n+210+27*n^3+162*n^2)*a(n+2),a(0)=1,a(1)=1} ogf A002294 5.61251 {(-15120-41250*n-41875*n^2-18750*n^3-3125*n^4)*a(n+1)+(6600*n+3024+5360*n^2+1920*n^3+256*n^4)*a(n+2),a(0)=1,a(1)=1} ogf A002299 29.3169 (x+1)*(x^2+14*x+1)/(x-1)^6 ogf A002299 12.704 -(1+15*x+x^3+15*x^2)/(-15*x^2-1+6*x-15*x^4+6*x^5+20*x^3-x^6) ogf A002299 15.88 -3*(7+35*x+x^3+21*x^2)/(-1+x)/(1+x)/(x^2+14*x+1) lgdogf A002299 12.4957 {(36+17*n+2*n^2)*a(n+1)+(-7*n-6-2*n^2)*a(n+2),a(0)=1,a(1)=21} ogf A002300 24.4338 -(-2-2*x-2*x^2-2*x^3-2*x^4-2*x^5-5*x^6)/(-1+x^7) ogf_with_Euler_Transform A002301 19.2079 (-2+(8+12*x)^(1/3))/(8+12*x)^(1/3) revegf A002301 24.1877 -2/(-1+4*x-6*x^2+4*x^3-x^4) egf A002301 10.2042 -4+(-8*x+12*x^2-8*x^3+2*x^4)*f(x)+(1+x^4-4*x+6*x^2-4*x^3)*f(x)^2 egf A002301 72.5632 -4/(-1+x) lgdegf A002301 72.5632 2/(x-1)^4 egf A002301 18.1408 {(-n-5)*a(n+1)+a(n+2),a(0)=2,a(1)=8} ogf A002302 5.36177 -(30+60*x-12*x^5+30*x^4-40*x^3+2*x^6+30*x^2)/(-225*x^2-15+90*x-225*x^4+300*x^3-15*x^6+90*x^5) egf A002302 8.45161 -60*(2+3*x)/(-1+x)/(x^6-6*x^5+15*x^4-20*x^3+15*x^2+30*x+15) lgdegf A002302 9.4084 2/15*(15+30*x+15*x^2-20*x^3+15*x^4-6*x^5+x^6)/(x-1)^6 egf A002302 4.61708 {(30*n+6*n^2)*a(n)+(-86-70*n-8*n^2)*a(n+1)+(146+63*n+5*n^2)*a(n+2)+(-5*n-15)*a(n+3),a(0)=2,a(1)=16,a(2)=136} ogf A002303 6.48093 16/63*(-441*x^2-504*x-63+x^9-9*x^8+36*x^7-84*x^6+126*x^5-126*x^4+84*x^3)/(x-1)^9 egf A002303 4.50847 {(-9156*n-2610*n^2-186*n^3)*a(n)+(6448-1802*n-1693*n^2-175*n^3)*a(n+1)+(129*n-442+175*n^2)*a(n+2),a(0)=16,a(1)=272} ogf A002309 21.379 (1+76*x+230*x^2+76*x^3+x^4)/(x-1)^6 ogf A002309 11.0039 -(1+76*x+x^4+76*x^3+230*x^2)/(-15*x^2-1+6*x-x^6-15*x^4+20*x^3+6*x^5) ogf A002309 11.0039 -2*(41+420*x+x^4+116*x^3+574*x^2)/(-1+x)/(x^4+76*x^3+230*x^2+76*x+1) lgdogf A002310 32.3858 -(-1+3*x)/(x^2+1-5*x) ogf A002310 20.003 -(2-2*x+3*x^2)/(3*x-1)/(x^2-5*x+1) lgdogf A002310 32.3858 -(3*x-1)/(-5*x+1+x^2) ogf A002310 17.0026 -1/2*(-1-5*x+(1-2*x+21*x^2)^(1/2))/(3+x) revogf A002310 11.5272 -61+183*x+(138-536*x+61*x^2)*f(x)+(-77*x^2-77+385*x)*f(x)^2 ogf A002310 18.8917 {a(n+2)-5*a(n+1)+a(n),a(0)=1,a(1)=2} ogf A002315 34.5643 (x+1)/(1-6*x+x^2) ogf A002315 18.9546 -(-7+2*x+x^2)/(1+x)/(1-6*x+x^2) lgdogf A002315 30.9259 -(1+x)/(-x^2-1+6*x) ogf A002315 13.9903 -1/2*(-6*x-1+(32*x^2+16*x+1)^(1/2))/(-1+x) revogf A002315 11.0866 -9-9*x+(-31-94*x+9*x^2)*f(x)+(40-240*x+40*x^2)*f(x)^2 ogf A002315 15.8809 {-a(n+2)+6*a(n+1)-a(n),a(0)=1,a(1)=7} ogf A002316 15.5119 (1-x+7*x^2+2*x^3)/(11*x^2+1-6*x+x^4+6*x^3) ogf A002316 4.79044 -(-1-x+434*x^5-13*x^8-196*x^4-12*x^3-189*x^6+57*x^7+2*x^9-21*x^2)/(15*x^2+1-4*x+15*x^8+209*x^4-4*x^9-56*x^3+x^10+209*x^6-780*x^5-56*x^7) ogf A002316 7.57558 -(-5+8*x+17*x^4+16*x^3+2*x^6+14*x^5+43*x^2)/(2*x^3+7*x^2-x+1)/(x^4+6*x^3+11*x^2-6*x+1) lgdogf A002317 15.5876 -(-2+7*x+x^2+x^3)/(11*x^2+1-6*x+x^4+6*x^3) ogf A002317 4.84947 -(2-3*x-226*x^5+9*x^8+404*x^4-39*x^3+138*x^6-61*x^7-x^9+17*x^2)/(-15*x^2-1+4*x-15*x^8-209*x^4+4*x^9+56*x^3-x^10-209*x^6+780*x^5+56*x^7) ogf A002317 8.08245 -(5-46*x+16*x^4+88*x^3+x^6+2*x^5+44*x^2)/(x^3+x^2+7*x-2)/(x^4+6*x^3+11*x^2-6*x+1) lgdogf A002317 4.74405 7798-27293*x-3899*x^2-3899*x^3+(37285-120750*x-63481*x^2-43986*x^3-3899*x^4)*f(x)+(-226512*x^2-20592+123552*x-20592*x^4-123552*x^3)*f(x)^2 ogf A002320 27.2306 -(-1+2*x)/(x^2+1-5*x) ogf A002320 27.2306 -(2*x-1)/(-5*x+1+x^2) ogf A002320 16.3384 -(3-2*x+2*x^2)/(-1+2*x)/(x^2-5*x+1) lgdogf A002320 14.2961 -1/2*(-1-5*x+(1+2*x+21*x^2)^(1/2))/(2+x) revogf A002320 10.997 -4+8*x+(17-46*x+4*x^2)*f(x)+(-13+65*x-13*x^2)*f(x)^2 ogf A002320 15.8845 {a(n+2)-5*a(n+1)+a(n),a(0)=1,a(1)=3} ogf A002337 1.4125 197+2744*x^4-198*f(x)+f(x)^2 ogf A002337 1.23594 28/97/x*(-7+(49+2716*x^4)^(1/2)) lgdogf A002337 1.71956 99-14*(49-14*x^4)^(1/2) ogf A002370 7.51606 {(-4*n^3-47*n-24*n^2-30)*a(n+1)+(4*n^2+25+20*n)*a(n+2)-a(n+3),a(0)=1,a(1)=1,a(2)=6} ogf A002370 7.60772 {(15+16*n+4*n^2)*a(n+1)+(-25-20*n-4*n^2)*a(n+2)+(n+3)*a(n+3),a(0)=1,a(1)=1,a(2)=3} egf A002378 82.1752 -2/(x-1)^3 ogf A002378 91.3058 -3/(-1+x) lgdogf A002378 30.4353 2*x+(-1+3*x-3*x^2+x^3)*f(x) ogf A002378 39.1311 2*x/(1-3*x+3*x^2-x^3) ogf A002378 15.8029 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=2,a(2)=6} ogf A002394 1.29965 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A002408 33.2078 -(-8-8*x^2-8*x^3)/(-1+x^4) ogf_with_Euler_Transform A002409 50.9517 -1/(2*x-1)^7 ogf A002409 50.9517 -14/(-1+2*x) lgdogf A002409 10.7267 1/(1-14*x+84*x^2-280*x^3+560*x^4-672*x^5+448*x^6-128*x^7) ogf A002409 13.2918 {(-2-n)*a(n+2)+(16+2*n)*a(n+1),a(0)=1,a(1)=14} ogf A002411 53.9878 (2*x+1)/(x-1)^4 ogf A002411 23.1376 -(-x-2*x^2)/(1-4*x+x^4+6*x^2-4*x^3) ogf A002411 35.2094 -6*(1+x)/(1+2*x)/(-1+x) lgdogf A002411 6.86285 6151*x+12302*x^2+(-6151+29734*x-26646*x^2+24604*x^3-6151*x^4)*f(x)+(-5130+20520*x-5130*x^4-30780*x^2+20520*x^3)*f(x)^2 ogf A002411 12.4587 {(n+2)*a(n+3)+(-5+n)*a(n+2)+(-6-2*n)*a(n+1),a(0)=0,a(1)=1,a(2)=6} ogf A002411 12.6534 {(n+2)*a(n+3)+(n-5)*a(n+2)+(-6-2*n)*a(n+1),a(0)=0,a(1)=1,a(2)=6} ogf A002412 47.4636 (3*x+1)/(x-1)^4 ogf A002412 20.3415 -(-x-3*x^2)/(1-4*x+x^4+6*x^2-4*x^3) ogf A002412 30.9545 -(7+9*x)/(3*x+1)/(-1+x) lgdogf A002412 5.27373 167481*x+502443*x^2+(-167481+775652*x-687702*x^2+669924*x^3-167481*x^4)*f(x)+(-105728*x^4-105728+422912*x+422912*x^3-634368*x^2)*f(x)^2 ogf A002412 10.7872 {(-2-n)*a(n+3)+(5-2*n)*a(n+2)+(9+3*n)*a(n+1),a(0)=0,a(1)=1,a(2)=7} ogf A002413 50.257 (4*x+1)/(x-1)^4 ogf A002413 22.8441 -(1+4*x)/(-6*x^2-1+4*x+4*x^3-x^4) ogf A002413 5.79888 -207901-831604*x+(144276-1086104*x+1247406*x^2-831604*x^3+207901*x^4)*f(x)+(63625-254500*x^3-254500*x+381750*x^2+63625*x^4)*f(x)^2 ogf A002413 30.1542 -4*(2+3*x)/(1+4*x)/(-1+x) lgdogf A002413 10.9254 {(n+3)*a(n+3)+(-2+3*n)*a(n+2)+(-16-4*n)*a(n+1),a(0)=1,a(1)=8,a(2)=26} ogf A002414 49.9228 (5*x+1)/(x-1)^4 ogf A002414 22.6922 -(1+5*x)/(-6*x^2-1+4*x+4*x^3-x^4) ogf A002414 29.9537 -3*(3+5*x)/(5*x+1)/(-1+x) lgdogf A002414 10.8528 {(n+3)*a(n+3)+(-1+4*n)*a(n+2)+(-20-5*n)*a(n+1),a(0)=1,a(1)=9,a(2)=30} ogf A002415 19.036 -(-x^3-x^2)/(1-5*x+10*x^2-x^5-10*x^3+5*x^4) ogf A002415 58.4678 -(x+1)/(x-1)^5 ogf A002415 35.5891 -2*(2*x+3)/(-1+x)/(1+x) lgdogf A002415 272.85 6-x ogf_with_Euler_Transform A002415 14.1129 {(n+1)*a(n+3)-6*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=0,a(2)=1} ogf A002415 14.1129 {(n+1)*a(n+3)-6*a(n+2)+(-n-3)*a(n+1),a(0)=0,a(1)=0,a(2)=1} ogf A002417 19.3901 -(-1-3*x)/(1-5*x+10*x^2-x^5-10*x^3+5*x^4) ogf A002417 49.687 -(3*x+1)/(x-1)^5 ogf A002417 31.7997 -4*(2+3*x)/(3*x+1)/(-1+x) lgdogf A002417 11.5216 {(n+3)*a(n+3)+(-4+2*n)*a(n+2)+(-15-3*n)*a(n+1),a(0)=1,a(1)=8,a(2)=30} ogf A002418 43.4502 -(4*x+1)/(x-1)^5 ogf A002418 28.9668 -(9+16*x)/(1+4*x)/(-1+x) lgdogf A002418 16.1675 -(x+4*x^2)/(-1+5*x-5*x^4-10*x^2+10*x^3+x^5) ogf A002418 10.3762 {(-2-n)*a(n+3)+(6-3*n)*a(n+2)+(16+4*n)*a(n+1),a(0)=0,a(1)=1,a(2)=9} ogf A002419 17.7428 -(-1-5*x)/(1-5*x+10*x^2-x^5-10*x^3+5*x^4) ogf A002419 45.4659 -(5*x+1)/(x-1)^5 ogf A002419 27.979 -10*(1+2*x)/(5*x+1)/(-1+x) lgdogf A002419 10.3922 {(n+3)*a(n+3)+(-2+4*n)*a(n+2)+(-25-5*n)*a(n+1),a(0)=1,a(1)=10,a(2)=40} ogf A002420 56.8854 (-4*x+1)^(1/2) ogf A002420 61.2612 -1+4*x+f(x)^2 ogf A002420 79.6396 2/(-1+4*x) lgdogf A002420 17.6977 {(n+2)*a(n+2)+(-2-4*n)*a(n+1),a(0)=1,a(1)=-2} ogf A002421 53.9333 (-4*x+1)^(3/2) ogf A002421 58.082 (1-4*x)^(3/2) ogf A002421 26.9667 -1+12*x-48*x^2+64*x^3+f(x)^2 ogf A002421 75.5066 6/(-1+4*x) lgdogf A002421 17.1606 {(n+2)*a(n+2)+(2-4*n)*a(n+1),a(0)=1,a(1)=-6} ogf A002422 45.6709 (-4*x+1)^(5/2) ogf A002422 49.1841 (1-4*x)^(5/2) ogf A002422 37.6114 -10+(-1+4*x)*f(x) lgdogf A002422 58.1266 10/(-1+4*x) lgdogf A002422 14.2087 {(n+2)*a(n+2)+(6-4*n)*a(n+1),a(0)=1,a(1)=-10} ogf A002423 40.7004 (-4*x+1)^(7/2) ogf A002423 43.8312 (1-4*x)^(7/2) ogf A002423 33.518 -14+(-1+4*x)*f(x) lgdogf A002423 51.8006 14/(-1+4*x) lgdogf A002423 12.3871 {(n+2)*a(n+2)+(10-4*n)*a(n+1),a(0)=1,a(1)=-14} ogf A002424 48.8259 (-4*x+1)^(9/2) ogf A002424 52.5817 (1-4*x)^(9/2) ogf A002424 40.2095 -18+(-1+4*x)*f(x) lgdogf A002424 62.142 18/(-1+4*x) lgdogf A002424 14.86 {(n+2)*a(n+2)+(14-4*n)*a(n+1),a(0)=1,a(1)=-18} ogf A002426 19.1571 (-x+(4*x^2+1)^(1/2))/(1+3*x^2)*x revogf A002426 27.8648 -(3*x+1)/(1+x)/(3*x-1) lgdogf A002426 26.6533 -1+(1-2*x-3*x^2)*f(x)^2 ogf A002426 25.5428 1/(-(x+1)*(3*x-1))^(1/2) ogf A002426 9.14965 {(n+3)*a(n+3)+(-5-2*n)*a(n+2)+(-6-3*n)*a(n+1),a(0)=1,a(1)=1,a(2)=3} ogf A002446 24.0806 -(-5+8*x)/(-1+4*x)/(-1+x) lgdogf A002446 26.1745 6*x+(-1+5*x-4*x^2)*f(x) ogf A002446 35.4126 6*x/(1-5*x+4*x^2) ogf A002446 37.6259 6/(-1+4*x)/(x-1) ogf A002446 15.8425 {a(n+2)-5*a(n+1)+4*a(n),a(0)=0,a(1)=6} ogf A002447 31.7389 -1/(-1+2*x^2+3*x^3) ogf A002447 10.0506 -207+(350-414*x^2-621*x^3)*f(x)+(429*x^3-143+286*x^2)*f(x)^2 ogf A002447 22.3348 -x*(4+9*x)/(-1+2*x^2+3*x^3) lgdogf A002447 35.4729 1/(1-2*x^2-3*x^3) ogf A002447 13.4009 {a(n+3)-2*a(n+1)-3*a(n),a(0)=1,a(1)=0,a(2)=2} ogf A002448 62.2467 -(-2-x)/(-1+x^2) ogf_with_Euler_Transform A002448 66.3965 -(-2-x)/(x^2-1) ogf_with_Euler_Transform A002448 33.1982 {-a(n+2)+a(n),a(0)=-2,a(1)=-1} ogf_with_Euler_Transform A002450 28.8016 -(-5+8*x)/(-1+4*x)/(-1+x) lgdogf A002450 17.562 -1/8*(-1-5*x+(x+1)^(1/2)*(9*x+1)^(1/2))/x revogf A002450 45.0025 1/(-1+4*x)/(x-1) ogf A002450 34.2876 x+(-1+5*x-4*x^2)*f(x) ogf A002450 48.0027 x/(1-5*x+4*x^2) ogf A002450 18.9484 {a(n+2)-5*a(n+1)+4*a(n),a(0)=0,a(1)=1} ogf A002451 28.862 -1/(x-1)/(-1+4*x)/(9*x-1) ogf A002451 6.01293 -1146960+(14098951-16057440*x+56201040*x^2-41290560*x^3)*f(x)+(-12951991+181327874*x-634647559*x^2+466271676*x^3)*f(x)^2 ogf A002451 16.7803 -2*(7-49*x+54*x^2)/(-1+x)/(-1+4*x)/(-1+9*x) lgdogf A002451 30.0646 1/(1-14*x+49*x^2-36*x^3) ogf A002451 12.0259 {a(n+3)-14*a(n+2)+49*a(n+1)-36*a(n),a(0)=1,a(1)=14,a(2)=147} ogf A002452 44.5936 -1/(-1+10*x-9*x^2) ogf A002452 17.4497 -1/18*(-10*x-1+(16*x+1)^(1/2)*(1+4*x)^(1/2))/x revogf A002452 29.7291 -2*(-5+9*x)/(-1+9*x)/(-1+x) lgdogf A002452 15.7389 -9+(-32-90*x+81*x^2)*f(x)+(41-410*x+369*x^2)*f(x)^2 ogf A002452 53.5124 1/(9*x-1)/(x-1) ogf A002452 19.5777 {-a(n+2)+10*a(n+1)-9*a(n),a(0)=1,a(1)=10} ogf A002453 12.1616 -(35-518*x+675*x^2)/(-1+x)/(25*x-1)/(-1+9*x) lgdogf A002453 21.4044 -1/(x-1)/(25*x-1)/(9*x-1) ogf A002453 20.5811 1/(1-35*x+259*x^2-225*x^3) ogf A002453 8.6308 {a(n+3)-35*a(n+2)+259*a(n+1)-225*a(n),a(0)=1,a(1)=35,a(2)=966} ogf A002454 10.7908 {(4*n^2+16*n+16)*a(n+1)-a(n+2),a(0)=1,a(1)=4} ogf A002457 19.4008 -1+(1-12*x+48*x^2-64*x^3)*f(x)^2 ogf A002457 56.4388 -6/(-1+4*x) lgdogf A002457 38.8017 1/(-4*x+1)^(3/2) ogf A002457 41.3885 1/(1-4*x)^(3/2) ogf A002457 13.7962 {(-n-2)*a(n+2)+(10+4*n)*a(n+1),a(0)=1,a(1)=6} ogf A002458 10.9926 -10+288*x+(1-64*x+768*x^2)*f(x)+(-64*x^2+512*x^3+2*x)*f(x)^2 lgdogf A002458 14.0331 2^(1/2)/(1-16*x)^(1/2)/(1+(1-16*x)^(1/2))^(1/2) ogf A002458 10.147 {(-126-128*n-32*n^2)*a(n+1)+(9*n+10+2*n^2)*a(n+2),a(0)=1,a(1)=10} ogf A002467 10.1853 {(n+2)*a(n+1)+(n+2)*a(n+2)-a(n+3),a(0)=0,a(1)=1,a(2)=1} ogf A002468 9.33653 -exp(-x)*(-3*x+1+4*x*exp(x)-3*x^2*exp(x)+x^3*exp(x))/(x-1)^3 egf A002469 23.6624 exp(-x)/(x-1)^4*(3*x^2+2*x+1) egf A002474 9.4234 {(4*n^2+20*n+24)*a(n+1)-a(n+2),a(0)=2,a(1)=16} ogf A002477 12.2173 -(-1-10*x)/(1110*x^2+1-111*x-1000*x^3) ogf A002477 13.6546 -(1+10*x)/(x-1)/(100*x-1)/(10*x-1) ogf A002477 6.92919 -(121-2220*x+20000*x^3-8100*x^2)/(-1+x)/(10*x+1)/(100*x-1)/(10*x-1) lgdogf A002477 6.82729 {a(n+3)-111*a(n+2)+1110*a(n+1)-1000*a(n),a(0)=1,a(1)=121,a(2)=12321} ogf A002478 25.6411 -(1+x)*(3*x+1)/(2*x^2-1+x+x^3) lgdogf A002478 40.4859 -1/(-1+x+2*x^2+x^3) ogf A002478 13.986 5+(-7+5*x+10*x^2+5*x^3)*f(x)+(2-2*x-4*x^2-2*x^3)*f(x)^2 ogf A002478 15.083 {-a(n+3)+a(n+2)+2*a(n+1)+a(n),a(0)=1,a(1)=1,a(2)=3} ogf A002492 35.8348 -(3*x+5)/(-1+x)/(1+x) lgdogf A002492 20.3387 -(4*x+4*x^2)/(-1+4*x-x^4-6*x^2+4*x^3) ogf A002492 50.1688 4*(x+1)/(x-1)^4 ogf A002492 6.90396 7172*x+7172*x^2+(-1793+9316*x-8614*x^2+7172*x^3-1793*x^4)*f(x)+(-536*x^4-536+2144*x+2144*x^3-3216*x^2)*f(x)^2 ogf A002492 12.7548 {(n+2)*a(n+3)-5*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=4,a(2)=20} ogf A002501 21.4068 -(-1-5*x)/(61*x^2+1-14*x-84*x^3) ogf A002501 11.6105 -(19-122*x+840*x^3-53*x^2)/(5*x+1)/(-1+4*x)/(3*x-1)/(7*x-1) lgdogf A002501 20.7581 -(5*x+1)/(3*x-1)/(7*x-1)/(-1+4*x) ogf A002501 6.17132 -63721-318605*x+(121777-601814*x+3886981*x^2-5352564*x^3)*f(x)+(-3541416*x^2-58056+812784*x+4876704*x^3)*f(x)^2 ogf A002501 11.4169 {a(n+3)-14*a(n+2)+61*a(n+1)-84*a(n),a(0)=1,a(1)=19,a(2)=205} ogf A002502 7.49013 (-1-27*x+136*x^2+480*x^3)/(6*x-1)/(5*x-1)/(15*x-1)/(-1+4*x)/(8*x-1) ogf A002502 6.96998 -(1+27*x-480*x^3-136*x^2)/(-539*x^2-1+38*x-11640*x^4+14400*x^5+3622*x^3) ogf A002506 10.1483 {(4*n^2+24*n+32)*a(n+1)-a(n+2),a(0)=8,a(1)=96} ogf A002507 24.1731 -(-2+8*x+12*x^2+8*x^3-2*x^4)/(1-x^6) ogf_with_Euler_Transform A002508 24.3479 -(2-8*x-12*x^2-8*x^3+2*x^4)/(1-x^6) ogf_with_Euler_Transform A002509 11.6922 -(-1+4*x-x^2+4*x^3-x^4+4*x^5+6*x^6+4*x^7-x^8+4*x^9-x^10+4*x^11-x^12)/(-1+x^14) ogf_with_Euler_Transform A002510 8.86921 -(1+x+6*x^2+x^3+8*x^4+6*x^5+x^6+x^7+6*x^8+8*x^9+x^10+6*x^11+x^12+x^13)/(-1+x^15) ogf_with_Euler_Transform A002512 24.3432 -(2+2*x+2*x^2+4*x^3)/(-1+x^4) ogf_with_Euler_Transform A002512 24.3432 -(2+2*x^2+2*x+4*x^3)/(-1+x^4) ogf_with_Euler_Transform A002512 16.8084 {-a(n+4)+a(n),a(0)=2,a(1)=2,a(2)=2,a(3)=4} ogf_with_Euler_Transform A002513 44.4123 -(-1-2*x)/(1-x^2) ogf_with_Euler_Transform A002513 27.9633 {a(n+2)-a(n),a(0)=1,a(1)=2} ogf_with_Euler_Transform A002521 2.06021 -1-2184*x^3+(3+4368*x^3)*f(x)+(-2184*x^3-3)*f(x)^2+f(x)^3 ogf A002522 26.5081 -(-1+x-2*x^2)/(3*x^2+1-3*x-x^3) ogf A002522 41.0876 -(2*x^2-x+1)/(x-1)^3 ogf A002522 26.5081 -2*(1+x+x^2)/(-1+x)/(2*x^2-x+1) lgdogf A002522 10.1451 -31+31*x-62*x^2+(107-169*x+245*x^2-31*x^3)*f(x)+(-76+228*x-228*x^2+76*x^3)*f(x)^2 ogf A002522 15.8029 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=2,a(2)=5} ogf A002523 9.58005 -(-1+3*x-7*x^3-2*x^4-17*x^2)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A002523 16.4229 -(1-3*x+17*x^2+7*x^3+2*x^4)/(x-1)^5 ogf A002523 9.12385 -2*(1+11*x+x^4+11*x^3+36*x^2)/(-1+x)/(2*x^4+7*x^3+17*x^2-3*x+1) lgdogf A002524 29.3255 -(-1+x)/(-2*x^3+1-2*x+x^5) ogf A002524 14.3861 -(1-5*x^4-4*x^3+4*x^5+6*x^2)/(-1+x)/(x^5-2*x^3-2*x+1) lgdogf A002524 30.4985 -(x-1)/(-2*x^3+1-2*x+x^5) ogf A002525 18.658 -(-2-6*x^2+5*x^4)/(x^5-2*x^3-2*x+1) lgdogf A002525 31.0967 -x/(-1+2*x+2*x^3-x^5) ogf A002525 32.6515 1/(-2*x^3+1-2*x+x^5) ogf A002525 12.0932 x+(-1+8*x+2*x^3-x^5)*f(x)+(12*x^3-6+12*x-6*x^5)*f(x)^2 ogf A002530 29.1991 -(-x+x^3-x^2)/(1+x^4-4*x^2) ogf A002530 14.0781 -(1+6*x-3*x^4-4*x^3+2*x^5+4*x^2)/(x^2-x-1)/(x^4-4*x^2+1) lgdogf A002530 32.8489 -(x^2-x-1)/(1-4*x^2+x^4) ogf A002530 10.2386 2*x+2*x^2-2*x^3+(-2+11*x+19*x^2-11*x^3-2*x^4)*f(x)+(-11-11*x^4+44*x^2)*f(x)^2 ogf A002531 24.5629 (1+x-2*x^2+x^3)/(1-4*x^2+x^4) ogf A002531 10.6317 -(-1-4*x+7*x^4+4*x^3+x^6-4*x^5-7*x^2)/(x^3-2*x^2+x+1)/(x^4-4*x^2+1) lgdogf A002531 22.9782 -(1+x+x^3-2*x^2)/(-1-x^4+4*x^2) ogf A002531 8.28285 -13-13*x+26*x^2-13*x^3+(-53-66*x+80*x^2-66*x^3+13*x^4)*f(x)+(66+66*x^4-264*x^2)*f(x)^2 ogf A002532 37.7556 -1/(-1+2*x+5*x^2) ogf A002532 26.7436 -2*(1+5*x)/(5*x^2-1+2*x) lgdogf A002532 30.5641 -x+(1-2*x-5*x^2)*f(x) ogf A002532 37.7556 -x/(-1+2*x+5*x^2) ogf A002532 17.829 1/10/x*(-2*x-1+(24*x^2+4*x+1)^(1/2)) revogf A002532 16.4576 {-a(n+2)+2*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A002533 30.7403 (x-1)/(-1+2*x+5*x^2) ogf A002533 16.6164 -(-1-10*x+5*x^2)/(-1+x)/(5*x^2-1+2*x) lgdogf A002533 29.2765 -(1-x)/(-1+2*x+5*x^2) ogf A002533 10.4204 -53+53*x+(107-160*x-265*x^2)*f(x)+(270*x^2-54+108*x)*f(x)^2 ogf A002533 15.7643 {-a(n+2)+2*a(n+1)+5*a(n),a(0)=1,a(1)=1} ogf A002534 38.8159 -1/(-1+2*x+9*x^2) ogf A002534 27.4946 -2*(1+9*x)/(9*x^2-1+2*x) lgdogf A002534 31.4224 -x+(1-2*x-9*x^2)*f(x) ogf A002534 38.8159 -x/(-1+2*x+9*x^2) ogf A002534 18.3297 1/18/x*(-2*x-1+(40*x^2+4*x+1)^(1/2)) revogf A002534 16.9198 {-a(n+2)+2*a(n+1)+9*a(n),a(0)=0,a(1)=1} ogf A002535 31.7805 (x-1)/(-1+2*x+9*x^2) ogf A002535 17.1786 -(-1-18*x+9*x^2)/(-1+x)/(9*x^2-1+2*x) lgdogf A002535 30.2671 -(1-x)/(-1+2*x+9*x^2) ogf A002535 9.93141 -129+129*x+(259-388*x-1161*x^2)*f(x)+(1170*x^2-130+260*x)*f(x)^2 ogf A002535 17.1786 1/2/(9*x-1)*(-2*x-1+(40*x^2+1)^(1/2)) revogf A002535 16.2977 {-a(n+2)+2*a(n+1)+9*a(n),a(0)=1,a(1)=1} ogf A002536 24.043 -(-1-x+3*x^2)/(1-8*x^2+9*x^4) ogf A002536 22.4918 -(-x+3*x^3-x^2)/(1+9*x^4-8*x^2) ogf A002536 10.8945 -(1+10*x-27*x^4-36*x^3+54*x^5+8*x^2)/(3*x^2-x-1)/(9*x^4-8*x^2+1) lgdogf A002536 8.60798 -9*x-9*x^2+27*x^3+(9-31*x-103*x^2+93*x^3+81*x^4)*f(x)+(31+279*x^4-248*x^2)*f(x)^2 ogf A002537 19.2864 (1+x-4*x^2+3*x^3)/(1-8*x^2+9*x^4) ogf A002537 8.15962 -(-1-8*x+51*x^4+36*x^3+27*x^6-72*x^5-17*x^2)/(3*x^3-4*x^2+x+1)/(9*x^4-8*x^2+1) lgdogf A002537 18.1843 -(1+x+3*x^3-4*x^2)/(-1-9*x^4+8*x^2) ogf A002537 6.30149 -153-153*x+612*x^2-459*x^3+(-281-434*x+512*x^2-1302*x^3+1377*x^4)*f(x)+(434+3906*x^4-3472*x^2)*f(x)^2 ogf A002538 4.39253 {(-80-56*n-13*n^2-n^3)*a(n+1)+(34+17*n+2*n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=8,a(2)=58} ogf A002544 25.8784 (2*x+1)/(-4*x+1)^(5/2) ogf A002544 27.1107 (2*x+1)/(1-4*x)^(5/2) ogf A002544 21.8971 -12*(1+x)/(1+2*x)/(-1+4*x) lgdogf A002544 8.75885 -6732-6732*x+(1365-318*x-4488*x^2)*f(x)+(536*x^2-67+134*x)*f(x)^2 lgdogf A002544 8.13322 {(-n-3)*a(n+3)+(16+2*n)*a(n+2)+(20+8*n)*a(n+1),a(0)=1,a(1)=12,a(2)=90} ogf A002561 16.2908 (1-4*x+36*x^2+56*x^3+31*x^4)/(x-1)^6 ogf A002561 8.2601 -(-x-36*x^3-31*x^5-56*x^4+4*x^2)/(1-6*x+15*x^2-20*x^3+15*x^4-6*x^5+x^6) ogf A002561 8.3781 -2*(1+26*x+31*x^4+146*x^3+156*x^2)/(-1+x)/(31*x^4+56*x^3+36*x^2-4*x+1) lgdogf A002570 15.2993 -(1+8*x+6*x^3-17*x^2)/(-1+x)/(1+x)/(x^2-3*x+1) lgdogf A002570 24.2678 -1/(x-1)/(-3*x+1+x^2)/(x+1)^3 ogf A002570 26.0654 1/(1-x-5*x^2+5*x^4+x^5-x^6) ogf A002571 16.6527 -(-1-4*x-x^2+x^3)/(-3*x+1+x^2)/(x+1)^2 ogf A002571 17.5778 -(1+4*x-x^3+x^2)/(4*x^2-1+x-x^4+x^3) ogf A002571 9.7354 -(5+5*x-3*x^4-4*x^3+x^5+10*x^2)/(1+x)/(x^2-3*x+1)/(x^3-x^2-4*x-1) lgdogf A002571 6.02668 73+292*x+73*x^2-73*x^3+(104+781*x+469*x^2-104*x^3-73*x^4)*f(x)+(708*x^2-177+177*x-177*x^4+177*x^3)*f(x)^2 ogf A002571 7.03113 {(-n-6)*a(n+1)+(2*n+13)*a(n+2)+(2*n+9)*a(n+3)+(-n-5)*a(n+4),a(0)=1,a(1)=5,a(2)=10,a(3)=30} ogf A002578 2.64798 -(x^4-x^3+1)/(x-1)^3 ogf A002593 24.902 -(x+1)*(x^2+22*x+1)/(x-1)^5 ogf A002593 12.2246 -(x+23*x^3+x^4+23*x^2)/(-1+5*x-10*x^2+10*x^3-5*x^4+x^5) ogf A002593 13.7215 -2*(14+69*x+x^3+36*x^2)/(-1+x)/(1+x)/(x^2+22*x+1) lgdogf A002593 6.86075 {(-54-47*n-10*n^2)*a(n+1)+(144+20*n^2+80*n)*a(n+2)+(-26-33*n-10*n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=28} ogf A002594 12.182 -(-1-237*x-1682*x^3-x^5-237*x^4-1682*x^2)/(-x^7+1-7*x+21*x^2-35*x^3+35*x^4-21*x^5+7*x^6) ogf A002594 23.8225 -(x+1)*(x^4+236*x^3+1446*x^2+236*x+1)/(x-1)^7 ogf A002594 12.0451 -2*(122+2393*x+358*x^4+3838*x^3+x^5+6728*x^2)/(-1+x)/(1+x)/(x^4+236*x^3+1446*x^2+236*x+1) lgdogf A002597 17.8818 -(1+2*x)*(7*x^2+4*x+1)/(-1+x)/(1+x)/(x^2+x+1) lgdogf A002597 9.57954 -1/(-1+x+2*x^2+x^3-4*x^4-5*x^5+3*x^6+6*x^7+3*x^8-5*x^9-4*x^10+x^11+2*x^12+x^13-x^14) ogf A002597 61.8986 1+2*x+3/2*x^2 egf_with_Euler_Transform A002597 27.7476 1/(x+1)^2/(x^2+x+1)^3/(x-1)^6 ogf A002597 26.8227 {-a(n+3),a(0)=1,a(1)=2,a(2)=3} ogf_with_Euler_Transform A002604 5.97194 -(-1+5*x-282*x^3-51*x^5-317*x^4-72*x^2-2*x^6)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A002604 10.4509 -(1-5*x+72*x^2+282*x^3+317*x^4+51*x^5+2*x^6)/(x-1)^7 ogf A002604 5.54537 -2*(1+57*x+603*x^4+1198*x^3+x^6+57*x^5+603*x^2)/(-1+x)/(2*x^6+51*x^5+317*x^4+282*x^3+72*x^2-5*x+1) lgdogf A002605 44.0155 -1/(-1+2*x+2*x^2) ogf A002605 31.1777 -2*(1+2*x)/(2*x^2+2*x-1) lgdogf A002605 44.0155 -x/(-1+2*x+2*x^2) ogf A002605 21.379 1/4/x*(-2*x-1+(12*x^2+4*x+1)^(1/2)) revogf A002605 17.8158 x+(-1+4*x+2*x^2)*f(x)+(4*x^2-2+4*x)*f(x)^2 ogf A002605 19.1863 {-a(n+2)+2*a(n+1)+2*a(n),a(0)=0,a(1)=1} ogf A002620 51.7706 -1/(x+1)/(x-1)^3 ogf A002620 36.0143 -2*(1+2*x)/(-1+x)/(1+x) lgdogf A002620 30.6789 -x^2+(1-2*x+2*x^3-x^4)*f(x) ogf A002620 276.11 x+2 ogf_with_Euler_Transform A002620 39.4443 x^2/(1-2*x+2*x^3-x^4) ogf A002620 14.0395 {a(n+4)-2*a(n+3)+2*a(n+1)-a(n),a(0)=0,a(1)=0,a(2)=1,a(3)=2} ogf A002621 11.8447 -(2+6*x+13*x^4+17*x^3+11*x^5+11*x^2)/(-1+x)/(1+x)/(1+x^2)/(x^2+x+1) lgdogf A002621 18.4557 -1/(-1+2*x-x^3-2*x^5+2*x^6+x^8-2*x^10+x^11) ogf A002621 22.0443 -1/(1+x^2)/(x^2+x+1)/(x+1)^2/(x-1)^5 ogf A002621 72.1451 2+x+x^2+x^3 ogf_with_Euler_Transform A002621 22.0443 {a(n+4),a(0)=2,a(1)=1,a(2)=1,a(3)=1} ogf_with_Euler_Transform A002622 7.43407 -(2+8*x+16*x^9+56*x^7+54*x^4+36*x^3+34*x^8+67*x^6+68*x^5+19*x^2)/(-1+x)/(1+x)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(1+x^2) lgdogf A002622 17.8734 -1/(-1+2*x-x^3-x^5+2*x^8-x^11-x^13+2*x^15-x^16) ogf A002622 15.85 1/(x^2+x+1)/(1+x+x^2+x^3+x^4)/(1+x^2)/(x+1)^2/(x-1)^6 ogf A002622 56.0034 2+x+x^2+x^3+x^4 ogf_with_Euler_Transform A002622 19.0921 {-a(n+5),a(0)=2,a(1)=1,a(2)=1,a(3)=1,a(4)=1} ogf_with_Euler_Transform A002623 36.8514 -(3+5*x)/(-1+x)/(1+x) lgdogf A002623 23.4509 -1/(-1+3*x-2*x^2-2*x^3+3*x^4-x^5) ogf A002623 51.592 1/(x+1)/(x-1)^4 ogf A002623 257.96 x+3 ogf_with_Euler_Transform A002623 13.3428 {(n+3)*a(n+3)-3*a(n+2)+(-6-n)*a(n+1),a(0)=1,a(1)=3,a(2)=7} ogf A002623 35.1764 {a(n+2),a(0)=3,a(1)=1} ogf_with_Euler_Transform A002624 36.5374 -(3+7*x)/(-1+x)/(1+x) lgdogf A002624 18.7143 -1/(-1+3*x-x^2-5*x^3+5*x^4+x^5-3*x^6+x^7) ogf A002624 42.6269 -1/(x+1)^2/(x-1)^5 ogf A002624 153.457 3+2*x ogf_with_Euler_Transform A002624 13.229 {(n+3)*a(n+3)-3*a(n+2)+(-8-n)*a(n+1),a(0)=1,a(1)=3,a(2)=8} ogf A002624 34.8766 {a(n+2),a(0)=3,a(1)=2} ogf_with_Euler_Transform A002625 20.1642 -(1+2*x)*(5*x^2+4*x+3)/(x^2+x+1)/(-1+x)/(1+x) lgdogf A002625 15.1231 -1/(-1+3*x-x^2-4*x^3+2*x^4+2*x^5+2*x^6-4*x^7-x^8+3*x^9-x^10) ogf A002625 33.607 1/(x^2+x+1)/(x+1)^2/(x-1)^6 ogf A002625 69.7991 3+2*x+1/2*x^2 egf_with_Euler_Transform A002625 30.2463 {-a(n+3),a(0)=3,a(1)=2,a(2)=1} ogf_with_Euler_Transform A002626 11.5776 -(3+10*x+17*x^4+24*x^3+14*x^5+16*x^2)/(-1+x)/(1+x)/(1+x^2)/(x^2+x+1) lgdogf A002626 10.0933 -1/(-1+3*x-x^2-4*x^3+3*x^4-x^5+3*x^6-3*x^8+x^9-3*x^10+4*x^11+x^12-3*x^13+x^14) ogf A002626 21.8688 -1/(1+x^2)/(x^2+x+1)/(x+1)^3/(x-1)^7 ogf A002626 60.5598 3+2*x+x^2+x^3 ogf_with_Euler_Transform A002626 21.2778 {-a(n+4),a(0)=3,a(1)=2,a(2)=1,a(3)=1} ogf_with_Euler_Transform A002627 22.7032 -exp(x)*(x-2+exp(-x))/(x-1)^2 egf A002627 11.757 {(-2-n)*a(n+1)+(n+4)*a(n+2)-a(n+3),a(0)=0,a(1)=1,a(2)=3} ogf A002633 25.371 -(3-2*x+x^2)/(-1+x)^2 lgdegf A002633 19.0282 -3+2*x-x^2+(-1+2*x-x^2)*f(x) lgdegf A002633 16.1452 1/exp(-2)*exp(-(x+1)*(x-2)/(x-1)) egf A002633 5.85485 {(-5*n-n^2-6)*a(n+1)+(-3*n-n^2)*a(n+2)+(3+2*n)*a(n+3)-a(n+4),a(0)=1,a(1)=-3,a(2)=5,a(3)=-3} ogf A002655 27.4339 -(-1-x-x^2-x^3-x^4-x^5-2*x^6)/(-1+x^7) ogf_with_Euler_Transform A002656 20.934 -(-3-3*x-3*x^2-3*x^3-3*x^4-3*x^5-6*x^6)/(-1+x^7) ogf_with_Euler_Transform A002662 30.6088 -(-5+8*x)/(-1+2*x)/(-1+x) lgdogf A002662 45.0129 1/(2*x-1)/(x-1)^3 ogf A002662 21.8634 x^3+(-1+5*x-9*x^2+7*x^3-2*x^4)*f(x) ogf A002662 26.3869 x^3/(1-5*x+9*x^2-7*x^3+2*x^4) ogf A002662 11.0901 {a(n+3)*n+(-2-3*n)*a(n+2)+(4+2*n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A002662 11.0901 {n*a(n+3)+(-2-3*n)*a(n+2)+(4+2*n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A002663 34.9122 -1/(2*x-1)/(x-1)^4 ogf A002663 24.17 -2*(5*x-3)/(-1+2*x)/(-1+x) lgdogf A002663 14.6144 x^4+(-1+6*x-14*x^2+16*x^3-9*x^4+2*x^5)*f(x) ogf A002663 16.9843 x^4/(1-6*x+14*x^2-16*x^3+9*x^4-2*x^5) ogf A002663 8.26869 {(1-n)*a(n+3)+3*a(n+2)*n+(-4-2*n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=1} ogf A002663 8.26869 {(1-n)*a(n+3)+3*n*a(n+2)+(-4-2*n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=1} ogf A002664 23.9059 -(-7+12*x)/(-1+2*x)/(-1+x) lgdogf A002664 36.5619 1/(2*x-1)/(x-1)^5 ogf A002664 13.8123 x^5/(1-7*x+20*x^2-30*x^3+25*x^4-11*x^5+2*x^6) ogf A002664 7.06309 {(2-n)*a(n+3)+(-2+3*n)*a(n+2)+(-4-2*n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=1} ogf A002671 9.14658 {(16*n^2+72*n+80)*a(n+1)-a(n+2),a(0)=1,a(1)=24} ogf A002674 13.8935 {(4*n^2+22*n+30)*a(n+1)-a(n+2),a(0)=1,a(1)=12} ogf A002690 23.6101 (-2*x+(4*x^2+1)^(1/2))*x revegf A002690 24.6366 -(2*x-1)/(-4*x+1)^(3/2) egf A002690 25.7565 -(2*x-1)/(1-4*x)^(3/2) egf A002690 13.4915 -1+4*x-4*x^2+(48*x^2+1-12*x-64*x^3)*f(x)^2 egf A002690 20.9867 -4*(-1+x)/(-1+4*x)/(-1+2*x) lgdegf A002690 10.897 {(-18-18*n-4*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=4} ogf A002691 29.1416 -(-1+x)/(1-4*x)^(5/2) egf A002691 29.1416 -(x-1)/(-4*x+1)^(5/2) egf A002691 9.71386 -1242+828*x+(-231-444*x+552*x^2)*f(x)+(41-205*x+164*x^2)*f(x)^2 lgdegf A002691 23.5374 -3*(2*x-3)/(-1+4*x)/(-1+x) lgdegf A002691 7.19969 {(-20-18*n-4*n^2)*a(n+1)+(-51-29*n-4*n^2)*a(n+2)+(n+3)*a(n+3),a(0)=1,a(1)=9,a(2)=120} ogf A002694 12.0188 -24+100*x+(4-36*x+80*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A002694 17.3956 16/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^4 ogf A002694 18.3621 16/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^4 ogf A002694 11.204 {(-56-30*n-4*n^2)*a(n+1)+(8*n+12+n^2)*a(n+2),a(0)=1,a(1)=6} ogf A002695 27.7105 -3*(x-3)/(1-6*x+x^2) lgdogf A002695 29.1689 1/(1-6*x+x^2)^(3/2) ogf A002695 10.8669 9-3*x+(287-90*x-x^2)*f(x)+(-32+192*x-32*x^2)*f(x)^2 lgdogf A002695 8.27179 {(-n-3)*a(n+3)+(21+6*n)*a(n+2)+(-4-n)*a(n+1),a(0)=1,a(1)=9,a(2)=66} ogf A002696 11.1982 -48+196*x+(6-52*x+112*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A002696 16.5026 64/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^6 ogf A002696 17.4194 64/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^6 ogf A002696 10.4516 {(-90-38*n-4*n^2)*a(n+1)+(10*n+16+n^2)*a(n+2),a(0)=1,a(1)=8} ogf A002697 50.2997 -8/(-1+4*x) lgdogf A002697 46.108 1/(-1+4*x)^2 ogf A002697 23.054 4*x/(1+(16*x+1)^(1/2))^2 revogf A002697 25.1498 x+(-1+8*x-16*x^2)*f(x) ogf A002697 34.581 x/(1-8*x+16*x^2) ogf A002697 14.1871 {a(n+2)-8*a(n+1)+16*a(n),a(0)=0,a(1)=1} ogf A002698 21.9287 (-1-6*x+8*x^2)/(-1+4*x)^3 ogf A002698 14.4268 -(-1-6*x+8*x^2)/(48*x^2+1-12*x-64*x^3) ogf A002698 13.0528 -2*(-9-16*x+16*x^2)/(-1+4*x)/(8*x^2-6*x-1) lgdogf A002698 4.68563 -21467-128802*x+171736*x^2+(30779-201732*x+955920*x^2-1373888*x^3)*f(x)+(-446976*x^2-9312+111744*x+595968*x^3)*f(x)^2 ogf A002698 9.13698 {a(n+3)-12*a(n+2)+48*a(n+1)-64*a(n),a(0)=1,a(1)=18,a(2)=160} ogf A002699 57.579 -8/(-1+4*x) lgdogf A002699 26.3904 2*x+(-1+8*x-16*x^2)*f(x) ogf A002699 27.5378 2*x/(1+(1+8*x)^(1/2))^2 revogf A002699 35.1872 2*x/(1-8*x+16*x^2) ogf A002699 52.7807 2/(-1+4*x)^2 ogf A002699 16.2402 {a(n+2)-8*a(n+1)+16*a(n),a(0)=0,a(1)=2} ogf A002700 15.8264 -(-3-4*x)/(48*x^2+1-12*x-64*x^3) ogf A002700 26.6549 -(4*x+3)/(-1+4*x)^3 ogf A002700 4.91693 -43425-57900*x+(28059-155588*x+694800*x^2-926400*x^3)*f(x)+(-217344*x^2-4528+54336*x+289792*x^3)*f(x)^2 ogf A002700 18.7572 -8*(5+4*x)/(4*x+3)/(-1+4*x) lgdogf A002700 8.44073 {a(n+3)-12*a(n+2)+48*a(n+1)-64*a(n),a(0)=3,a(1)=40,a(2)=336} ogf A002714 7.18263 -(19-46*x+15*x^4+76*x^3+3*x^6-18*x^5-21*x^2)/(3*x^3-9*x^2-9*x+7)/(x^4-4*x^3-2*x^2+4*x-1) lgdogf A002714 14.046 -(7-9*x-9*x^2+3*x^3)/(-2*x^2-1+4*x+x^4-4*x^3) ogf A002714 5.96294 889-1143*x-1143*x^2+381*x^3+(27+310*x-452*x^2-442*x^3+127*x^4)*f(x)+(-22+88*x-44*x^2-88*x^3+22*x^4)*f(x)^2 ogf A002717 37.8853 (2*x+1)/(x+1)/(x-1)^4 ogf A002717 19.4047 -(-x-2*x^2)/(1-3*x-3*x^4+2*x^2+2*x^3+x^5) ogf A002717 22.0998 -(5+11*x+8*x^2)/(-1+x)/(1+2*x)/(1+x) lgdogf A002717 9.04082 {(-3-n)*a(n+4)+(1-2*n)*a(n+3)+(12+n)*a(n+2)+(8+2*n)*a(n+1),a(0)=0,a(1)=1,a(2)=5,a(3)=13} ogf A002717 9.04082 {(-n-3)*a(n+4)+(1-2*n)*a(n+3)+(12+n)*a(n+2)+(8+2*n)*a(n+1),a(0)=0,a(1)=1,a(2)=5,a(3)=13} ogf A002720 51.1052 -(x-2)/(-1+x)^2 lgdegf A002720 26.4337 -1/exp(1)*exp(-1/(x-1))/(x-1) egf A002720 16.3102 -10+5*x+(1-8*x+5*x^2)*f(x)+(2-4*x+2*x^2)*f(x)^2 lgdegf A002720 11.9778 {(-4*n-n^2-4)*a(n+1)+(6+2*n)*a(n+2)-a(n+3),a(0)=1,a(1)=2,a(2)=7} ogf A002727 14.8019 (1+x^2+2*x^3+x^4+x^6)/(x+1)^2/(x^2+x+1)^2/(x-1)^8 ogf A002727 6.47582 -(1+x^4+x^6+x^2+2*x^3)/(3*x^8-1+4*x-4*x^2-4*x^12-2*x^3-x^14+2*x^4-12*x^7+4*x^5+3*x^6+2*x^10-2*x^11+4*x^9+4*x^13) ogf A002727 6.65405 -2*(2+7*x+4*x^9+11*x^7+24*x^4+22*x^3+6*x^8+23*x^6+30*x^5+15*x^2)/(-1+x)/(1+x)/(x^2+x+1)/(x^6+x^4+2*x^3+x^2+1) lgdogf A002736 25.6869 -12*(1+x)/(1+2*x)/(-1+4*x) lgdogf A002736 27.8275 2*(2*x+1)/(-4*x+1)^(5/2) ogf A002736 26.7144 2*x*(2*x+1)/(1-4*x)^(5/2) ogf A002736 9.54085 {(n+2)*a(n+3)+(-14-2*n)*a(n+2)+(-12-8*n)*a(n+1),a(0)=0,a(1)=2,a(2)=24} ogf A002740 11.7331 -1/2*(6*x^2-6*x+1+4*(-4*x+1)^(1/2)*x-(-4*x+1)^(1/2))/(-4*x+1)^(3/2)/x^3 ogf A002740 13.0164 -1/2*(6*x^2-6*x+1-(1-4*x)^(1/2)+4*(1-4*x)^(1/2)*x)/(1-4*x)^(3/2) ogf A002740 11.9007 2*x^3-9*x^4+(-1+12*x-48*x^2+64*x^3)*f(x)+(1-12*x+48*x^2-64*x^3)*f(x)^2 ogf A002740 13.0164 {(2*n-4*n^2)*a(n)+(-n-2+n^2)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=2} ogf A002741 11.0615 {(-n-2)*a(n+1)+(-2*n-4)*a(n+2)+(-n-1)*a(n+3)+a(n+4),a(0)=0,a(1)=1,a(2)=-1,a(3)=2} ogf A002747 16.1944 -(-2+7*x+2*x^4+x^5)/(-1+x)/(1+x)/(x^3+x^2-x+1) lgdegf A002747 6.4219 {(60+47*n+12*n^2+n^3)*a(n+1)+(80+56*n+13*n^2+n^3)*a(n+2)+(-5-n)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=-2,a(2)=9,a(3)=-28} ogf A002754 23.5668 -(-11+27*x)/(-1+9*x)/(-1+x) lgdogf A002754 35.3503 -4/(9*x-1)/(x-1)^2 ogf A002754 19.282 4*x^2+(-1+11*x-19*x^2+9*x^3)*f(x) ogf A002754 23.5668 4*x^2/(1-11*x+19*x^2-9*x^3) ogf A002754 11.3626 {a(n+3)-11*a(n+2)+19*a(n+1)-9*a(n),a(0)=0,a(1)=0,a(2)=4} ogf A002775 40.3462 (x^2+4*x+1)/(x-1)^4 egf A002775 36.5037 -2*(x+2)/(-1+x)/(1+x) lgdegf A002775 10.221 63*x+63*x^2+(-63+97*x-281*x^2+63*x^3)*f(x)+(92-276*x+276*x^2-92*x^3)*f(x)^2 egf A002775 10.0866 {(-4-4*n-n^2)*a(n+1)+(-13-6*n-n^2)*a(n+2)+(n+2)*a(n+3),a(0)=0,a(1)=1,a(2)=8} ogf A002776 22.2433 (1+x+3*x^2+x^3)/(x-1)^4 egf A002776 12.4779 -(-1-x-3*x^2-x^3)/(6*x^2+1-4*x+x^4-4*x^3) egf A002776 12.4779 -(5+9*x+x^3+9*x^2)/(-1+x)/(x^3+3*x^2+x+1) lgdegf A002776 4.19341 {(-1724-2364*n-1071*n^2-160*n^3)*a(n+1)+(-953+231*n+278*n^2+19*n^3)*a(n+2)+(-4*n+159-19*n^2)*a(n+3),a(0)=1,a(1)=5,a(2)=34} ogf A002783 21.2891 -(-1+3*x-4*x^2)/(11*x^2+1-6*x-6*x^3) ogf A002783 11.2707 -(3-14*x+24*x^4-36*x^3+27*x^2)/(-1+x)/(3*x-1)/(-1+2*x)/(4*x^2-3*x+1) lgdogf A002783 21.2891 -(4*x^2-3*x+1)/(x-1)/(3*x-1)/(2*x-1) ogf A002783 9.4618 -13+39*x-52*x^2+(51-192*x+295*x^2-78*x^3)*f(x)+(-418*x^2-38+228*x+228*x^3)*f(x)^2 ogf A002783 13.6858 {a(n+3)-6*a(n+2)+11*a(n+1)-6*a(n),a(0)=1,a(1)=3,a(2)=11} ogf A002793 11.688 {(-4*n-4-n^2)*a(n+1)+(6+2*n)*a(n+2)-a(n+3),a(0)=0,a(1)=1,a(2)=4} ogf A002793 11.688 {(-4*n-n^2-4)*a(n+1)+(2*n+6)*a(n+2)-a(n+3),a(0)=0,a(1)=1,a(2)=4} ogf A002793 11.688 {(-4*n-n^2-4)*a(n+1)+(6+2*n)*a(n+2)-a(n+3),a(0)=0,a(1)=1,a(2)=4} ogf A002798 20.0989 -(-18-27*x-6*x^2)/(-x^2+1-x+x^3) ogf A002798 12.8633 -(15+31*x+2*x^3+20*x^2)/(-1+x)/(1+x)/(2*x^2+9*x+6) lgdogf A002798 5.6418 -331830-497745*x-110610*x^2+(199893+253752*x+42051*x^2+18435*x^3)*f(x)+(-10081+10081*x+10081*x^2-10081*x^3)*f(x)^2 ogf A002798 22.1781 3*(6+9*x+2*x^2)/(x+1)/(x-1)^2 ogf A002798 12.6111 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=18,a(1)=45,a(2)=69} ogf A002801 25.1735 (-1)^(1/4)*exp(1/2*x)/(2*x-1)^(1/4) egf A002801 58.7382 (-1+x)/(-1+2*x) lgdegf A002801 51.8278 -1+x+(1-2*x)*f(x) lgdegf A002801 15.1909 {(n+2)*a(n+1)+(-2*n-5)*a(n+2)+a(n+3),a(0)=1,a(1)=1,a(2)=2} ogf A002802 42.917 -10+(1-4*x)*f(x) lgdogf A002802 57.2227 -10/(-1+4*x) lgdogf A002802 42.917 1/(-4*x+1)^(5/2) ogf A002802 45.7782 1/(1-4*x)^(5/2) ogf A002802 14.9277 {(-n-2)*a(n+2)+(14+4*n)*a(n+1),a(0)=1,a(1)=10} ogf A002803 27.4109 (x+1)/(-4*x+1)^(7/2) ogf A002803 28.8536 (x+1)/(1-4*x)^(7/2) ogf A002803 21.9287 -5*(2*x+3)/(1+x)/(-1+4*x) lgdogf A002803 8.43413 3750+2500*x+(-1105+180*x+1000*x^2)*f(x)+(57-171*x-228*x^2)*f(x)^2 lgdogf A002803 7.72139 {(-n-3)*a(n+3)+(21+3*n)*a(n+2)+(14+4*n)*a(n+1),a(0)=1,a(1)=15,a(2)=140} ogf A002807 7.11278 {(-n^2-5*n-6)*a(n+1)+(2*n^2+10*n+12)*a(n+2)+(-n^2-6*n-7)*a(n+3)+(n+1)*a(n+4),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A002817 16.2479 -(-x-x^2-x^3)/(1-5*x+10*x^2-x^5-10*x^3+5*x^4) ogf A002817 40.6198 -(x^2+x+1)/(x-1)^5 ogf A002817 23.5857 -3*(2+2*x+x^2)/(-1+x)/(x^2+x+1) lgdogf A002817 146.231 6-x^2 ogf_with_Euler_Transform A002817 9.74874 {(-3-n)*a(n+4)+6*a(n+3)+6*a(n+2)+(n+3)*a(n+1),a(0)=0,a(1)=1,a(2)=6,a(3)=21} ogf A002834 2.00335 110592-6912*f(x)+144*f(x)^2-f(x)^3 ogf A002865 88.6846 -x/(-1+x) ogf_with_Euler_Transform A002865 99.7702 -x/(x-1) ogf_with_Euler_Transform A002865 26.6054 {-a(n+2)+a(n+1),a(0)=0,a(1)=1} ogf_with_Euler_Transform A002866 38.2418 (x-1)/(2*x-1) egf A002866 33.1429 -(-1+x)/(1-2*x) egf A002866 29.2437 -1+x+(1-2*x)*f(x) egf A002866 29.2437 1/(-1+2*x)/(-1+x) lgdegf A002866 7.42005 {(2*n+2*n^2)*a(n)+(-8-9*n-2*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=1} ogf A002867 7.42665 -(2*x+1)*(x^8+10*x^6-45*x^4+35*x^2-7)/(231*x^8+7+297*x^4-77*x^2-462*x^6) egf A002867 5.51256 -(7+14*x-35*x^2+45*x^4-10*x^6-x^8+90*x^5-2*x^9-20*x^7-70*x^3)/(-231*x^8-7-297*x^4+77*x^2+462*x^6) egf A002867 19.8044 -2*(1+4*x)/(-1+2*x)/(1+2*x) lgdegf A002867 17.249 1+(-1+4*x-16*x^3+16*x^4)*f(x)^2 egf A002867 25.4628 x*(1+x)/(1+2*x+2*x^2) revegf A002867 8.62449 {(4*n^2+20*n+24)*a(n+1)+2*a(n+2)-a(n+3),a(0)=1,a(1)=2,a(2)=12} ogf A002871 14.5626 -1-2*x-x^2+(2-2*x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 egf A002872 35.9488 exp(x)+exp(2*x) lgdegf A002872 7.92987 {2*a(n+1)+(-3*n-6)*a(n+2)+(5*n+6+n^2)*a(n+3),a(0)=2,a(1)=3,a(2)=5/2} lgdegf A002874 34.7444 exp(x)+exp(3*x) lgdegf A002874 7.7786 {-3*a(n+1)+(4*n+8)*a(n+2)+(-5*n-6-n^2)*a(n+3),a(0)=2,a(1)=4,a(2)=5} lgdegf A002876 1.15524 1+(-2+4*x)*f(x)+(4*x^2+1-4*x)*f(x)^2 ogf A002878 43.8377 (x+1)/(-3*x+1+x^2) ogf A002878 25.4541 -(-4+2*x+x^2)/(1+x)/(x^2-3*x+1) lgdogf A002878 41.5304 -(1+x)/(-x^2-1+3*x) ogf A002878 19.2458 -1/2*(-1-3*x+(1+10*x+5*x^2)^(1/2))/(-1+x) revogf A002878 16.1036 -3-3*x+(-2-14*x+3*x^2)*f(x)+(5-15*x+5*x^2)*f(x)^2 ogf A002878 21.3264 {-a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=4} ogf A002881 19.492 x^8*f(x)-f(x)^2 ogf A002889 6.95061 -(1+3*x+3*x^2+x^3)/(-7*x^9-1+7*x+21*x^7-17*x^2-29*x^5+11*x^3+x^11+19*x^4-3*x^6-3*x^8+x^10) ogf A002889 22.3413 -(x+1)^3/(x-1)^3/(x-1+x^2)^4 ogf A002889 14.2172 -2*(-5-x+4*x^3+5*x^2)/(-1+x)/(1+x)/(x^2+x-1) lgdogf A002892 3.65305 -1-x^6+(2*x^6+3)*f(x)+(-x^6-3)*f(x)^2+f(x)^3 ogf A002893 25.8784 HeunG(1/9,1/3,1,1,1,1,x) ogf A002893 6.90091 {(36+36*n+9*n^2)*a(n+1)+(-63-50*n-10*n^2)*a(n+2)+(n^2+6*n+9)*a(n+3),a(0)=1,a(1)=3,a(2)=15} ogf A002894 18.9258 2*EllipticK(4*x^(1/2))/Pi ogf A002894 8.01942 {(-36-48*n-16*n^2)*a(n+1)+(n^2+4*n+4)*a(n+2),a(0)=1,a(1)=4} ogf A002895 5.63902 {(512+768*n+384*n^2+64*n^3)*a(n+1)+(-320-378*n-150*n^2-20*n^3)*a(n+2)+(n^3+9*n^2+27*n+27)*a(n+3),a(0)=1,a(1)=4,a(2)=28} ogf A002896 4.69898 {(-1080-1692*n-864*n^2-144*n^3)*a(n+1)+(630+752*n+300*n^2+40*n^3)*a(n+2)+(-n^3-9*n^2-27*n-27)*a(n+3),a(0)=1,a(1)=6,a(2)=90} ogf A002897 6.55633 {(216+432*n+288*n^2+64*n^3)*a(n+1)+(-n^3-6*n^2-12*n-8)*a(n+2),a(0)=1,a(1)=8} ogf A002898 12.9392 -HeunG(8/9,2/3,1,1,1,1,8*x/(6*x-1))/(6*x-1) ogf A002898 4.52347 {(216+180*n+36*n^2)*a(n+1)+(216+144*n+24*n^2)*a(n+2)+(7*n+12+n^2)*a(n+3)+(-n^2-8*n-16)*a(n+4),a(0)=1,a(1)=0,a(2)=6,a(3)=12} ogf A002901 16.1432 (1+5*x+5*x^2+7*x^3)/(x^2+x+1)/(x-1)^4 ogf A002901 10.1237 -(-x-5*x^2-7*x^4-5*x^3)/(1-3*x+x^6+3*x^2-2*x^3+3*x^4-3*x^5) ogf A002901 8.29582 -(3*x^2+2*x+1)*(7*x^3+9*x^2+12*x+8)/(-1+x)/(x^2+x+1)/(7*x^3+5*x^2+5*x+1) lgdogf A002901 4.29711 {(-3*n^3-27*n^2-86*n-97)*a(n+1)+(-9*n^2-45*n-62)*a(n+2)+(-9*n^2-45*n-62)*a(n+3)+(3*n^3+18*n^2+41*n+35)*a(n+4),a(0)=0,a(1)=1,a(2)=8,a(3)=26} ogf A002928 18.8108 4*x/(-1+x)/(1+x)/(1-6*x+x^2) lgdogf A002928 7.98033 8*x+(2+408*x-2*x^4+12*x^3)*f(x)+(105-630*x+630*x^3-105*x^4)*f(x)^2 lgdogf A002928 5.66346 {(-n-4)*a(n+4)+(6*n+18)*a(n+3)-4*a(n+2)+(-6*n-6)*a(n+1)+a(n)*n,a(0)=1,a(1)=0,a(2)=-2,a(3)=-8} ogf A002928 5.66346 {(-n-4)*a(n+4)+(6*n+18)*a(n+3)-4*a(n+2)+(-6*n-6)*a(n+1)+n*a(n),a(0)=1,a(1)=0,a(2)=-2,a(3)=-8} ogf A002933 1.7895 27*(1/3+x)^3+81*(x-1/3)*(1/3+x)^2*f(x)+81*(x-1/3)^2*(1/3+x)*f(x)^2+27*(x-1/3)^3*f(x)^3 ogf A002939 25.9575 -(-2*x-6*x^2)/(1-3*x+3*x^2-x^3) ogf A002939 44.7045 -2*(3*x+1)/(x-1)^3 ogf A002939 34.9861 -6*(1+x)/(3*x+1)/(-1+x) lgdogf A002939 8.9409 2730*x+8190*x^2+(-1365+3023*x-7311*x^2+1365*x^3)*f(x)+(536-1608*x+1608*x^2-536*x^3)*f(x)^2 ogf A002939 15.1827 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=2,a(2)=12} ogf A002940 20.5844 -(-1-x)/(x^2+1-3*x-x^5+3*x^3-x^4) ogf A002940 28.3035 -(x+1)/(x-1)/(x-1+x^2)^2 ogf A002940 15.4383 -2*(-2-x+2*x^3+2*x^2)/(-1+x)/(1+x)/(x^2+x-1) lgdogf A002940 6.28968 {(15+8*n+n^2)*a(n+1)+(-6-n)*a(n+2)+(-17-13*n-2*n^2)*a(n+3)+(6*n+8+n^2)*a(n+4),a(0)=1,a(1)=4,a(2)=11,a(3)=26} ogf A002941 15.1529 -(-7-2*x+6*x^3+7*x^2)/(-1+x)/(1+x)/(x^2+x-1) lgdogf A002941 11.1121 -(1+2*x+x^2)/(-7*x^2-1+5*x+10*x^4-2*x^5-5*x^6-2*x^3+x^8+x^7) ogf A002941 23.8116 -(x+1)^2/(x-1)^2/(x-1+x^2)^3 ogf A002941 4.93871 {(28-24*n-11*n^2-n^3)*a(n+1)+(44+17*n+n^2)*a(n+2)+(-94+5*n+15*n^2+2*n^3)*a(n+3)+(-n+28-6*n^2-n^3)*a(n+4),a(0)=1,a(1)=7,a(2)=29,a(3)=94} ogf A002943 19.4787 -(6*x+2*x^2)/(-1+3*x-3*x^2+x^3) ogf A002943 37.74 -2*(x+3)/(x-1)^3 ogf A002943 28.7543 -2*(x+5)/(x+3)/(-1+x) lgdogf A002943 6.4929 -20202*x-6734*x^2+(3367-4197*x+12069*x^2-3367*x^3)*f(x)+(-984+2952*x-2952*x^2+984*x^3)*f(x)^2 ogf A002943 11.3932 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=6,a(2)=20} ogf A002965 20.5572 (-x-x^2+x^3)*f(x)+(1-x^4-2*x^2)*f(x)^2 ogf A002965 32.5489 (x^2-x-1)/(-1+2*x^2+x^4) ogf A002965 13.7048 -(-1-2*x-3*x^4-4*x^3+2*x^5-2*x^2)/(x^2-x-1)/(x^4+2*x^2-1) lgdogf A002965 28.9323 -(x^2-x^3+x)/(-1+x^4+2*x^2) ogf A002999 14.1182 (-1+6*x-15*x^2+18*x^3-14*x^4+8*x^5)/(x-1)^2/(2*x-1)^3 ogf A002999 10.5389 -(1-8*x^5+14*x^4-6*x+15*x^2-18*x^3)/(-25*x^2-1+8*x-28*x^4+38*x^3+8*x^5) ogf A002999 8.503 -2*(1+x)*(14*x^4-26*x^3+18*x^2-6*x+1)/(-1+x)/(-1+2*x)/(8*x^5-14*x^4+18*x^3-15*x^2+6*x-1) lgdogf A003007 1.00706 -(x-1)^2+4*(x-1/2)*(x-1)*f(x)-4*(x-1/2)^2*f(x)^2 ogf A003008 1.00706 -(x-1)^2+4*(x-1/2)*(x-1)*f(x)-4*(x-1/2)^2*f(x)^2 ogf A003013 10.512 (-1+7*x-21*x^2+30*x^3-22*x^4+8*x^5)/(x-1)^2/(2*x-1)^3 ogf A003013 7.84697 -(-1+8*x^5-22*x^4+7*x-21*x^2+30*x^3)/(25*x^2+1-8*x+28*x^4-38*x^3-8*x^5) ogf A003013 6.47832 -(1+x)*(12*x^4-20*x^3+12*x^2-4*x+1)/(-1+x)/(-1+2*x)/(8*x^5-22*x^4+30*x^3-21*x^2+7*x-1) lgdogf A003014 5.5019 (-1+19*x-159*x^2+762*x^3-2305*x^4+4577*x^5-5997*x^6+5070*x^7-2598*x^8+648*x^9)/(x-1)^2/(2*x-1)^3/(3*x-1)^4 ogf A003031 3.43483 {(-160-224*n-104*n^2-16*n^3)*a(n+1)+(-686-587*n-168*n^2-16*n^3)*a(n+2)+(n+3)*a(n+3),a(0)=6,a(1)=336,a(2)=42240} ogf A003048 19.0839 -(2*exp(x)-1)*exp(-x)/(x-1) egf A003048 4.81557 {(8+8*n+2*n^2)*a(n+1)+(20+15*n+3*n^2)*a(n+2)+(8+5*n+n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=2,a(2)=3,a(3)=10} ogf A003052 7.64071 -(-1-11*x^6-11*x^5-2*x^4-11*x^9-11*x^8-11*x^7-9*x^11-2*x-10*x^10-2*x^2-2*x^3-9*x^13-9*x^12)/(-x^10+1-x+x^11) ogf A003058 12.4351 -(-1-x-x^2)/(1+x^2) ogf_with_Euler_Transform A003058 3.52636 -(x^4+1)*(x^8-x^6-1)*(1+x^2)^2/(x-1)/(x^14+x^12+x^10-x^6-x^4-x^2-1) ogf A003058 6.56295 {a(n+3)+a(n+1),a(0)=1,a(1)=1,a(2)=0} ogf_with_Euler_Transform A003063 33.3924 (-1+4*x)/(3*x-1)/(2*x-1) ogf A003063 34.8442 -(-4*x+1)/(6*x^2+1-5*x) ogf A003063 19.0814 -(1-12*x+24*x^2)/(3*x-1)/(-1+2*x)/(-1+4*x) lgdogf A003063 22.2616 -(1-4*x+2*x^2+12*x^3)/(-6*x^2-1+5*x) ogf A003063 17.0514 -1+4*x+(9*x-2-6*x^2)*f(x)+(-6*x^2-1+5*x)*f(x)^2 ogf A003063 20.5492 1/4*(-1+5*x+(1+6*x+x^2)^(1/2))/(-2+3*x) revogf A003063 20.0354 {a(n+2)-5*a(n+1)+6*a(n),a(0)=-1,a(1)=-1} ogf A003066 7.66972 (2-x^23-2*x^21+2*x^26-x^27-x^28-2*x^17-2*x^5+x^6-x^24-x^25+x^29+x^3-x^8-x^16)/(x^26-x^21-x^17-x^5+1)/(x-1)^2 ogf A003073 7.09897 (1+x+2*x^2+x^4-2*x^11+x^12+2*x^14-x^17+2*x^19+2*x^20-x^10+x^6+x^7+x^8)/(x-1)/(x^2+x+1)/(x^6+x^3+1)/(2*x^3-1) ogf A003073 8.33357 -(1+x^6+x^4+x^8+x^7-2*x^11+x-x^10+2*x^2+2*x^20+2*x^19-x^17+2*x^14+x^12)/(2*x^3-1-2*x^12+x^9) ogf A003079 7.41233 -(14+14*x+40*x^7+25*x^4+40*x^3+10*x^8+21*x^6+56*x^5+60*x^2)/(-1+x)/(10*x^4+20*x^3+7*x^2+14*x+5)/(x^4+x^3+x^2+x+1) lgdogf A003079 22.0419 -(5+14*x+7*x^2+20*x^3+10*x^4)/(-1+x^5) ogf A003079 15.8036 -(5+14*x+7*x^2+20*x^3+10*x^4)/(x-1)/(1+x+x^2+x^3+x^4) ogf A003082 12.7174 (1-x+x^2+x^4+x^6-x^7+x^8)/(1+x^2)/(x+1)^2/(x^2+x+1)^2/(x-1)^6 ogf A003082 9.23523 -(1+x^6+x^4+x^8-x^7-x+x^2)/(-2*x^9-1+2*x-x^14+3*x^6-2*x^4-2*x^10-2*x^5+3*x^8+2*x^13) ogf A003105 50.8851 -(-1-x^4)/(1-x^6) ogf_with_Euler_Transform A003106 52.5976 -(x+x^2)/(-1+x^5) ogf_with_Euler_Transform A003106 52.5976 -(x^2+x)/(-1+x^5) ogf_with_Euler_Transform A003114 51.265 -(-1-x^3)/(1-x^5) ogf_with_Euler_Transform A003120 10.5327 -(-1-x^5+2*x+2*x^2-3*x^3)/(-x^2+1-3*x-x^6-3*x^4+x^5+7*x^3-x^7) ogf A003120 5.02331 -(-2*x+2*x^11+12*x^9-12*x^7-7*x^4+22*x^3+x^10-4*x^8+9*x^6-10*x^5-8*x^2+1)/(-1+x)/(x^2+2*x-1)/(x^5+3*x^3-2*x^2-2*x+1)/(x^4+2*x^2-1) lgdogf A003120 11.6613 -(1-2*x-2*x^2+3*x^3+x^5)/(x-1)/(x^2+2*x-1)/(x^4+2*x^2-1) ogf A003143 12.3533 (1+x^3-x^4+x^5-x^6+x^7)/(x-1)/(2*x^2-1)/(1+x^2+x)/(1-x+x^2) ogf A003143 12.3533 -(-1+x^6-x^5+x^4-x^7-x^3)/(x^3+1-x-x^2+x^5-x^4+2*x^7-2*x^6) ogf A003143 5.78449 -(-2*x+2*x^11+6*x^9+2*x^7-2*x^4+2*x^3-4*x^10+2*x^8+5*x^6-4*x^5-1)/(-1+x)/(x^2+x+1)/(x^2-x+1)/(2*x^2-1)/(x^7-x^6+x^5-x^4+x^3+1) lgdogf A003148 12.6737 -(1+6*x)/(-1+2*x)/(1+2*x) lgdegf A003148 10.9256 -1+(1-2*x-4*x^2+8*x^3)*f(x)^2 egf A003148 13.2017 -1/(1+2*x)^(1/2)/(2*x-1) egf A003148 5.2807 {(-4*n^2-18*n-20)*a(n+1)-a(n+2)+a(n+3),a(0)=1,a(1)=1,a(2)=7} ogf A003149 8.81548 {(n^2+6*n+9)*a(n+1)+(-3*n-10)*a(n+2)+2*a(n+3),a(0)=1,a(1)=2,a(2)=5} ogf A003154 23.2724 -(-1-10*x-x^2)/(3*x^2+1-3*x-x^3) ogf A003154 35.4627 -(1+10*x+x^2)/(x-1)^3 ogf A003154 21.9035 -(13+22*x+x^2)/(-1+x)/(x^2+10*x+1) lgdogf A003154 8.55997 -374-3740*x-374*x^2+(433-532*x+1181*x^2-374*x^3)*f(x)+(-177*x^2-59+177*x+59*x^3)*f(x)^2 ogf A003154 13.7911 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=13,a(2)=37} ogf A003168 21.0861 -1+f(x)+x*f(x)^2-2*x*f(x)^3 ogf A003168 19.6319 1/2*(1+x+(1-6*x+x^2)^(1/2))*x revogf A003168 3.77037 {(2*n+6*n^2+4*n^3)*a(n)+(14*n+48-81*n^2-47*n^3)*a(n+1)+(-6872*n-5304-2946*n^2-418*n^3)*a(n+2)+(1128*n+1008+408*n^2+48*n^3)*a(n+3),a(0)=1,a(1)=1,a(2)=4} ogf A003169 17.3103 -1+(1-x)*f(x)-2*x*f(x)^2+x^2*f(x)^3 ogf A003169 37.8662 x*(-1+x)^2/(x+1) revogf A003185 25.6044 (-5-30*x+3*x^2)/(x-1)^3 ogf A003185 17.3207 -(-5-30*x+3*x^2)/(3*x^2+1-3*x-x^3) ogf A003185 5.94851 -20195-121170*x+12117*x^2+(4919-6837*x+11589*x^2-4039*x^3)*f(x)+(-528*x^2-176+528*x+176*x^3)*f(x)^2 ogf A003185 15.1001 -3*(-15-18*x+x^2)/(-1+x)/(3*x^2-30*x-5) lgdogf A003185 10.7073 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=5,a(1)=45,a(2)=117} ogf A003199 1.72041 -8*(1/2+x)^3-24*(1/2+x)^2*(x-1/2)*f(x)-24*(1/2+x)*(x-1/2)^2*f(x)^2-8*(x-1/2)^3*f(x)^3 ogf A003215 25.8333 -(-1-4*x-x^2)/(3*x^2+1-3*x-x^3) ogf A003215 40.0416 -(1+4*x+x^2)/(x-1)^3 ogf A003215 25.026 -(7+10*x+x^2)/(-1+x)/(x^2+4*x+1) lgdogf A003215 10.0104 -80-320*x-80*x^2+(109-124*x+269*x^2-80*x^3)*f(x)+(-87*x^2-29+87*x+29*x^3)*f(x)^2 ogf A003215 15.11 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=7,a(2)=19} ogf A003221 27.0906 -x^2*(x-2)/(-1+x)/(x^2-2) lgdegf A003221 26.0487 1/2*exp(-x)*(-2+x^2)/(x-1) egf A003221 10.4195 4*x^3-8*x^2+(8-8*x+7*x^3-10*x^2)*f(x)+(-3*x^2+6-6*x+3*x^3)*f(x)^2 lgdegf A003221 6.15696 {(-16-12*n-2*n^2)*a(n+1)+(-17*n-22-3*n^2)*a(n+2)+(-5*n-6-n^2)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=2} ogf A003222 8.09721 -(-5-8*x+56*x^4+528*x^3+17*x^2)/(-1+x)/(-1+8*x)/(7*x^3+26*x^2-6*x+1) lgdogf A003222 10.3889 -(2-12*x+52*x^2+14*x^3)/(-27*x^2-1+11*x-8*x^4+25*x^3) ogf A003222 14.4897 2*(1-6*x+26*x^2+7*x^3)/(8*x-1)/(x-1)^3 ogf A003229 30.6936 -(-1-2*x^2)/(1-x-2*x^3) ogf A003229 30.6936 -(1+2*x^2)/(-1+x+2*x^3) ogf A003229 16.8084 -(1+4*x+4*x^4+4*x^2)/(2*x^2+1)/(2*x^3+x-1) lgdogf A003229 14.1191 -1-2*x^2+(2-x+2*x^2-2*x^3)*f(x)+(2*x^3-1+x)*f(x)^2 ogf A003229 16.4175 {a(n+3)-a(n+2)-2*a(n),a(0)=1,a(1)=1,a(2)=3} ogf A003230 21.8294 -1/(x-1)/(2*x-1)/(-1+x+2*x^3) ogf A003230 10.9147 -2*(2-5*x+10*x^4-12*x^3+6*x^2)/(-1+x)/(-1+2*x)/(2*x^3+x-1) lgdogf A003230 19.1834 1/(1-4*x+5*x^2-4*x^3+6*x^4-4*x^5) ogf A003232 11.3355 (-7+4*x+2*x^3-3*x^2)/(-1+x)/(-1+2*x)/(x^2-4*x-1) lgdogf A003232 20.152 (x-1)*(x^2-4*x-1)/(2*x-1)^2 ogf A003232 16.488 -(-1-3*x+5*x^2-x^3)/(4*x^2+1-4*x) ogf A003232 5.28255 4283+12849*x-21415*x^2+4283*x^3+(-862+27395*x-34237*x^2+3421*x^3)*f(x)+(-13684*x^2-3421+13684*x)*f(x)^2 ogf A003232 9.71612 {a(n+4)-4*a(n+3)+4*a(n+2),a(0)=1,a(1)=7,a(2)=19,a(3)=49} ogf A003245 6.07758 (-240+1008*x+8*x^7-475*x^4+1056*x^3-35*x^6+144*x^5-1440*x^2)/(504*x^2+24-240*x+x^8+264*x^4-480*x^3+24*x^6-95*x^5-5*x^7) lgdogf A003245 12.6883 -24+240*x-504*x^2+480*x^3-264*x^4+95*x^5-24*x^6+5*x^7-x^8 ogf A003261 21.3261 (-1-2*x+4*x^2)/(x-1)/(2*x-1)^2 ogf A003261 18.2795 -(1+2*x-4*x^2)/(-8*x^2-1+5*x+4*x^3) ogf A003261 12.5448 -(7-10*x+8*x^3-4*x^2)/(-1+x)/(-1+2*x)/(4*x^2-2*x-1) lgdogf A003261 7.03058 -609-1218*x+2436*x^2+(668-2927*x+4636*x^2-2436*x^3)*f(x)+(-59+295*x-472*x^2+236*x^3)*f(x)^2 ogf A003261 11.4247 {-a(n+3)+5*a(n+2)-8*a(n+1)+4*a(n),a(0)=1,a(1)=7,a(2)=23} ogf A003264 10.5628 (24-240*x+480*x^2-240*x^3-240*x^4+386*x^5-240*x^6+90*x^7-23*x^8+4*x^9)/(x-1)/(x+1) ogf A003264 10.3113 -(24*x-240*x^5-240*x^4-240*x^2+90*x^8+480*x^3+386*x^6-240*x^7-23*x^9+4*x^10)/(1-x^2) ogf A003264 10.19 -(24*x-240*x^7-386*x^6+240*x^2+240*x^4+480*x^3-240*x^5-90*x^8-23*x^9-4*x^10)/(-1+x^2) ogf A003269 40.9568 -(1+4*x^3)/(-1+x+x^4) lgdogf A003269 66.1609 -1/(-1+x+x^4) ogf A003269 50.5937 x+(-1+x+x^4)*f(x) ogf A003269 17.5529 {-a(n+4)+a(n+3)+a(n),a(0)=1,a(1)=1,a(2)=1,a(3)=5} lgdogf A003272 8.76709 (24-240*x+480*x^2-240*x^3-240*x^4+385*x^5-240*x^6+90*x^7-24*x^8+4*x^9)/(x-1)/(x+1) ogf A003272 8.35932 -(-24*x+240*x^5+240*x^4+240*x^2-90*x^8-480*x^3-385*x^6+240*x^7+24*x^9-4*x^10)/(-1+x^2) ogf A003272 8.45766 -(-24*x+240*x^7+385*x^6-240*x^2-240*x^4-480*x^3+240*x^5+90*x^8+24*x^9+4*x^10)/(1-x^2) ogf A003274 13.3536 -(-1+x-3*x^2+2*x^3-x^5)/(3*x^2+1-3*x+2*x^4-x^5-2*x^3) ogf A003274 17.6935 -(1-x+3*x^2-2*x^3+x^5)/(x^3+x-1)/(x-1)^2 ogf A003274 8.95874 -2*(x^2-x+1)*(x^5-2*x^4+5*x^3+x^2-2*x-1)/(-1+x)/(x^3+x-1)/(x^5-2*x^3+3*x^2-x+1) lgdogf A003293 50.9065 1/(1-x-x^2+x^3) ogf_with_Euler_Transform A003293 15.9083 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=1,a(1)=1,a(2)=2} ogf_with_Euler_Transform A003400 3.59685 1+8*x^5+(-2-8*x^5)*f(x)+f(x)^2 ogf A003402 4.47371 -(1+5*x+18*x^9+59*x^7+52*x^4+33*x^3+37*x^8+70*x^6+69*x^5+16*x^2)/(-1+x)/(1+x)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(1+x^2) lgdogf A003402 29.737 1+x+2*x^2+x^3+x^4 ogf_with_Euler_Transform A003402 9.19143 1/(1+x^2)/(1+x+x^2+x^3+x^4)/(x+1)^2/(1+x^2+x)^2/(x-1)^6 ogf A003402 11.4893 {-a(n+5),a(0)=1,a(1)=1,a(2)=2,a(3)=1,a(4)=1} ogf_with_Euler_Transform A003403 16.0357 1+x+2*x^2+2*x^3+2*x^4+x^5+x^6 ogf_with_Euler_Transform A003408 6.56117 1296-9261*x+(-144+2709*x-11907*x^2)*f(x)+(-96*x-5103*x^3+1404*x^2)*f(x)^2+(-16*x^2+216*x^3-729*x^4)*f(x)^3 lgdogf A003408 8.27957 {(1320+1086*n+297*n^2+27*n^3)*a(n+1)+(-166*n-180-46*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=9} ogf A003409 23.1029 -9+(3-12*x)*f(x)+(x-4*x^2)*f(x)^2 ogf A003409 21.7827 6/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2)) ogf A003409 23.1029 6/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) ogf A003409 44.8468 x*(3+x)/(3+2*x)^2 revogf A003409 16.9421 {(-4*n-10)*a(n+1)+(n+3)*a(n+2),a(0)=3,a(1)=9} ogf A003410 31.6954 -(-1-x-x^3-x^2)/(1-x-x^3) ogf A003410 18.8663 -(2+2*x+x^4+5*x^2)/(1+x)/(1+x^2)/(x^3+x-1) lgdogf A003410 33.0161 -(x+1)*(1+x^2)/(x^3+x-1) ogf A003410 12.1906 5+5*x+5*x^2+5*x^3+(-1+9*x+4*x^2+9*x^3)*f(x)+(-4+4*x^3+4*x)*f(x)^2 ogf A003410 15.8477 {a(n+4)-a(n+3)-a(n+1),a(0)=1,a(1)=2,a(2)=3,a(3)=5} ogf A003411 27.0113 -(-1-x-x^3-x^2-x^4)/(1-x-x^4) ogf A003411 27.0113 -(1+x+x^2+x^3+x^4)/(-1+x+x^4) ogf A003411 13.5056 -(2+2*x+6*x^3+x^6+2*x^5+2*x^2)/(x^4+x^3+x^2+x+1)/(x^4+x-1) lgdogf A003411 11.3526 -3-3*x-3*x^2-3*x^3-3*x^4+(4-2*x+x^2+x^3-2*x^4)*f(x)+(-1+x+x^4)*f(x)^2 ogf A003412 11.3854 -(1+x+x^2+x^3+2*x^4+3*x^11+2*x^10+2*x^5+2*x^6+x^7+x^8+2*x^9)/(x^6-1+x) ogf A003412 11.3854 -(1+x+x^8+x^3+x^7+2*x^6+x^2+2*x^4+3*x^11+2*x^9+2*x^5+2*x^10)/(x^6-1+x) ogf A003413 8.09081 (-2-2*x-2*x^9+2*x^7-7*x^4-2*x^3+x^12-2*x^10-3*x^8-7*x^6-4*x^5-2*x^2)/(x^2+x+1)/(x^5+x^3+1)/(x^6+x-1) lgdogf A003413 19.2638 -(1+x+x^3+x^7+x^6+x^2+x^4+2*x^5)/(x^6-1+x) ogf A003413 25.2838 -(1+x^2+x)*(1+x^3+x^5)/(x^6-1+x) ogf A003417 13.1455 (-1-4*x-8*x^4-x^3+2*x^6+3*x^5-3*x^2)/(-1+x)/(x^2+x+1)/(x^6-x^4-3*x^3+2*x^2+x+2) lgdogf A003417 23.0777 (2+x+2*x^2-3*x^3-x^4+x^6)/(x-1)^2/(1+x^2+x)^2 ogf A003422 6.61588 -(1-Ei(1,x-1)*exp(x-1)*x+Ei(1,x-1)*exp(x-1)+exp(x)*Ei(1,-1)*exp(-1)*x-exp(x)*Ei(1,-1)*exp(-1))/(x-1) egf A003422 11.8141 {(-2-n)*a(n+1)+(n+3)*a(n+2)-a(n+3),a(0)=0,a(1)=1,a(2)=2} ogf A003440 12.7545 -1+2*x-x^2+(1-3*x+3*x^3-x^4)*f(x)+(x^2-3*x^3+x^4)*f(x)^2 ogf A003440 12.7545 -1+2*x-x^2+(1-3*x-x^4+3*x^3)*f(x)+(x^2-3*x^3+x^4)*f(x)^2 ogf A003451 27.8993 -(-1-2*x+x^2)/(x+1)^2/(x-1)^4 ogf A003451 18.3882 -(1+2*x-x^2)/(x^2-1+2*x+x^4+2*x^5-x^6-4*x^3) ogf A003451 17.5887 -4*(-1-2*x+x^3-2*x^2)/(-1+x)/(1+x)/(x^2-2*x-1) lgdogf A003451 5.65791 {(-720-409*n-53*n^2)*a(n+1)+(4464+1758*n+169*n^2)*a(n+2)+(1148+535*n+53*n^2)*a(n+3)+(-1188*n-2048-169*n^2)*a(n+4),a(0)=1,a(1)=4,a(2)=8,a(3)=16} ogf A003453 15.0448 -(-3-6*x+4*x^3-3*x^2)/(-1+x)/(1+x)/(x^2-x-1) lgdogf A003453 15.7612 -(1+x-x^2)/(x^2-1+2*x+x^4+2*x^5-x^6-4*x^3) ogf A003453 25.4604 -(x^2-x-1)/(x+1)^2/(x-1)^4 ogf A003453 4.44276 {(4750+3480*n+506*n^2)*a(n+1)+(-21280-9037*n-973*n^2)*a(n+2)+(-3690-3402*n-506*n^2)*a(n+3)+(6157*n+9060+973*n^2)*a(n+4),a(0)=1,a(1)=3,a(2)=6,a(3)=11} ogf A003461 24.3797 -(-4+5*x+3*x^2)/(2*x^2+1-3*x) ogf A003461 24.3797 -(-4+5*x+3*x^2)/(x-1)/(2*x-1) ogf A003461 15.3698 -(7-22*x+19*x^2)/(-1+x)/(-1+2*x)/(3*x^2+5*x-4) lgdogf A003461 11.2224 212-265*x-159*x^2+(-57+164*x-103*x^2)*f(x)+(1-3*x+2*x^2)*f(x)^2 ogf A003461 14.7294 {a(n+3)-3*a(n+2)+2*a(n+1),a(0)=4,a(1)=7,a(2)=10} ogf A003462 18.8334 -1/6*(-1-4*x+(1+8*x+4*x^2)^(1/2))/x revogf A003462 25.3526 -2*(-2+3*x)/(3*x-1)/(-1+x) lgdogf A003462 43.9445 1/(3*x-1)/(x-1) ogf A003462 31.389 x+(-1+4*x-3*x^2)*f(x) ogf A003462 43.9445 x/(1-4*x+3*x^2) ogf A003462 17.3465 {a(n+2)-4*a(n+1)+3*a(n),a(0)=0,a(1)=1} ogf A003463 17.8974 -1/10*(-6*x-1+(16*x^2+12*x+1)^(1/2))/x revogf A003463 27.2041 -2*(5*x-3)/(5*x-1)/(-1+x) lgdogf A003463 45.3402 1/(5*x-1)/(x-1) ogf A003463 32.3858 x+(-1+6*x-5*x^2)*f(x) ogf A003463 45.3402 x/(1-6*x+5*x^2) ogf A003463 17.8974 {a(n+2)-6*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A003464 24.3574 -(-7+12*x)/(6*x-1)/(-1+x) lgdogf A003464 35.8197 -1/(-1+7*x-6*x^2) ogf A003464 16.0246 -1/12*(-1-7*x+(1+14*x+25*x^2)^(1/2))/x revogf A003464 11.7103 -12+(-25-84*x+72*x^2)*f(x)+(37-259*x+222*x^2)*f(x)^2 ogf A003464 40.5957 1/(6*x-1)/(x-1) ogf A003464 15.6137 {-a(n+2)+7*a(n+1)-6*a(n),a(0)=1,a(1)=7} ogf A003467 7.85195 (5+460*x^2-1512*x^3+2690*x^4-72*x-2960*x^5+2656*x^6-1280*x^7+256*x^8)/(4*x-1)^4/(x-1)^4 ogf A003467 7.59022 {(-80-36*n-4*n^2)*a(n)+(5*n^2+30*n+25)*a(n+1)+(-2-3*n-n^2)*a(n+2),a(0)=5,a(1)=28,a(2)=190} ogf A003468 14.5321 -1/(-1+22*x-179*x^2+638*x^3-840*x^4) ogf A003468 8.17433 -2*(-11+179*x+1680*x^3-957*x^2)/(6*x-1)/(-1+4*x)/(7*x-1)/(5*x-1) lgdogf A003468 15.8532 1/(6*x-1)/(4*x-1)/(7*x-1)/(5*x-1) ogf A003469 26.3593 (-1+x+x^2)/(2*x-1)^2/(x-1)^3 ogf A003469 16.0448 -(1-x-x^2)/(-19*x^2-1+7*x-16*x^4+4*x^5+25*x^3) ogf A003469 15.7034 -(6-16*x+6*x^3+7*x^2)/(-1+x)/(-1+2*x)/(x^2+x-1) lgdogf A003472 50.3191 -1/(2*x-1)^5 ogf A003472 50.3191 -10/(-1+2*x) lgdogf A003472 15.8902 1/(1-10*x+40*x^2-80*x^3+80*x^4-32*x^5) ogf A003472 13.1267 {(-n-2)*a(n+2)+(12+2*n)*a(n+1),a(0)=1,a(1)=10} ogf A003476 18.6893 -(-1-x-x^2)/(1-x-2*x^3) ogf A003476 18.6893 -(1+x^2+x)/(-1+x+2*x^3) ogf A003476 9.7694 -(x^2+2*x+2)*(2*x^2+1)/(x^2+x+1)/(2*x^3+x-1) lgdogf A003476 7.67596 1+x+x^2+(-9-7*x-8*x^2+2*x^3)*f(x)+(-16*x^3+8-8*x)*f(x)^2 ogf A003476 9.9966 {a(n+3)-a(n+2)-2*a(n),a(0)=1,a(1)=2,a(2)=3} ogf A003477 10.354 -(-3+6*x-10*x^4+24*x^3+24*x^5-15*x^2)/(-1+2*x)/(1+x^2)/(2*x^3+x-1) lgdogf A003477 16.6674 -1/(-1+3*x-3*x^2+5*x^3-6*x^4+2*x^5-4*x^6) ogf A003477 22.7788 1/(2*x-1)/(1+x^2)/(-1+x+2*x^3) ogf A003478 18.2957 -(-3+4*x+16*x^3-6*x^2)/(-1+2*x)/(2*x^3+x-1) lgdogf A003478 27.1281 -1/(-1+3*x-2*x^2+2*x^3-4*x^4) ogf A003478 9.83393 -16+(-31-48*x+32*x^2-32*x^3+64*x^4)*f(x)+(47+188*x^4-141*x+94*x^2-94*x^3)*f(x)^2 ogf A003478 35.7598 1/(2*x-1)/(-1+x+2*x^3) ogf A003479 18.1864 -2*(-1+x+4*x^3-3*x^2)/(-1+x)/(2*x^3+x-1) lgdogf A003479 29.0982 1/(1-2*x+x^2-2*x^3+2*x^4) ogf A003479 36.3727 1/(x-1)/(-1+x+2*x^3) ogf A003479 9.96513 6+(-1+12*x-6*x^2+12*x^3-12*x^4)*f(x)+(-5-10*x^4+10*x-5*x^2+10*x^3)*f(x)^2 ogf A003480 29.2765 (x-1)^2/(2*x^2+1-4*x) ogf A003480 22.7706 -(1-2*x+x^2)/(-2*x^2-1+4*x) ogf A003480 26.7307 -2/(-1+x)/(2*x^2-4*x+1) lgdogf A003480 10.0788 9-18*x+9*x^2+(-50+118*x-59*x^2)*f(x)+(82*x^2+41-164*x)*f(x)^2 ogf A003480 12.8085 {-a(n+3)+4*a(n+2)-2*a(n+1),a(0)=1,a(1)=2,a(2)=7} ogf A003481 24.4192 (-2-4*x+x^2)/(x-1)/(x^2-7*x+1) ogf A003481 12.4166 -(-20+34*x+x^4-8*x^3+18*x^2)/(-1+x)/(x^2-7*x+1)/(x^2-4*x-2) lgdogf A003481 23.6315 -(2+4*x-x^2)/(-8*x^2-1+8*x+x^3) ogf A003481 6.78312 7282+14564*x-3641*x^2+(-97921-159432*x+18012*x^2+3641*x^3)*f(x)+(47140-377120*x+377120*x^2-47140*x^3)*f(x)^2 ogf A003481 13.0817 {-a(n+3)+8*a(n+2)-8*a(n+1)+a(n),a(0)=2,a(1)=20,a(2)=143} ogf A003482 17.2325 (-5*x+x^2)*f(x)+(1-8*x+8*x^2-x^3)*f(x)^2 ogf A003482 29.9696 (x-5)/(x-1)/(x^2-7*x+1) ogf A003482 14.0674 -(-39+80*x+2*x^3-23*x^2)/(-1+x)/(x-5)/(x^2-7*x+1) lgdogf A003482 23.769 -(-5*x+x^2)/(1-8*x+8*x^2-x^3) ogf A003482 12.7649 {-a(n+3)+8*a(n+2)-8*a(n+1)+a(n),a(0)=0,a(1)=5,a(2)=39} ogf A003485 20.8219 (1+x+2*x^2+4*x^3)/(x+1)/(1+x^2)/(x-1)^2 ogf A003485 24.6077 -(1+x+4*x^3+2*x^2)/(-1+x-x^5+x^4) ogf A003485 10.2792 -2*(1+3*x+5*x^4+6*x^3+4*x^6+5*x^5+8*x^2)/(-1+x)/(1+x)/(1+x^2)/(4*x^3+2*x^2+x+1) lgdogf A003486 14.8858 -(-1+3*x-18*x^2)/(27*x^2+1-9*x-27*x^3) ogf A003486 22.6264 -(1-3*x+18*x^2)/(3*x-1)^3 ogf A003486 6.50184 -31+93*x-558*x^2+(107-507*x+2205*x^2-837*x^3)*f(x)+(-76+684*x-2052*x^2+2052*x^3)*f(x)^2 ogf A003486 14.5041 -6*(1+3*x+9*x^2)/(3*x-1)/(18*x^2-3*x+1) lgdogf A003486 9.92387 {a(n+3)-9*a(n+2)+27*a(n+1)-27*a(n),a(0)=1,a(1)=6,a(2)=45} ogf A003499 34.0425 -(-2+6*x)/(x^2+1-6*x) ogf A003499 21.0262 -(3-2*x+3*x^2)/(3*x-1)/(1-6*x+x^2) lgdogf A003499 32.4951 -2*(3*x-1)/(1-6*x+x^2) ogf A003499 10.9983 -398+1194*x+(479-2034*x+199*x^2)*f(x)+(-140*x^2-140+840*x)*f(x)^2 ogf A003499 19.8581 {a(n+2)-6*a(n+1)+a(n),a(0)=2,a(1)=6} ogf A003500 29.5105 -(-2+4*x)/(x^2+1-4*x) ogf A003500 10.3287 -116+232*x+(148-412*x+58*x^2)*f(x)+(-45*x^2-45+180*x)*f(x)^2 ogf A003500 18.7794 -2*(1-x+x^2)/(-1+2*x)/(x^2-4*x+1) lgdogf A003500 28.1691 -2*(2*x-1)/(1-4*x+x^2) ogf A003500 17.2144 {a(n+2)-4*a(n+1)+a(n),a(0)=2,a(1)=4} ogf A003501 26.6953 -(-2+5*x)/(-5*x+1+x^2) ogf A003501 27.9666 -(-2+5*x)/(x^2+1-5*x) ogf A003501 17.2735 -(5-4*x+5*x^2)/(5*x-2)/(x^2-5*x+1) lgdogf A003501 10.3035 -34+85*x+(59-190*x+17*x^2)*f(x)+(-21+105*x-21*x^2)*f(x)^2 ogf A003501 16.3138 {a(n+2)-5*a(n+1)+a(n),a(0)=2,a(1)=5} ogf A003507 1.45561 x^2+2*x+1+(-2-2*x)*f(x)+f(x)^2 ogf A003512 5.97282 -(3+4*x+3*x^3+4*x^5+4*x^6+4*x^2+4*x^4+4*x^9+4*x^8+3*x^7+x^15+4*x^13+3*x^14+4*x^12+3*x^11+4*x^10)/(x^15-1+x-x^16) ogf A003516 10.1723 -35+144*x+(5-44*x+96*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A003516 14.7231 32/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^5 ogf A003516 15.5411 32/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^5 ogf A003516 9.48268 {(-72-34*n-4*n^2)*a(n+1)+(9*n+14+n^2)*a(n+2),a(0)=1,a(1)=7} ogf A003517 18.8814 -36+(6-24*x)*f(x)+(x-4*x^2)*f(x)^2 lgdogf A003517 18.8814 12/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A003517 27.9116 64/(1+(-4*x+1)^(1/2))^6 ogf A003517 29.1803 64/(1+(1-4*x)^(1/2))^6 ogf A003517 10.6994 {(-72-34*n-4*n^2)*a(n+1)+(10*n+16+n^2)*a(n+2),a(0)=1,a(1)=6} ogf A003518 18.0752 -64+(8-32*x)*f(x)+(x-4*x^2)*f(x)^2 lgdogf A003518 18.0752 16/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A003518 25.6065 256/(1+(-4*x+1)^(1/2))^8 ogf A003518 26.7198 256/(1+(1-4*x)^(1/2))^8 ogf A003518 10.0747 {(-110-42*n-4*n^2)*a(n+1)+(12*n+20+n^2)*a(n+2),a(0)=1,a(1)=8} ogf A003519 9.60143 -100+(10-40*x)*f(x)+(x-4*x^2)*f(x)^2 lgdogf A003519 13.2943 1024/(1+(-4*x+1)^(1/2))^10 ogf A003519 13.8261 1024/(1+(1-4*x)^(1/2))^10 ogf A003519 10.1662 20/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2)) lgdogf A003519 5.57503 {(-156-50*n-4*n^2)*a(n+1)+(14*n+24+n^2)*a(n+2),a(0)=1,a(1)=10} ogf A003520 26.9085 -(1+5*x^4)/(x^2-x+1)/(x^3+x^2-1) lgdogf A003520 35.8779 -1/(1-x+x^2)/(x^3+x^2-1) ogf A003520 22.0787 -2+(3-2*x-2*x^5)*f(x)+(-1+x+x^5)*f(x)^2 ogf A003522 12.0628 -(-1+3*x+2*x^4-3*x^3-3*x^2)/(-1+x)/(x^4+x^3-3*x^2+3*x-1) lgdogf A003522 19.3005 -(1-2*x+x^2)/(-3*x^2-1+3*x+x^4+x^3) ogf A003522 21.7909 -(x-1)^2/(-3*x^2-1+3*x+x^4+x^3) ogf A003522 8.77294 -2+4*x-2*x^2+(5-12*x+9*x^2-2*x^3-2*x^4)*f(x)+(3*x^4-9*x^2-3+9*x+3*x^3)*f(x)^2 ogf A003539 19.4168 -(-587+571*x)/(3*x-1)/(x-1) ogf A003539 10.4851 -(1777-3522*x+1713*x^2)/(-1+x)/(3*x-1)/(571*x-587) lgdogf A003539 19.4168 -(587-571*x)/(-3*x^2-1+4*x) ogf A003539 9.89156 -1/2*(-587-4*x+(344569+2412*x+4*x^2)^(1/2))/(571+3*x) revogf A003539 5.6984 -617962489+601118537*x+(-1052235-2163382*x+3158241*x^2)*f(x)+(3586-14344*x+10758*x^2)*f(x)^2 ogf A003539 11.9148 {-a(n+2)+4*a(n+1)-3*a(n),a(0)=587,a(1)=1777} ogf A003555 12.7493 (-1+45*x)/(x-1)/(100*x-1)/(10*x-1) ogf A003555 11.4073 -(-1+45*x)/(1110*x^2+1-111*x-1000*x^3) ogf A003555 6.37466 -6*(-11+370*x+15000*x^3-8825*x^2)/(-1+x)/(100*x-1)/(10*x-1)/(45*x-1) lgdogf A003555 6.56783 {a(n+3)-111*a(n+2)+1110*a(n+1)-1000*a(n),a(0)=1,a(1)=66,a(2)=6216} ogf A003575 14.395 {-3*a(n)+(n+1)*a(n+1),a(0)=2,a(1)=3} lgdegf A003576 13.2475 {4*a(n)+(-n-1)*a(n+1),a(0)=2,a(1)=4} lgdegf A003577 13.9701 {5*a(n)+(-n-1)*a(n+1),a(0)=2,a(1)=5} lgdegf A003578 4.10974 2*(25025+51975*x^4+81*x^8+5670*x^6+105105*x^2)/(-20790*x^5+25025-75075*x+105105*x^2+81*x^8-90090*x^3+51975*x^4-972*x^7+5670*x^6) lgdegf A003578 14.6124 {6*a(n)+(-n-1)*a(n+1),a(0)=2,a(1)=6} lgdegf A003579 47.8812 1+exp(7*x) lgdegf A003579 13.3003 {-7*a(n)+(n+1)*a(n+1),a(0)=2,a(1)=7} lgdegf A003580 49.2979 1+exp(8*x) lgdegf A003580 13.6938 {8*a(n)+(-n-1)*a(n+1),a(0)=2,a(1)=8} lgdegf A003581 50.4311 1+exp(9*x) lgdegf A003581 14.0086 {-9*a(n)+(n+1)*a(n+1),a(0)=2,a(1)=9} lgdegf A003582 13.4205 {10*a(n)+(-n-1)*a(n+1),a(0)=2,a(1)=10} lgdegf A003583 13.0914 -(-1+2*x+(-x^2*(4*x-1))^(1/2))/(4*x-1)^2 ogf A003583 6.16068 1-4*x+3*x^2+4*x^3+(-2+20*x-64*x^2+64*x^3)*f(x)+(96*x^2+1-16*x+256*x^4-256*x^3)*f(x)^2 ogf A003583 6.16068 1-4*x+4*x^3+3*x^2+(-2+20*x+64*x^3-64*x^2)*f(x)+(96*x^2+1-16*x+256*x^4-256*x^3)*f(x)^2 ogf A003584 10.0624 -1+18*x-81*x^2+(1-20*x+96*x^2)*f(x)+(16*x^2-128*x^3)*f(x)^2 ogf A003584 4.3653 {(-1296-1512*n-432*n^2)*a(n+1)+(1368+996*n+174*n^2)*a(n+2)+(-342-181*n-23*n^2)*a(n+3)+(10*n+24+n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=9,a(3)=52} ogf A003590 18.6494 1331-363*f(x)+33*f(x)^2-f(x)^3 lgdegf A003600 24.6819 (1-2*x+4*x^2-3*x^3+x^4)/(x-1)^4 ogf A003600 15.6151 -(-1+2*x+3*x^3-4*x^2-x^4)/(6*x^2+1-4*x+x^4-4*x^3) ogf A003600 16.2795 -(2+2*x+x^3-x^2)/(-1+x)/(x^4-3*x^3+4*x^2-2*x+1) lgdogf A003600 7.57563 11-22*x+44*x^2-33*x^3+11*x^4+(-19+60*x-98*x^2+68*x^3-19*x^4)*f(x)+(8-32*x+48*x^2-32*x^3+8*x^4)*f(x)^2 ogf A003600 6.48423 {(-11*n-7*n^2)*a(n)+(48+74*n+22*n^2)*a(n+1)+(-354-283*n-47*n^2)*a(n+2)+(148*n+156+32*n^2)*a(n+3),a(0)=1,a(1)=2,a(2)=6} ogf A003619 6.77447 (3-x+5*x^4+4*x^6-9*x^5+16*x^18-33*x^17+17*x^16)/(-1+x)/(x^18-x^17+x^6-x^5+x^2-x-1) lgdogf A003619 15.0137 -(-1-x+x^2-x^17+x^18-x^5+x^6)/(x-1)^2 ogf A003619 13.5489 -(-1-x-x^5+x^6+x^2+x^18-x^17)/(x^2+1-2*x) ogf A003645 26.4277 -1+(1-4*x)*f(x)-4*x^2*f(x)^2 ogf A003645 35.2369 4/(1+(1-8*x)^(1/2))^2 ogf A003645 22.4235 8/(1-8*x)^(1/2)/(1+(1-8*x)^(1/2)) lgdogf A003645 67.2705 x/(2*x+1)^2 revogf A003645 16.4439 {(-8*n-20)*a(n+1)+(n+4)*a(n+2),a(0)=1,a(1)=4} ogf A003662 6.58572 (-4-8*x+6*x^11-x^9-18*x^7-13*x^4-20*x^3-2*x^10-3*x^8-6*x^6-15*x^5-12*x^2)/(-1+x)/(1+x)/(1+x^2)/(2*x^8+x^6-x^5+2*x^4+2*x^3+2*x^2+3*x+1) lgdogf A003662 14.467 (1+3*x+2*x^2+2*x^3+2*x^4-x^5+x^6+2*x^8)/(x+1)/(1+x^2)/(x-1)^2 ogf A003662 16.0452 -(1+3*x+2*x^3+2*x^8-x^5+x^6+2*x^2+2*x^4)/(-x^5-1+x+x^4) ogf A003663 6.45428 (-6-10*x-2*x^9-15*x^7-7*x^4-6*x^3+8*x^10-2*x^8-x^6+x^5-14*x^2)/(-1+x)/(x^2+x+1)/(2*x^8+x^5-3*x^4+x^3+2*x^2+5*x+1) lgdogf A003663 14.3007 (1+5*x+2*x^2+x^3-3*x^4+x^5+2*x^8)/(1+x^2+x)/(x-1)^2 ogf A003663 14.8844 -(1+5*x+x^3+2*x^8+x^5+2*x^2-3*x^4)/(-1+x-x^4+x^3) ogf A003664 11.0057 (2+3*x+x^2+3*x^3+x^4+x^10+x^5+x^6+2*x^7-2*x^8+2*x^9)/(1+x+x^2+x^3+x^4)/(x-1)^2 ogf A003664 12.6242 -(2+3*x+3*x^3-2*x^8+x^5+x^6+x^2+x^4+2*x^7+x^10+2*x^9)/(-1+x+x^5-x^6) ogf A003665 26.8756 (x-1)/(1+2*x)/(4*x-1) ogf A003665 14.1097 -(-1-16*x+8*x^2)/(-1+x)/(1+2*x)/(-1+4*x) lgdogf A003665 28.2194 -(1-x)/(8*x^2-1+2*x) ogf A003665 9.10304 -107+107*x+(215-322*x-856*x^2)*f(x)+(864*x^2-108+216*x)*f(x)^2 ogf A003665 15.2537 1/2/(8*x-1)*(-2*x-1+(36*x^2+1)^(1/2)) revogf A003665 14.4715 {-a(n+2)+2*a(n+1)+8*a(n),a(0)=1,a(1)=1} ogf A003674 20.7871 -2*(1+8*x)/(1+2*x)/(-1+4*x) lgdogf A003674 24.4023 -3*x+(1-2*x-8*x^2)*f(x) ogf A003674 29.5396 -3*x/(-1+2*x+8*x^2) ogf A003674 31.1807 -3/(1+2*x)/(4*x-1) ogf A003674 12.7557 1/16*(-3-2*x+(3+4*x+12*x^2)^(1/2)*3^(1/2))/x revogf A003674 14.3911 {-a(n+2)+2*a(n+1)+8*a(n),a(0)=0,a(1)=3} ogf A003682 22.0509 -(1+x+x^3-x^2)/(-3*x^2-1+3*x+x^3) ogf A003682 33.0763 -(1+x-x^2+x^3)/(x-1)^3 ogf A003682 23.4735 -2*(2+x^2)/(-1+x)/(x^3-x^2+x+1) lgdogf A003682 9.21112 13+13*x-13*x^2+13*x^3+(-10+42*x-42*x^2+16*x^3)*f(x)+(-3+9*x-9*x^2+3*x^3)*f(x)^2 ogf A003682 11.7367 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=4,a(2)=8,a(3)=14} ogf A003683 32.8398 -1/(1+2*x)/(4*x-1) ogf A003683 21.8932 -2*(1+8*x)/(1+2*x)/(-1+4*x) lgdogf A003683 28.1484 -x+(1-2*x-8*x^2)*f(x) ogf A003683 34.7716 -x/(-1+2*x+8*x^2) ogf A003683 16.4199 1/16/x*(-2*x-1+(36*x^2+4*x+1)^(1/2)) revogf A003683 15.1569 {-a(n+2)+2*a(n+1)+8*a(n),a(0)=0,a(1)=1} ogf A003685 8.80653 (1+5*x-6*x^2-2*x^3-2*x^4+12*x^5-8*x^6+2*x^7)/(x-1)/(2*x-1)/(2*x^2-1)^2 ogf A003685 7.08571 -(-1-5*x+2*x^3-12*x^5+8*x^6+6*x^2+2*x^4-2*x^7)/(-2*x^2+1-3*x-4*x^4+12*x^3+8*x^6-12*x^5) ogf A003688 36.9134 -(-1-x)/(-x^2+1-3*x) ogf A003688 24.6089 -(4+2*x+x^2)/(1+x)/(x^2+3*x-1) lgdogf A003688 41.0149 -(x+1)/(x^2-1+3*x) ogf A003688 16.7788 1+x+(6+10*x+x^2)*f(x)+(-7+21*x+7*x^2)*f(x)^2 ogf A003688 18.4567 1/2/(x+1)*(-1-3*x+(1+10*x+13*x^2)^(1/2)) revogf A003688 20.5074 {a(n+2)-3*a(n+1)-a(n),a(0)=1,a(1)=4} ogf A003689 11.336 -(3+9*x+24*x^3-18*x^2-12*x^4)/(-16*x^2-1+7*x+12*x^3) ogf A003689 7.27743 2*(-5+12*x-26*x^4+22*x^3+12*x^5-3*x^2)/(3*x-1)/(-1+2*x)/(4*x^4-8*x^3+6*x^2-3*x-1) lgdogf A003689 12.8146 3*(-1-3*x+6*x^2-8*x^3+4*x^4)/(3*x-1)/(2*x-1)^2 ogf A003689 7.27743 {-a(n+5)+7*a(n+4)-16*a(n+3)+12*a(n+2),a(0)=3,a(1)=30,a(2)=144,a(3)=588,a(4)=2160} ogf A003690 16.0615 -(-3-3*x)/(24*x^2+1-24*x-x^3) ogf A003690 9.50581 -(25-48*x+2*x^3-21*x^2)/(-1+x)/(1+x)/(x^2-23*x+1) lgdogf A003690 17.2513 -3*(x+1)/(x-1)/(x^2-23*x+1) ogf A003690 8.03077 {a(n+3)-24*a(n+2)+24*a(n+1)-a(n),a(0)=3,a(1)=75,a(2)=1728} ogf A003691 13.6781 -(3+12*x+12*x^2)/(8*x^2-1+8*x) ogf A003691 16.4137 -12/(1+2*x)/(8*x^2+8*x-1) lgdogf A003691 15.7824 -3*(1+2*x)^2/(8*x^2-1+8*x) ogf A003691 5.947 63+252*x+252*x^2+(246+1236*x+1236*x^2)*f(x)+(712*x^2-89+712*x)*f(x)^2 ogf A003691 8.04595 {-a(n+3)+8*a(n+2)+8*a(n+1),a(0)=3,a(1)=36,a(2)=324} ogf A003692 10.5775 12-6*x+2*x^3+(-12+18*x-6*x^3)*f(x)+9*x^3*f(x)^2 egf A003692 5.23309 {(-6*n-5*n^2-n^3)*a(n)+(-26*n-15-13*n^2-2*n^3)*a(n+1)+(17*n+10+8*n^2+n^3)*a(n+2),a(0)=1,a(1)=1} egf A003693 11.279 -(-2*x+2*x^3+x^2-x^4)/(1-2*x-7*x^2+2*x^3+3*x^4-x^5) ogf A003693 5.93018 -(3+24*x+2*x^7+16*x^4-24*x^3-9*x^6+8*x^5-12*x^2)/(-1+x)/(x-2)/(1+x)/(x^5-3*x^4-2*x^3+7*x^2+2*x-1) lgdogf A003693 11.9839 -(x-1)*(x-2)*(x+1)/(7*x^2-1+2*x-3*x^4+x^5-2*x^3) ogf A003697 7.10516 -(-1+x)/(-3*x^2+1-3*x+x^3) ogf A003697 7.69726 -(x-1)/(x+1)/(1-4*x+x^2) ogf A003697 2.17334 -111+111*x+(1429-1651*x-333*x^2+111*x^3)*f(x)+(-1318-1318*x^3+3954*x+3954*x^2)*f(x)^2 ogf A003697 4.1052 -2*(1+3*x+x^3-3*x^2)/(-1+x)/(1+x)/(x^2-4*x+1) lgdogf A003697 3.48555 {-a(n+3)+3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=2,a(2)=9} ogf A003698 16.1241 -(1+3*x-4*x^2)/(3*x^2-1+6*x-4*x^3) ogf A003698 16.1241 -(4*x+1)*(x-1)/(x+1)/(4*x^2-7*x+1) ogf A003698 8.56592 -(9-2*x+16*x^4-24*x^3+21*x^2)/(-1+x)/(1+4*x)/(1+x)/(4*x^2-7*x+1) lgdogf A003698 5.0761 1036+3108*x-4144*x^2+(-30607-82497*x+121392*x^2-4144*x^3)*f(x)+(-88713*x^2+29571-177426*x+118284*x^3)*f(x)^2 ogf A003698 9.96761 {a(n+3)-6*a(n+2)-3*a(n+1)+4*a(n),a(0)=1,a(1)=9,a(2)=53} ogf A003699 22.9518 -(-1-2*x+x^2)/(1-4*x+x^2) ogf A003699 22.9518 -(-1-2*x+x^2)/(x^2+1-4*x) ogf A003699 15.0999 -2*(3-2*x+x^2)/(x^2-4*x+1)/(x^2-2*x-1) lgdogf A003699 10.6258 4+8*x-4*x^2+(1+26*x-9*x^2)*f(x)+(-5+20*x-5*x^2)*f(x)^2 ogf A003699 12.4738 {a(n+3)-4*a(n+2)+a(n+1),a(0)=1,a(1)=6,a(2)=22} ogf A003703 44.3993 cos(ln(x+1)) egf A003703 4.47724 {(-4-6*n-4*n^2-n^3)*a(n+1)+(14+14*n+n^3+6*n^2)*a(n+2)+(18+2*n^2+12*n)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=0,a(2)=-1,a(3)=3} ogf A003703 4.47724 {(-4-6*n-4*n^2-n^3)*a(n+1)+(14+14*n+n^3+6*n^2)*a(n+2)+(2*n^2+12*n+18)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=0,a(2)=-1,a(3)=3} ogf A003708 13.2668 {a(n)*n-a(n+1)+(n+2)*a(n+2),a(0)=0,a(1)=1} revegf A003724 27.6531 1/2*exp(x)+1/2*exp(-x) lgdegf A003724 11.9288 {a(n+1)+(-5*n-6-n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=1/2} lgdegf A003725 38.462 -exp(-x)*(-1+x) lgdegf A003725 10.4896 {(-n-3)*a(n+3)+n*a(n+2)+a(n+1),a(0)=1,a(1)=-2,a(2)=3/2} lgdegf A003727 13.4905 1/2*exp(x)+1/2*exp(x)*x+1/2*exp(-x)-1/2*exp(-x)*x lgdegf A003727 7.26411 {a(n+1)+(-6-3*n-n^2)*a(n+3)+(18*n+40+2*n^2)*a(n+5),a(0)=1,a(1)=0,a(2)=3/2,a(3)=0,a(4)=5/24} lgdegf A003729 10.5811 -(-11+33*x-18*x^2+x^3)/(41*x^2+1-19*x+x^4-19*x^3) ogf A003729 10.5811 -(11-33*x-x^3+18*x^2)/(-41*x^2-1+19*x-x^4+19*x^3) ogf A003730 11.1168 -(1+2*x+3*x^3-14*x^2)/(-4*x^2-1+9*x+3*x^4-22*x^3) ogf A003730 11.1168 -(1+2*x-14*x^2+3*x^3)/(-4*x^2-1+9*x+3*x^4-22*x^3) ogf A003730 5.79491 -(11-36*x+338*x^4-130*x^3+9*x^6-84*x^5+61*x^2)/(3*x^3-14*x^2+2*x+1)/(3*x^4-22*x^3-4*x^2+9*x-1) lgdogf A003731 19.2313 (-1+x-4*x^2+2*x^3)/(-4*x^2-1+6*x+2*x^3) ogf A003731 19.2313 -(-1+x+2*x^3-4*x^2)/(4*x^2+1-6*x-2*x^3) ogf A003731 9.2595 13-13*x+52*x^2-26*x^3+(-6+71*x-24*x^2+12*x^3)*f(x)+(-28*x^2-7+42*x+14*x^3)*f(x)^2 ogf A003731 13.6367 5*(1+4*x^3-4*x^2)/(2*x^3-4*x^2+x-1)/(2*x^3-4*x^2+6*x-1) lgdogf A003731 11.3639 {a(n+4)-6*a(n+3)+4*a(n+2)-2*a(n+1),a(0)=1,a(1)=5,a(2)=30,a(3)=160} ogf A003735 13.3639 -(-29+87*x-43*x^2+x^3)/(102*x^2+1-44*x+x^4-44*x^3) ogf A003735 13.3639 -(29-87*x-x^3+43*x^2)/(-102*x^2-1+44*x-x^4+44*x^3) ogf A003736 7.98737 -(-4-72*x+1100*x^3+24*x^5+40*x^2-1088*x^4)/(-149*x^2+1-21*x+1354*x^4+285*x^3+24*x^6-1098*x^5) ogf A003736 8.44119 -4*(x-1)*(6*x^4-266*x^3+9*x^2+19*x+1)/(-149*x^2+1-21*x+1354*x^4+285*x^3+24*x^6-1098*x^5) ogf A003742 6.43127 -(-6-171*x+5559*x^3+405*x^5-162*x^2-7164*x^4)/(-396*x^2+1-26*x+6539*x^4+707*x^3+405*x^6-7239*x^5) ogf A003742 6.43127 -3*(-2-57*x-54*x^2+1853*x^3-2388*x^4+135*x^5)/(-396*x^2+1-26*x+6539*x^4+707*x^3+405*x^6-7239*x^5) ogf A003743 7.33301 -(6+108*x-1404*x^3-1536*x^5+72*x^2+3024*x^4)/(136*x^2-1+16*x+432*x^4-460*x^3+256*x^5) ogf A003743 7.50971 6*(-1-18*x-12*x^2+234*x^3-504*x^4+256*x^5)/(136*x^2-1+16*x+432*x^4-460*x^3+256*x^5) ogf A003747 18.879 -(56-75*x+x^2)/(-76*x^2-1+76*x+x^3) ogf A003747 20.0232 -(56-75*x+x^2)/(x-1)/(x^2-75*x+1) ogf A003747 10.3244 {-a(n+3)+76*a(n+2)-76*a(n+1)+a(n),a(0)=56,a(1)=4181,a(2)=313501} ogf A003748 15.6273 -(12+250*x-436*x^2)/(288*x^2-1+47*x-436*x^3) ogf A003748 7.90347 -(407+3020*x+95048*x^4-109000*x^3+38398*x^2)/(436*x^3-288*x^2-47*x+1)/(218*x^2-125*x-6) lgdogf A003748 14.6298 -2*(-6-125*x+218*x^2)/(-288*x^2+1-47*x+436*x^3) ogf A003748 10.2627 {-a(n+3)+47*a(n+2)+288*a(n+1)-436*a(n),a(0)=12,a(1)=814,a(2)=41278} ogf A003749 14.1258 -(-12-144*x+144*x^2)/(-12*x^2+1-28*x) ogf A003749 13.4014 -12-144*x+144*x^2+(-12*x^2+1-28*x)*f(x) ogf A003749 14.933 12*(-1-12*x+12*x^2)/(12*x^2-1+28*x) ogf A003749 11.6145 40*(1+12*x^2)/(12*x^2-12*x-1)/(12*x^2+28*x-1) lgdogf A003749 9.3331 {a(n+3)-28*a(n+2)-12*a(n+1),a(0)=12,a(1)=480,a(2)=13440} ogf A003752 6.90938 -(-4-28*x-120*x^3+148*x^5-16*x^6+64*x^2-84*x^4-8*x^7)/(36*x^2+1-11*x-67*x^4-16*x^3+10*x^6+9*x^5-2*x^7) ogf A003752 8.38997 -4*(1+7*x-16*x^2+30*x^3+21*x^4-37*x^5+4*x^6+2*x^7)/(x+1)/(2*x^2+4*x-1)/(1-4*x+x^2)^2 ogf A003755 10.9731 (1+6*x-16*x^2+6*x^3+x^4)/(1-6*x+x^2)/(x^4-42*x^3+83*x^2-42*x+1) ogf A003755 9.87576 -(1+6*x+6*x^3-16*x^2+x^4)/(-336*x^2-1+48*x-x^6-336*x^4+582*x^3+48*x^5) ogf A003756 17.6731 -(1-2*x+2*x^3+8*x^2)/(16*x^2-1+2*x+4*x^3) ogf A003756 17.6731 -(1-2*x+8*x^2+2*x^3)/(16*x^2-1+2*x+4*x^3) ogf A003756 12.2813 6*x*(-8+4*x^2+5*x)/(4*x^3+16*x^2+2*x-1)/(2*x^3+8*x^2-2*x+1) lgdogf A003756 10.8149 {-a(n+4)+2*a(n+3)+16*a(n+2)+4*a(n+1),a(0)=1,a(1)=0,a(2)=24,a(3)=54} ogf A003757 9.83602 -(1+10*x-x^4-4*x^3+2*x^5+4*x^2)/(-1+x)/(1+x)/(x^4-x^3-6*x^2-x+1) lgdogf A003757 19.672 -(x-1)*(x+1)/(1-x-6*x^2-x^3+x^4) ogf A003757 21.7071 -(x-x^3)/(-1+x-x^4+6*x^2+x^3) ogf A003757 7.15347 31*x-31*x^3+(-31+10*x+186*x^2+52*x^3-31*x^4)*f(x)+(21*x^4+21-21*x-21*x^3-126*x^2)*f(x)^2 ogf A003758 10.5562 -(3*x-2*x^3-2*x^2+x^4)/(-1+3*x+9*x^2-3*x^3-3*x^4+x^5) ogf A003758 5.88924 -(7+50*x+2*x^7+30*x^4-30*x^3-9*x^6+4*x^5-36*x^2)/(-1+x)/(x^2-x-3)/(x^5-3*x^4-3*x^3+9*x^2+3*x-1) lgdogf A003758 12.1626 -(x-1)*(x^2-x-3)/(9*x^2-1+3*x-3*x^4+x^5-3*x^3) ogf A003759 13.3623 -(3+6*x+4*x^3-6*x^2)/(3*x^2-1+3*x+x^4-2*x^3) lgdogf A003759 20.2738 -2*x/(-1+3*x+3*x^2-2*x^3+x^4) ogf A003759 21.7755 -2/(-1+3*x+3*x^2-2*x^3+x^4) ogf A003759 8.39913 -4*x+(2-12*x-6*x^2+4*x^3-2*x^4)*f(x)+(-9*x^2+3-9*x-3*x^4+6*x^3)*f(x)^2 ogf A003764 8.11952 -(-1-7*x+16*x^3+9*x^2-16*x^4)/(-16*x^2+1-6*x+16*x^4+29*x^3-16*x^5) ogf A003764 8.37325 -(1+7*x-9*x^2-16*x^3+16*x^4)/(16*x^2-1+6*x-16*x^4-29*x^3+16*x^5) ogf A003765 7.29395 -(-1-5*x+7*x^2+3*x^3-12*x^4+4*x^5)/(-3*x^2+1-5*x-20*x^4+19*x^3+4*x^5) ogf A003765 7.51168 -(1+5*x-3*x^3-4*x^5-7*x^2+12*x^4)/(3*x^2-1+5*x+20*x^4-19*x^3-4*x^5) ogf A003769 15.8212 -(-3-4*x+x^2)/(x+1)/(-5*x+1+x^2) ogf A003769 8.88208 -(16+22*x+x^4-8*x^3+11*x^2)/(1+x)/(x^2-5*x+1)/(x^2-4*x-3) lgdogf A003769 16.8759 -(3+4*x-x^2)/(4*x^2-1+4*x-x^3) ogf A003769 4.48034 71616+95488*x-23872*x^2+(352859+597796*x-30089*x^2-23872*x^3)*f(x)+(502308*x^2-125577+502308*x-125577*x^3)*f(x)^2 ogf A003769 9.20506 {-a(n+3)+4*a(n+2)+4*a(n+1)-a(n),a(0)=3,a(1)=16,a(2)=75} ogf A003770 11.9146 -(3+9*x-12*x^2)/(8*x^2-1+11*x-12*x^3) ogf A003770 3.83341 -11889-35667*x+47556*x^2+(-55434-221784*x+205884*x^2+47556*x^3)*f(x)+(-158392*x^2+19799-217789*x+237588*x^3)*f(x)^2 ogf A003770 6.48297 -2*(7+4*x+24*x^4-36*x^3+16*x^2)/(-1+x)/(1+4*x)/(12*x^3-8*x^2-11*x+1) lgdogf A003770 11.3036 -3*(4*x+1)*(x-1)/(-8*x^2+1-11*x+12*x^3) ogf A003770 7.4719 {a(n+3)-11*a(n+2)-8*a(n+1)+12*a(n),a(0)=3,a(1)=42,a(2)=474} ogf A003771 18.3774 -(-3-9*x+6*x^2)/(2*x^2+1-7*x) ogf A003771 12.1124 -2*(5-4*x+4*x^2)/(2*x^2-3*x-1)/(2*x^2-7*x+1) lgdogf A003771 17.1917 -3*(-1-3*x+2*x^2)/(2*x^2+1-7*x) ogf A003771 7.95438 171+513*x-342*x^2+(36+678*x-300*x^2)*f(x)+(-31+217*x-62*x^2)*f(x)^2 ogf A003771 10.6589 {a(n+3)-7*a(n+2)+2*a(n+1),a(0)=3,a(1)=30,a(2)=198} ogf A003772 6.23413 -(-12-132*x-3300*x^3-1968*x^5+288*x^6+660*x^2+4776*x^4)/(173*x^2+1-23*x-62*x^4-421*x^3-24*x^6+132*x^5) ogf A003772 7.85039 12*(-1-11*x+55*x^2-275*x^3+398*x^4-164*x^5+24*x^6)/(-1+9*x+6*x^2)/(2*x^2+1-7*x)^2 ogf A003773 9.14447 -(16+192*x+16*x^2)/(-1190*x^2-1+204*x-x^4+204*x^3) ogf A003773 11.1518 16*(1+12*x+x^2)/(1-6*x+x^2)/(x^2-198*x+1) ogf A003774 8.16924 -(-4-48*x^3-192*x^5-96*x^6-80*x^2)/(1-12*x-4*x^2-48*x^3) ogf A003774 8.02592 -4*(1+20*x^2+12*x^3+48*x^5+24*x^6)/(-1+12*x+4*x^2+48*x^3) ogf A003775 15.2391 -(1-7*x-x^3+7*x^2)/(-32*x^2-1+15*x-x^4+15*x^3) ogf A003775 7.87641 -(8-50*x+94*x^4-184*x^3+x^6-14*x^5+161*x^2)/(-1+x)/(1-6*x+x^2)/(x^4-15*x^3+32*x^2-15*x+1) lgdogf A003775 15.5778 -(x-1)*(1-6*x+x^2)/(32*x^2+1-15*x+x^4-15*x^3) ogf A003775 5.39231 -179+1253*x-1253*x^2+179*x^3+(-7687+52377*x-49334*x^2+5181*x^3+179*x^4)*f(x)+(7866-117990*x+251712*x^2-117990*x^3+7866*x^4)*f(x)^2 ogf A003776 9.76452 -(3-18*x+15*x^2)/(-57*x^2-1+24*x+26*x^3) ogf A003776 5.27812 -2*(9-52*x+65*x^4-156*x^3+150*x^2)/(-1+x)/(-1+2*x)/(5*x-1)/(13*x^2-22*x+1) lgdogf A003776 9.76452 -3*(5*x-1)*(x-1)/(2*x-1)/(13*x^2-22*x+1) ogf A003776 3.25484 85377-512262*x+426885*x^2+(211922-759270*x-420258*x^2+739934*x^3)*f(x)+(-80127+1923048*x-4567239*x^2+2083302*x^3)*f(x)^2 ogf A003776 6.29969 {-a(n+3)+24*a(n+2)-57*a(n+1)+26*a(n),a(0)=3,a(1)=54,a(2)=1140} ogf A003777 32.2935 (1+7*x-3*x^2+x^3)/(x-1)^4 ogf A003777 18.7753 -(1+7*x+x^3-3*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A003777 17.9408 -(11+15*x+x^3-3*x^2)/(-1+x)/(x^3-3*x^2+7*x+1) lgdogf A003777 5.80818 -20042-140294*x+60126*x^2-20042*x^3+(12563-132521*x+142689*x^2-87647*x^3+20042*x^4)*f(x)+(7479-29916*x+44874*x^2-29916*x^3+7479*x^4)*f(x)^2 ogf A003777 7.47534 {(482+339*n+49*n^2)*a(n+1)+(-2684-1580*n-218*n^2)*a(n+2)+(881*n+1122+169*n^2)*a(n+3),a(0)=1,a(1)=11,a(2)=35} ogf A003784 24.4045 -(-2-x-2*x^2-19*x^3)/(-1+x^4) ogf_with_Euler_Transform A003815 17.7436 (1+3*x-x^2+x^3)/(1+x^2)/(x-1)^2/(x+1)^2 ogf A003815 19.7714 -(-x+x^3-3*x^2-x^4)/(1-x^4-x^2+x^6) ogf A003815 9.61111 -(3+17*x^4+4*x^3+3*x^6-4*x^5+9*x^2)/(-1+x)/(1+x)/(1+x^2)/(x^3-x^2+3*x+1) lgdogf A003816 19.5829 (1-x+3*x^2+x^3)/(1+x^2)/(x-1)^2/(x+1)^2 ogf A003816 10.0491 -(-1+8*x-3*x^4+12*x^3+3*x^6+12*x^5+x^2)/(-1+x)/(1+x)/(1+x^2)/(x^3+3*x^2-x+1) lgdogf A003816 21.8209 -(-x-x^4+x^2-3*x^3)/(1-x^4-x^2+x^6) ogf A003816 21.8209 -(x+3*x^3+x^2-x^4)/(-1+x^4+x^2-x^6) ogf A003823 41.7525 -(1-x^2)/(-1-x^3-x-x^2-x^4) ogf_with_Euler_Transform A003878 9.59027 -(-1+2*x-43*x^2+21*x^3-3*x^4)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A003878 16.2502 -(1-2*x+43*x^2-21*x^3+3*x^4)/(x-1)^5 ogf A003878 9.14072 -3*(1+26*x+x^4-10*x^3+22*x^2)/(-1+x)/(3*x^4-21*x^3+43*x^2-2*x+1) lgdogf A003880 1.69785 -(x^6+x^5+1+6*x)/(x-1) ogf A003884 5.78447 -(x^10+x^9+14*x+1)/(x-1) ogf A003884 2.52413 1+28*x+196*x^2+(-2-26*x+28*x^2)*f(x)+(x^2+1-2*x)*f(x)^2 ogf A003885 2.48354 -(1+8*x+7*x^3+x^7+x^8)/(x-1) ogf A003886 2.8399 -(x^7+x^8+9*x^3+8*x+1)/(x-1) ogf A003887 3.51875 -(x^9+x^8+10*x+1+11*x^3)/(x-1) ogf A003888 3.75633 -(x^10+x^9+12*x+1+11*x^3)/(x-1) ogf A003889 2.50077 -(1+x^2)*(x^8+x^7-x^6-x^5+x^4+x^3-x^2+12*x+1)/(x-1) ogf A003890 2.52413 -(1+x^2)*(x^9+x^8-x^7-x^6+x^5+x^4-x^3-x^2+14*x+1)/(x-1) ogf A003892 13.5665 -(x^17+x^18+1+30*x)/(x-1) ogf A003945 52.8954 -(-1-x)/(1-2*x) ogf A003945 56.6736 -(x+1)/(2*x-1) ogf A003945 46.6724 -1-x+(1-2*x)*f(x) ogf A003945 26.4477 -1/2-x+1/2*(1+8*x+4*x^2)^(1/2) revogf A003945 46.6724 -3/(1+x)/(-1+2*x) lgdogf A003945 25.5945 {a(n+2)-2*a(n+1),a(0)=1,a(1)=3} ogf A003946 42.7897 -(-1-x)/(1-3*x) ogf A003946 45.8461 -(x+1)/(3*x-1) ogf A003946 37.7556 -1-x+(1-3*x)*f(x) ogf A003946 17.829 -1/2-3/2*x+1/2*((1+x)*(9*x+1))^(1/2) revogf A003946 40.1154 -4/(1+x)/(3*x-1) lgdogf A003946 20.7047 {a(n+2)-3*a(n+1),a(0)=1,a(1)=4} ogf A003947 46.9956 -(-1-x)/(1-4*x) ogf A003947 50.3525 -(x+1)/(4*x-1) ogf A003947 41.4667 -1-x+(1-4*x)*f(x) ogf A003947 20.7334 -1/2-2*x+1/2*(1+12*x+16*x^2)^(1/2) revogf A003947 41.4667 -5/(1+x)/(-1+4*x) lgdogf A003947 22.7398 {a(n+2)-4*a(n+1),a(0)=1,a(1)=5} ogf A003948 48.7301 -(-1-x)/(1-5*x) ogf A003948 52.2108 -(x+1)/(5*x-1) ogf A003948 42.9971 -1-x+(1-5*x)*f(x) ogf A003948 20.3042 -1/2-5/2*x+1/2*(1+14*x+25*x^2)^(1/2) revogf A003948 45.6845 -6/(1+x)/(5*x-1) lgdogf A003948 23.5791 {a(n+2)-5*a(n+1),a(0)=1,a(1)=6} ogf A003949 48.4956 -(-1-x)/(1-6*x) ogf A003949 51.9595 -(x+1)/(6*x-1) ogf A003949 42.7902 -1-x+(1-6*x)*f(x) ogf A003949 21.3951 -3*x-1/2+1/2*(36*x^2+16*x+1)^(1/2) revogf A003949 45.4646 -7/(1+x)/(6*x-1) lgdogf A003949 23.4656 {a(n+2)-6*a(n+1),a(0)=1,a(1)=7} ogf A003950 46.9838 -(-1-x)/(1-7*x) ogf A003950 50.3398 -(x+1)/(7*x-1) ogf A003950 41.4563 -1-x+(1-7*x)*f(x) ogf A003950 19.5766 -1/2-7/2*x+1/2*(1+18*x+49*x^2)^(1/2) revogf A003950 44.0473 -8/(1+x)/(7*x-1) lgdogf A003950 22.7341 {a(n+2)-7*a(n+1),a(0)=1,a(1)=8} ogf A003951 44.8559 -(-1-x)/(1-8*x) ogf A003951 48.0599 -(x+1)/(8*x-1) ogf A003951 39.5788 -1-x+(1-8*x)*f(x) ogf A003951 18.1848 -4*x-1/2+1/2*((1+4*x)*(16*x+1))^(1/2) revogf A003951 39.5788 -9/(1+x)/(-1+8*x) lgdogf A003951 21.7045 {a(n+2)-8*a(n+1),a(0)=1,a(1)=9} ogf A003952 47.0886 -(-1-x)/(1-9*x) ogf A003952 47.0886 -(x+1)/(-1+9*x) ogf A003952 41.5487 -1-x+(1-9*x)*f(x) ogf A003952 39.2405 -10/(1+x)/(-1+9*x) lgdogf A003952 19.6202 -9/2*x-1/2+1/2*(81*x^2+22*x+1)^(1/2) revogf A003952 22.0728 {a(n+2)-9*a(n+1),a(0)=1,a(1)=10} ogf A003953 29.9258 -(-1-x)/(1-10*x) ogf A003953 31.9208 -(x+1)/(10*x-1) ogf A003953 26.6007 -1-x+(1-10*x)*f(x) ogf A003953 26.6007 -11/(1+x)/(10*x-1) lgdogf A003953 13.6804 -5*x-1/2+1/2*(100*x^2+24*x+1)^(1/2) revogf A003953 14.5095 {a(n+2)-10*a(n+1),a(0)=1,a(1)=11} ogf A003954 29.9258 -(-1-x)/(1-11*x) ogf A003954 29.9258 -(x+1)/(-1+11*x) ogf A003954 26.6007 -1-x+(1-11*x)*f(x) ogf A003954 12.6003 -1/2-11/2*x+1/2*(1+26*x+121*x^2)^(1/2) revogf A003954 26.6007 -12/(1+x)/(11*x-1) lgdogf A003954 14.5095 {a(n+2)-11*a(n+1),a(0)=1,a(1)=12} ogf A003955 2.85464 {(-50-65*n-28*n^2-4*n^3)*a(n+1)+(369+315*n+88*n^2+8*n^3)*a(n+2)+(-2*n-6)*a(n+3),a(0)=4,a(1)=54,a(2)=1800} ogf A003982 88.4252 x^3/(1+x^4) ogf_with_Euler_Transform A003982 23.7238 {a(n+4)+a(n),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf_with_Euler_Transform A003993 18.5967 -(-2-2*x)/(7*x^2+1-5*x-3*x^3) ogf A003993 5.5031 -17058-17058*x+(20197-30977*x+59703*x^2-25587*x^3)*f(x)+(-5834+17502*x^3+29170*x-40838*x^2)*f(x)^2 ogf A003993 14.1922 -2*(-3+4*x+3*x^2)/(-1+x)/(3*x-1)/(1+x) lgdogf A003993 22.471 -2*(x+1)/(3*x-1)/(x-1)^2 ogf A003993 9.63043 {a(n+3)-5*a(n+2)+7*a(n+1)-3*a(n),a(0)=2,a(1)=12,a(2)=46} ogf A004004 13.9263 -(-x-3*x^2)/(1-11*x+19*x^2-9*x^3) ogf A004004 18.3828 -(3*x+1)/(-1+9*x)/(x-1)^2 ogf A004004 10.9421 -2*(9*x+7)*(3*x-1)/(-1+x)/(3*x+1)/(-1+9*x) lgdogf A004004 4.25527 12261*x+36783*x^2+(-12261+79463*x-399183*x^2+110349*x^3)*f(x)+(55408-609488*x+1052752*x^2-498672*x^3)*f(x)^2 ogf A004004 8.06261 {a(n+3)-11*a(n+2)+19*a(n+1)-9*a(n),a(0)=0,a(1)=1,a(2)=14} ogf A004005 9.22743 -(-1-89*x+69*x^2+405*x^3)/(-1+25*x)/(-1+9*x)^2/(x-1)^3 ogf A004005 6.38822 -(-1-89*x+69*x^2+405*x^3)/(663*x^2+1-46*x+7711*x^4-6606*x^5-3748*x^3+2025*x^6) ogf A004005 4.93348 -3*(-45-7*x+14895*x^4-48286*x^3+91125*x^5+16046*x^2)/(-1+x)/(25*x-1)/(-1+9*x)/(405*x^3+69*x^2-89*x-1) lgdogf A004006 45.7185 (1-x+x^2)/(x-1)^4 ogf A004006 21.0058 -(-x+x^2-x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A004006 26.8005 -(3-x+2*x^2)/(-1+x)/(x^2-x+1) lgdogf A004006 70.6558 3+x+x^2-x^5 ogf_with_Euler_Transform A004006 10.0937 x-x^2+x^3+(-1+9*x-11*x^2+9*x^3-x^4)*f(x)+(-5+20*x-30*x^2+20*x^3-5*x^4)*f(x)^2 ogf A004006 8.93349 {(n+3)*a(n+4)+(-7-2*n)*a(n+3)+(3+2*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=3,a(3)=7} ogf A004018 33.1722 -(4-2*x+2*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A004018 19.2399 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=4,a(1)=-6,a(2)=4} ogf_with_Euler_Transform A004020 46.0016 {-a(n+1)-a(n),a(0)=2} ogf_with_Euler_Transform A004024 19.0993 {a(n+3)+a(n+2)+a(n+1)+a(n),a(0)=1,a(1)=1,a(2)=1} ogf_with_Euler_Transform A004040 12.2813 -1+11*x+x^2+(1-14*x+14*x^2+2*x^3)*f(x)+(3*x^2+x+3*x^3+x^4)*f(x)^2 ogf A004040 12.2813 -1+11*x+x^2+(1-14*x+2*x^3+14*x^2)*f(x)+(3*x^2+x+3*x^3+x^4)*f(x)^2 ogf A004040 6.28569 {(672+528*n+96*n^2)*a(n+1)+(288+308*n+92*n^2)*a(n+2)+(-44-31*n-5*n^2)*a(n+3)+(-9*n-20-n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=6,a(3)=23} ogf A004041 7.92787 {(-20*n-4*n^2-25)*a(n+1)+(12+4*n)*a(n+2)-a(n+3),a(0)=1,a(1)=4,a(2)=23} ogf A004047 1.02133 1+(-3+2*x)*f(x)+(3-4*x+x^2)*f(x)^2+(-1-x^2+2*x)*f(x)^3 ogf A004052 1.62111 -(3*x^2+x^5+x^4+1+4*x^9+2*x)/(-3*x^9-1-x+x^11-x^2+3*x^3-x^4+x^8+x^6+x^7+x^10) ogf A004052 1.98135 -1+(3-3*x)*f(x)+(-3+6*x-3*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 ogf A004054 21.7379 -(1-x)/(-x^2-1+4*x-6*x^3) ogf A004054 10.4509 -(3-2*x+12*x^3-17*x^2)/(-1+x)/(3*x-1)/(-1+2*x)/(1+x) lgdogf A004054 19.4088 -(x-1)/(3*x-1)/(2*x-1)/(x+1) ogf A004054 8.49135 57-57*x+(-58+229*x-57*x^2-342*x^3)*f(x)+(x^2+1-4*x+6*x^3)*f(x)^2 ogf A004054 10.0638 {-a(n+3)+4*a(n+2)-a(n+1)-6*a(n),a(0)=1,a(1)=3,a(2)=11} ogf A004056 1.50447 1+(-3+2*x)*f(x)+(3-4*x+x^2)*f(x)^2+(-1-x^2+2*x)*f(x)^3 ogf A004057 16.25 (x-1)/(4*x-1)/(3*x-1)/(2*x-1)/(x+1) ogf A004057 8.01058 -(-7+34*x+72*x^4-100*x^3-11*x^2)/(-1+x)/(-1+4*x)/(3*x-1)/(-1+2*x)/(1+x) lgdogf A004057 16.25 -(1-x)/(-17*x^2-1+8*x-2*x^3+24*x^4) ogf A004057 4.70042 -14472+14472*x+(4645-105949*x+246024*x^2+28944*x^3-347328*x^4)*f(x)+(9827+19654*x^3-78616*x+167059*x^2-235848*x^4)*f(x)^2 ogf A004058 10.7963 -(1-x)/(-57*x^2-1+13*x-120*x^5+83*x^3+34*x^4) ogf A004058 11.0417 -(x-1)/(4*x-1)/(3*x-1)/(2*x-1)/(5*x-1)/(x+1) ogf A004058 5.64922 -6*(2-19*x-117*x^4-5*x^3+80*x^5+51*x^2)/(-1+x)/(-1+4*x)/(3*x-1)/(-1+2*x)/(5*x-1)/(1+x) lgdogf A004068 38.2479 (x^2+3*x+1)/(x-1)^4 ogf A004068 21.3738 -(7+11*x+2*x^2)/(-1+x)/(x^2+3*x+1) lgdogf A004068 18.6336 -(x+3*x^2+x^3)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A004068 7.73095 19*x+57*x^2+19*x^3+(-19+91*x-69*x^2+91*x^3-19*x^4)*f(x)+(-90*x^2-15+60*x-15*x^4+60*x^3)*f(x)^2 ogf A004068 8.07455 {(n+3)*a(n+4)+(-3+2*n)*a(n+3)+(-13-2*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=7,a(3)=23} ogf A004082 8.26812 (1+6*x+6*x^2+6*x^3+7*x^4+6*x^5+6*x^6+5*x^7+x^8)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004082 10.6304 -(-1-6*x-7*x^4-6*x^5-5*x^7-6*x^3-x^8-6*x^2-6*x^6)/(1-x+x^8-x^7) ogf A004083 9.75278 (x+1)*(2*x^7+3*x^6+4*x^5+2*x^4+4*x^3+3*x^2+3*x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004083 12.4535 -(-1-4*x-6*x^4-6*x^5-5*x^7-7*x^3-2*x^8-6*x^2-7*x^6)/(1-x+x^8-x^7) ogf A004084 9.57355 (x+1)*(x^7+x^6+2*x^5+x^4+2*x^3+x^2+2*x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004084 11.3971 -(-1-3*x-3*x^4-3*x^5-2*x^7-3*x^3-x^8-3*x^2-3*x^6)/(1-x+x^8-x^7) ogf A004112 22.2814 (1+2*x^2+330*x^5+22*x^6)/(x-1)^2 ogf A004112 18.7633 -(x+22*x^7+2*x^3+330*x^6)/(-1+2*x-x^2) ogf A004112 10.9693 2*(-1-2*x-825*x^4+44*x^6+429*x^5)/(-1+x)/(22*x^6+330*x^5+2*x^2+1) lgdogf A004116 21.2111 (-1-x+x^3)/(x+1)/(x-1)^3 ogf A004116 12.1206 -(-3-6*x+x^4+2*x^3)/(-1+x)/(1+x)/(x^3-x-1) lgdogf A004116 17.554 -(1+x-x^3)/(-2*x^3-1+2*x+x^4) ogf A004116 6.20812 205+205*x-205*x^3+(-221+394*x-394*x^3+205*x^4)*f(x)+(32*x^3+16-32*x-16*x^4)*f(x)^2 ogf A004116 3.799 {(-382-249*n-29*n^2)*a(n+1)+(-364-10*n+14*n^2)*a(n+2)+(162+219*n+29*n^2)*a(n+3)+(-20*n+144-14*n^2)*a(n+4),a(0)=1,a(1)=3,a(2)=6,a(3)=9} ogf A004119 29.3863 -(-1-x+3*x^2)/(x-1)/(2*x-1) ogf A004119 18.4519 -(4-10*x+7*x^2)/(-1+x)/(-1+2*x)/(3*x^2-x-1) lgdogf A004119 14.1684 7+7*x-21*x^2+(-6+22*x-17*x^2)*f(x)+(-1+3*x-2*x^2)*f(x)^2 ogf A004119 16.8815 {a(n+3)-3*a(n+2)+2*a(n+1),a(0)=1,a(1)=4,a(2)=7} ogf A004120 36.1633 (-1-x+x^5)/(x-1)^3 ogf A004120 15.4985 (2*x^2-x-2)*(x^3-2*x^2-2)/(-1+x)/(x^5-x-1) lgdogf A004120 22.4462 -(-1-x+x^5)/(3*x^2+1-3*x-x^3) ogf A004120 4.64956 {(12-4*n^2-8*n)*a(n+1)+(-36-17*n+3*n^2)*a(n+2)+(-14+40*n+6*n^2)*a(n+3)+(-15*n+20-5*n^2)*a(n+4),a(0)=1,a(1)=4,a(2)=9,a(3)=16,a(4)=25,a(5)=35} ogf A004126 37.4069 (1+5*x+x^2)/(x-1)^4 ogf A004126 20.9038 -(9+17*x+2*x^2)/(-1+x)/(x^2+5*x+1) lgdogf A004126 18.2239 -(x+x^3+5*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A004126 6.76886 185*x+925*x^2+185*x^3+(-185+831*x-655*x^2+831*x^3-185*x^4)*f(x)+(-546*x^2-91+364*x-91*x^4+364*x^3)*f(x)^2 ogf A004126 7.89701 {(n+3)*a(n+4)+(-1+4*n)*a(n+3)+(-21-4*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=9,a(3)=31} ogf A004129 1.58561 (1+x^2+x)*(x^4+x^3+2*x^2+2*x+1)/(x-1)/(x^5+x^4+x^3-x-1) ogf A004138 9.42942 -(-1+2*x^4-4*x^3+x^2)/(2*x^3+1-2*x+2*x^5-3*x^4) ogf A004138 9.42942 -(-1+x^2-4*x^3+2*x^4)/(x-1)/(2*x^4-x^3+x^2+x-1) ogf A004138 4.56889 -2*(1-x-8*x^7+2*x^4-6*x^3+2*x^8+7*x^6-3*x^5+4*x^2)/(-1+x)/(2*x^4-4*x^3+x^2-1)/(2*x^4-x^3+x^2+x-1) lgdogf A004142 17.7003 -(-1+6*x^2)/(2*x-1)^2/(3*x-1)^2 ogf A004142 13.3832 -(-x+6*x^3)/(1-10*x+36*x^4+37*x^2-60*x^3) ogf A004142 11.9285 -2*(5-18*x+36*x^3)/(3*x-1)/(-1+2*x)/(-1+6*x^2) lgdogf A004142 4.32056 34567*x-207402*x^3+(-34567+345312*x-1278979*x^2+2076168*x^3-1244412*x^4)*f(x)+(12888*x^4+358-3580*x-21480*x^3+13246*x^2)*f(x)^2 ogf A004142 6.16529 {(36+30*n+6*n^2)*a(n+1)+(-15-5*n^2-20*n)*a(n+2)+(2+3*n+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=10} ogf A004146 22.8267 -(-x-x^2)/(1-4*x+4*x^2-x^3) ogf A004146 14.3331 -(5-8*x+2*x^3-x^2)/(-1+x)/(1+x)/(x^2-3*x+1) lgdogf A004146 25.6801 -(x+1)/(x-1)/(x^2-3*x+1) ogf A004146 10.8127 x+x^2+(-1+9*x+x^2+x^3)*f(x)+(-20*x^2-5+20*x+5*x^3)*f(x)^2 ogf A004146 11.8523 {a(n+3)-4*a(n+2)+4*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=5} ogf A004148 26.8482 -1+(1-x+x^2)*f(x)-x^2*f(x)^2 ogf A004148 14.184 -1/2*(-x^2+x-1+(1+x^2+x)^(1/2)*(x^2-3*x+1)^(1/2))/x^2 ogf A004149 21.1976 -1+(1-x+x^2+x^3)*f(x)-x^2*f(x)^2 ogf A004149 21.1976 -1+(1-x+x^3+x^2)*f(x)-x^2*f(x)^2 ogf A004154 11.3963 (10+10*x+10*x^2+10*x^3+10*x^4)*f(x)+(-10+x^5)*f(x)^2 egf A004154 14.4538 -(-10-10*x-10*x^2-10*x^3-10*x^4)/(10-x^5) egf A004154 7.50136 -(10+20*x+2*x^7+5*x^4+40*x^3+x^8+3*x^6+4*x^5+30*x^2)/(x^4+x^3+x^2+x+1)/(x^5-10) lgdegf A004154 19.1164 -10*(1+x+x^2+x^3+x^4)/(-10+x^5) egf A004171 48.0686 -2+(1-4*x)*f(x) ogf A004171 72.1029 -2/(4*x-1) ogf A004171 65.5481 -4/(-1+4*x) lgdogf A004171 55.4638 1/2*x/(1+2*x) revogf A004171 55.4638 1/4*ln(1+2*x) revegf A004171 80.1143 2/(1-4*x) ogf A004171 32.7741 {a(n+1)-4*a(n),a(0)=2} ogf A004183 6.54659 -(x+3*x^3+x^18+10*x^10+7*x^7+4*x^16+5*x^5+6*x^6+5*x^15+7*x^13+9*x^11+9*x^9+4*x^4+2*x^2+8*x^12+6*x^14+3*x^17+x^19)/(-1+2*x^10-x^20) ogf A004184 6.4474 -(-x-3*x^3-2*x^18-10*x^10-7*x^7-4*x^16-5*x^5-6*x^6-5*x^15-7*x^13-9*x^11-4*x^4-2*x^2-8*x^8-8*x^12-6*x^14-3*x^17-x^19)/(1-2*x^10+x^20) ogf A004187 34.0425 -(-7+2*x)/(x^2+1-7*x) lgdogf A004187 16.6254 -1/2*(-7*x-1+(9*x+1)^(1/2)*(5*x+1)^(1/2))/x revogf A004187 54.9917 1/(x^2-7*x+1) ogf A004187 37.6259 x+(-1+7*x-x^2)*f(x) ogf A004187 54.9917 x/(1-7*x+x^2) ogf A004187 19.8581 {a(n+2)-7*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A004188 36.7588 (1+7*x+x^2)/(x-1)^4 ogf A004188 17.9081 -(-x-x^3-7*x^2)/(1-4*x+6*x^2-4*x^3+x^4) ogf A004188 20.5417 -(x+11)*(1+2*x)/(-1+x)/(x^2+7*x+1) lgdogf A004188 5.86905 2153*x+15071*x^2+2153*x^3+(-2153+9377*x-7563*x^2+9377*x^3-2153*x^4)*f(x)+(-4590*x^2-765+3060*x-765*x^4+3060*x^3)*f(x)^2 ogf A004188 7.76019 {(n+3)*a(n+4)+(1+6*n)*a(n+3)+(-29-6*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=11,a(3)=39} ogf A004189 12.8484 -1/2*(-1-10*x+(8*x+1)^(1/2)*(12*x+1)^(1/2))/x revogf A004189 27.5322 -2*(x-5)/(x^2+1-10*x) lgdogf A004189 41.2983 1/(1-10*x+x^2) ogf A004189 28.9088 x+(-1+10*x-x^2)*f(x) ogf A004189 41.2983 x/(1-10*x+x^2) ogf A004189 15.6264 {a(n+2)-10*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A004190 23.6256 -(-11+2*x)/(x^2+1-11*x) lgdogf A004190 33.9618 -1/(-1+11*x-x^2) ogf A004190 12.0753 -1/2*(-11*x-1+(9*x+1)^(1/2)*(13*x+1)^(1/2))/x revogf A004190 10.2526 -2+(-117-22*x+2*x^2)*f(x)+(119-1309*x+119*x^2)*f(x)^2 ogf A004190 38.8135 1/(1-11*x+x^2) ogf A004190 13.9331 {-a(n+2)+11*a(n+1)-a(n),a(0)=1,a(1)=11} ogf A004191 14.9787 -1+(-70-12*x+x^2)*f(x)+(71-852*x+71*x^2)*f(x)^2 ogf A004191 43.9998 -1/(-1+12*x-x^2) ogf A004191 15.3043 -1/2*(-12*x-1+(14*x+1)^(1/2)*(1+10*x)^(1/2))/x revogf A004191 31.9998 -2*(-6+x)/(x^2+1-12*x) lgdogf A004191 50.2855 1/(1-12*x+x^2) ogf A004191 18.0512 {-a(n+2)+12*a(n+1)-a(n),a(0)=1,a(1)=12} ogf A004211 70.7851 exp(2*x) lgdegf A004211 14.9021 {(-n-2)*a(n+2)+2*a(n+1),a(0)=1,a(1)=2} lgdegf A004212 69.6507 exp(3*x) lgdegf A004212 14.6633 {(-n-2)*a(n+2)+3*a(n+1),a(0)=1,a(1)=3} lgdegf A004213 66.986 exp(4*x) lgdegf A004213 14.1023 {(-n-2)*a(n+2)+4*a(n+1),a(0)=1,a(1)=4} lgdegf A004216 12.969 (-3*x^2-2*x-1-5*x^4-4*x^3+90*x^87+90*x^88)/(-x^2-1-x+90*x^87-x^4-x^3+5*x^5) lgdogf A004216 21.6151 -(x^9+x^10+x^11+x^12+x^13+x^14)/(-1+x^6+x^90) ogf A004218 13.8727 (-1+8*x^9-9*x^8)/(-1+x)/(1+x)/(x^2-x+1)/(x^6-x^3+1) lgdogf A004218 20.809 -(x+1)*(1-x+x^2)*(1-x^3+x^6)/(x-1) ogf A004218 44.2192 -(x+x^10)/(-1+x) ogf A004218 70.7506 1+x^8-x^17 ogf_with_Euler_Transform A004218 7.7748 {a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=2} ogf A004253 30.7477 -(-1+x)/(x^2+1-5*x) ogf A004253 18.8454 -(4-2*x+x^2)/(-1+x)/(x^2-5*x+1) lgdogf A004253 30.7477 -(x-1)/(-5*x+1+x^2) ogf A004253 12.7001 -1+x+(10-14*x+x^2)*f(x)+(-9+45*x-9*x^2)*f(x)^2 ogf A004253 14.6052 -1/2*(-5*x-1+(21*x^2+6*x+1)^(1/2))/(1+x) revogf A004253 16.228 {a(n+2)-5*a(n+1)+a(n),a(0)=1,a(1)=4} ogf A004254 28.6673 -(-5+2*x)/(x^2-5*x+1) lgdogf A004254 14.0003 -1/2*(-5*x-1+(7*x+1)^(1/2)*(3*x+1)^(1/2))/x revogf A004254 43.001 1/(-5*x+1+x^2) ogf A004254 31.685 x+(-1+5*x-x^2)*f(x) ogf A004254 46.3088 x/(x^2+1-5*x) ogf A004254 16.7226 {a(n+2)-5*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A004255 16.2132 -(1-2*x+4*x^2)/(-10*x^2-1+5*x-5*x^4+x^5+10*x^3) ogf A004255 34.6373 -(1-2*x+4*x^2)/(x-1)^5 ogf A004255 23.0915 -3*(4*x^2+1)/(-1+x)/(1-2*x+4*x^2) lgdogf A004255 8.19377 {(n+4)*a(n+4)+(-12-3*n)*a(n+3)+(6*n+12)*a(n+2)+(-16-4*n)*a(n+1),a(0)=1,a(1)=3,a(2)=9,a(3)=25} ogf A004256 25.4459 (3+14*x+3*x^2)/(x-1)^6 ogf A004256 9.4883 -(-3*x-3*x^3-14*x^2)/(1-6*x+15*x^2-6*x^5-20*x^3+15*x^4+x^6) ogf A004256 14.3541 -4*(8+19*x+3*x^2)/(-1+x)/(3*x^2+14*x+3) lgdogf A004256 5.5981 {(9+3*n)*a(n+4)+(-10+11*n)*a(n+3)+(-87-11*n)*a(n+2)+(-12-3*n)*a(n+1),a(0)=0,a(1)=3,a(2)=32,a(3)=150} ogf A004271 42.7449 (1+x^4)/(x-1)^2 ogf A004271 20.683 2*(-1+x^4-2*x^3)/(-1+x)/(1+x^4) lgdogf A004271 71.2414 2+x^3-x^7 ogf_with_Euler_Transform A004271 9.56974 {-a(n+3)+2*a(n+2)-a(n+1),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=6} ogf A004271 9.56974 {-a(n+3)-a(n+1)+2*a(n+2),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=6} ogf A004272 24.1521 (1+x^2)*(x^4-x^2+1)/(x-1)^2 ogf A004272 14.4913 2*(-1+2*x^6-3*x^5)/(-1+x)/(x^2+1)/(x^4-x^2+1) lgdogf A004272 65.2107 2+x^5-x^11 ogf_with_Euler_Transform A004272 8.0507 {-2*a(n+2)+a(n+3)+a(n+1),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=5,a(6)=6,a(7)=8} ogf A004272 8.15133 {a(n+3)+a(n+1)-2*a(n+2),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=5,a(6)=6,a(7)=8} ogf A004273 27.5933 (-x-x^2)*f(x)+(1-2*x+x^2)*f(x)^2 ogf A004273 67.9219 (x+1)/(x-1)^2 ogf A004273 25.2281 -(-x-x^2+2*x^26-2*x^25)/(1-2*x+x^2) ogf A004273 46.4729 -(x+3)/(-1+x)/(1+x) lgdogf A004273 25.9701 -1/2*(-1-2*x+(8*x+1)^(1/2))/(-1+x) revogf A004273 294.328 3-x ogf_with_Euler_Transform A004273 19.6219 {a(n+3)+a(n+1)-2*a(n+2),a(0)=0,a(1)=1,a(2)=3} ogf A004273 19.6219 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=1,a(2)=3} ogf A004274 24.1767 (-2+x^3-3*x^2)/(-1+x)/(1+x)/(x^2-x+1) lgdogf A004274 38.8929 (1-x+x^2)*(x+1)/(x-1)^2 ogf A004274 25.5582 -(x+x^4-2*x^27+2*x^26)/(-1+2*x-x^2) ogf A004274 99.3929 2+x^2-x^5 ogf_with_Euler_Transform A004274 14.428 5*x+5*x^4+(-5+22*x-5*x^2+12*x^4)*f(x)+(-12*x^2-12+24*x)*f(x)^2 ogf A004274 15.1616 {a(n+5)-2*a(n+4)+a(n+3),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=5} ogf A004275 42.0173 (1+x^2)/(x-1)^2 ogf A004275 27.4026 -2*(1+x)/(x^2+1)/(-1+x) lgdogf A004275 90.037 2+x-x^3 ogf_with_Euler_Transform A004275 12.358 x+x^3+(-1+4*x-x^2+2*x^3)*f(x)+(-2+4*x-2*x^2)*f(x)^2 ogf A004275 11.8917 {-a(n+4)+2*a(n+3)-a(n+2),a(0)=0,a(1)=1,a(2)=2,a(3)=4} ogf A004276 19.2787 (-2-5*x^4+3*x^5)/(-1+x)/(1+x)/(x^4-x^3+x^2-x+1) lgdogf A004276 29.229 (x+1)*(x^4-x^3+x^2-x+1)/(x-1)^2 ogf A004276 25.8886 -(-x-x^6+4*x^27-4*x^26)/(1-2*x+x^2) ogf A004276 100.678 2+x^4-x^9 ogf_with_Euler_Transform A004276 12.2446 {-2*a(n+2)+a(n+3)+a(n+1),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=5,a(6)=7} ogf A004276 12.4123 {a(n+3)+a(n+1)-2*a(n+2),a(0)=0,a(1)=1,a(2)=2,a(3)=3,a(4)=4,a(5)=5,a(6)=7} ogf A004277 59.4263 (1+x^2)/(x-1)^2 ogf A004277 25.4684 -(1+x^2-2*x^26+2*x^25)/(-1+2*x-x^2) ogf A004277 38.7563 -2*(1+x)/(x^2+1)/(-1+x) lgdogf A004277 38.7563 1+x^2+(-1+2*x-x^2)*f(x) ogf A004277 127.342 2+x-x^3 ogf_with_Euler_Transform A004277 19.8088 {a(n+3)+a(n+1)-2*a(n+2),a(0)=1,a(1)=2,a(2)=4} ogf A004277 24.0917 {a(n+4),a(0)=2,a(1)=1,a(2)=0,a(3)=-1} ogf_with_Euler_Transform A004278 19.6956 (-1-x^4)*f(x)+(1-2*x+x^2)*f(x)^2 ogf A004278 42.0173 (1+x^4)/(x-1)^2 ogf A004278 20.3309 2*(-1+x^4-2*x^3)/(-1+x)/(1+x^4) lgdogf A004278 70.0288 2+x^3-x^7 ogf_with_Euler_Transform A004278 10.5043 {-a(n+5)+2*a(n+4)-a(n+3),a(0)=1,a(1)=2,a(2)=3,a(3)=4,a(4)=6} ogf A004278 4.96267 {7*a(n+4)*n-84*a(n+4)+7*a(n+4)*n^2+24*a(n+1)-16*a(n+1)*n+2*a(n+1)*n^2,a(0)=2,a(1)=0,a(2)=0,a(3)=1,a(4)=0,a(5)=0,a(6)=0,a(7)=-1} ogf_with_Euler_Transform A004279 23.7471 (1+x^2)*(x^4-x^2+1)/(x-1)^2 ogf A004279 14.2483 2*(-1+2*x^6-3*x^5)/(-1+x)/(x^2+1)/(x^4-x^2+1) lgdogf A004279 64.1173 2+x^5-x^11 ogf_with_Euler_Transform A004279 6.82099 {-a(n),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=1,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=0,a(11)=-1} ogf_with_Euler_Transform A004279 8.78319 {a(n+3)+a(n+1)-2*a(n+2),a(0)=1,a(1)=2,a(2)=3,a(3)=4,a(4)=5,a(5)=6,a(6)=8} ogf A004280 23.8645 (-2+x^3-3*x^2)/(-1+x)/(1+x)/(x^2-x+1) lgdogf A004280 38.3906 (1-x+x^2)*(x+1)/(x-1)^2 ogf A004280 25.2281 -(1+x^3+2*x^25-2*x^26)/(-1+2*x-x^2) ogf A004280 38.3906 1+x^3+(-1+2*x-x^2)*f(x) ogf A004280 98.1094 2+x^2-x^5 ogf_with_Euler_Transform A004280 7.67813 {10*a(n+3)*n-60*a(n+3)+10*a(n+3)*n^2+12*a(n+1)-15*a(n+1)*n+3*a(n+1)*n^2,a(0)=2,a(1)=0,a(2)=1,a(3)=0,a(4)=0,a(5)=-1} ogf_with_Euler_Transform A004280 16.9805 {a(n+4)-2*a(n+3)+a(n+2),a(0)=1,a(1)=2,a(2)=3,a(3)=5} ogf A004281 18.608 (-2-5*x^4+3*x^5)/(-1+x)/(1+x)/(x^4-x^3+x^2-x+1) lgdogf A004281 28.2121 (x+1)*(x^4-x^3+x^2-x+1)/(x-1)^2 ogf A004281 41.6465 -(1+x^5)/(-1+2*x-x^2) ogf A004281 97.1751 2+x^4-x^9 ogf_with_Euler_Transform A004281 11.2125 {-a(n),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=1,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=-1} ogf_with_Euler_Transform A004281 13.2511 {a(n+3)+a(n+1)-2*a(n+2),a(0)=1,a(1)=2,a(2)=3,a(3)=4,a(4)=5,a(5)=7} ogf A004282 31.6849 (3+6*x+x^2)/(x-1)^6 ogf A004282 10.7502 -(-3*x-x^3-6*x^2)/(1-6*x+15*x^2-6*x^5-20*x^3+15*x^4+x^6) ogf A004282 18.2428 -4*(6+8*x+x^2)/(-1+x)/(x^2+6*x+3) lgdogf A004282 6.33697 {(9+3*n)*a(n+4)+(-18+3*n)*a(n+3)+(-37-5*n)*a(n+2)+(-4-n)*a(n+1),a(0)=0,a(1)=3,a(2)=24,a(3)=100} ogf A004291 27.1695 (x+1)^2/(1-10*x+x^2) ogf A004291 20.8996 -(1+2*x+x^2)/(-x^2-1+10*x) ogf A004291 18.7376 -12*(-1+x)/(1+x)/(x^2-10*x+1) lgdogf A004291 19.4068 1+2*x+x^2+(-x^2-1+10*x)*f(x) ogf A004291 10.8678 {-a(n+3)+10*a(n+2)-a(n+1),a(0)=1,a(1)=12,a(2)=120} ogf A004292 24.2602 (x+1)^2/(x^2+1-18*x) ogf A004292 18.6617 -(1+2*x+x^2)/(-x^2-1+18*x) ogf A004292 16.7311 -20*(-1+x)/(1+x)/(x^2-18*x+1) lgdogf A004292 17.3287 1+2*x+x^2+(-x^2-1+18*x)*f(x) ogf A004292 9.70406 {-a(n+3)+18*a(n+2)-a(n+1),a(0)=1,a(1)=20,a(2)=360} ogf A004293 26.8941 (x+1)^2/(x^2+1-26*x) ogf A004293 20.6878 -(1+2*x+x^2)/(-x^2-1+26*x) ogf A004293 18.5477 -28*(-1+x)/(1+x)/(x^2-26*x+1) lgdogf A004293 19.2101 1+2*x+x^2+(-x^2-1+26*x)*f(x) ogf A004293 10.7576 {-a(n+3)+26*a(n+2)-a(n+1),a(0)=1,a(1)=28,a(2)=728} ogf A004294 24.7787 (x+1)^2/(x^2+1-34*x) ogf A004294 19.0605 -(1+2*x+x^2)/(-x^2-1+34*x) ogf A004294 17.0887 -36*(-1+x)/(1+x)/(x^2-34*x+1) lgdogf A004294 17.699 1+2*x+x^2+(-x^2-1+34*x)*f(x) ogf A004294 9.71712 {-a(n+3)+34*a(n+2)-a(n+1),a(0)=1,a(1)=36,a(2)=1224} ogf A004295 26.1327 (x+1)^2/(x^2+1-42*x) ogf A004295 20.1021 -(1+2*x+x^2)/(-x^2-1+42*x) ogf A004295 18.0225 -44*(-1+x)/(1+x)/(x^2-42*x+1) lgdogf A004295 18.6662 1+2*x+x^2+(-x^2-1+42*x)*f(x) ogf A004295 10.2481 {-a(n+3)+42*a(n+2)-a(n+1),a(0)=1,a(1)=44,a(2)=1848} ogf A004296 27.2159 (x+1)^2/(x^2+1-50*x) ogf A004296 20.9353 -(1+2*x+x^2)/(-x^2-1+50*x) ogf A004296 18.7696 -52*(-1+x)/(1+x)/(x^2-50*x+1) lgdogf A004296 19.4399 1+2*x+x^2+(-x^2-1+50*x)*f(x) ogf A004296 10.6729 {-a(n+3)+50*a(n+2)-a(n+1),a(0)=1,a(1)=52,a(2)=2600} ogf A004297 28.0283 (x+1)^2/(x^2+1-58*x) ogf A004297 21.5602 -(1+2*x+x^2)/(-x^2-1+58*x) ogf A004297 19.3299 -60*(-1+x)/(1+x)/(x^2-58*x+1) lgdogf A004297 20.0202 1+2*x+x^2+(-x^2-1+58*x)*f(x) ogf A004297 10.9915 {-a(n+3)+58*a(n+2)-a(n+1),a(0)=1,a(1)=60,a(2)=3480} ogf A004298 24.5433 (x+1)^2/(x^2+1-66*x) ogf A004298 18.8794 -(1+2*x+x^2)/(-x^2-1+66*x) ogf A004298 16.9264 -68*(-1+x)/(1+x)/(x^2-66*x+1) lgdogf A004298 17.5309 1+2*x+x^2+(-x^2-1+66*x)*f(x) ogf A004298 9.62481 {-a(n+3)+66*a(n+2)-a(n+1),a(0)=1,a(1)=68,a(2)=4488} ogf A004299 25.0711 (x+1)^2/(x^2+1-74*x) ogf A004299 19.2854 -(1+2*x+x^2)/(-x^2-1+74*x) ogf A004299 17.2904 -76*(-1+x)/(1+x)/(x^2-74*x+1) lgdogf A004299 17.9079 1+2*x+x^2+(-x^2-1+74*x)*f(x) ogf A004299 9.83179 {-a(n+3)+74*a(n+2)-a(n+1),a(0)=1,a(1)=76,a(2)=5624} ogf A004301 10.5544 -(-29+136*x+144*x^4-78*x^3-149*x^2)/(-1+x)/(3*x-1)/(-1+2*x)/(6*x^2+x-3) lgdogf A004301 11.7088 -(-6*x+12*x^3+2*x^2)/(1-10*x+40*x^2-52*x^5-82*x^3+91*x^4+12*x^6) ogf A004301 18.2771 -2*(-3+x+6*x^2)/(3*x-1)/(2*x-1)^2/(x-1)^3 ogf A004302 28.3433 (1+6*x+3*x^2)/(x-1)^6 ogf A004302 10.6288 -(-x-3*x^3-6*x^2)/(1-6*x+15*x^2-6*x^5-20*x^3+15*x^4+x^6) ogf A004302 16.5336 -12*(x^2+3*x+1)/(-1+x)/(3*x^2+6*x+1) lgdogf A004302 6.33202 {(n+3)*a(n+4)+(-2+5*n)*a(n+3)+(-39-3*n)*a(n+2)+(-12-3*n)*a(n+1),a(0)=0,a(1)=1,a(2)=12,a(3)=60} ogf A004306 5.46677 (-1+12*x^9-120*x^7+90*x^4-40*x^3+30*x^10+3*x^8+12*x^6+12*x^5-6*x^2)/(-1+x)/(x^3+x^2+x-1)/(10*x^7+6*x^6+3*x^5-13*x^4-2*x^3+x-1) lgdogf A004306 13.5061 -(-1+x-2*x^3+6*x^6+10*x^7+3*x^5-13*x^4)/(1-2*x+x^4) ogf A004306 11.6748 -(-1+x-2*x^3-13*x^4+3*x^5+6*x^6+10*x^7)/(x-1)/(x^3+x^2+x-1) ogf A004310 9.67722 -80+324*x+(8-68*x+144*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A004310 13.8955 256/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^8 ogf A004310 14.6466 256/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^8 ogf A004310 8.74072 {(-132-46*n-4*n^2)*a(n+1)+(12*n+20+n^2)*a(n+2),a(0)=1,a(1)=10} ogf A004311 8.72894 -120+484*x+(10-84*x+176*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A004311 12.3483 1024/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^10 ogf A004311 12.9815 1024/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^10 ogf A004311 8.16578 {(-182-54*n-4*n^2)*a(n+1)+(14*n+24+n^2)*a(n+2),a(0)=1,a(1)=12} ogf A004312 8.88564 -168+676*x+(12-100*x+208*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A004312 12.7867 4096/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^12 ogf A004312 13.4424 4096/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^12 ogf A004312 8.45569 {(-240-62*n-4*n^2)*a(n+1)+(16*n+28+n^2)*a(n+2),a(0)=1,a(1)=14} ogf A004313 8.28436 -224+900*x+(14-116*x+240*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A004313 11.6375 16384/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^14 ogf A004313 12.2194 16384/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^14 ogf A004313 7.8835 {(-306-70*n-4*n^2)*a(n+1)+(18*n+32+n^2)*a(n+2),a(0)=1,a(1)=16} ogf A004314 8.39165 -288+1156*x+(16-132*x+272*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A004314 11.9881 65536/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^16 ogf A004314 12.5875 65536/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^16 ogf A004314 8.12096 {(-380-78*n-4*n^2)*a(n+1)+(20*n+36+n^2)*a(n+2),a(0)=1,a(1)=18} ogf A004315 8.53888 -360+1444*x+(18-148*x+304*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A004315 11.9147 262144/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^18 ogf A004315 12.4959 262144/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^18 ogf A004315 8.26343 {(-462-86*n-4*n^2)*a(n+1)+(22*n+40+n^2)*a(n+2),a(0)=1,a(1)=20} ogf A004316 8.78425 -440+1764*x+(20-164*x+336*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A004316 11.9785 1048576/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^20 ogf A004316 12.5489 1048576/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^20 ogf A004316 8.50088 {(-552-94*n-4*n^2)*a(n+1)+(24*n+44+n^2)*a(n+2),a(0)=1,a(1)=22} ogf A004317 8.88239 -528+2116*x+(22-180*x+368*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A004317 12.1124 4194304/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^22 ogf A004317 12.6891 4194304/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^22 ogf A004317 8.45942 {(-650-102*n-4*n^2)*a(n+1)+(26*n+48+n^2)*a(n+2),a(0)=1,a(1)=24} ogf A004318 9.07869 -624+2500*x+(24-196*x+400*x^2)*f(x)+(-8*x^2+16*x^3+x)*f(x)^2 lgdogf A004318 12.1049 16777216/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^24 ogf A004318 12.6679 16777216/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^24 ogf A004318 8.64637 {(-756-110*n-4*n^2)*a(n+1)+(28*n+52+n^2)*a(n+2),a(0)=1,a(1)=26} ogf A004319 14.6548 1+(-1+6*x)*f(x)+(4*x^3-27*x^4)*f(x)^3 ogf A004319 16.4311 hypergeom([4/3,5/3],[5/2],27/4*x) ogf A004319 8.34196 {(-168-135*n-27*n^2)*a(n+1)+(22*n+28+4*n^2)*a(n+2),a(0)=1,a(1)=6} ogf A004320 16.9629 -(3*x+x^2)/(-1+5*x-5*x^4-10*x^2+10*x^3+x^5) ogf A004320 52.1004 -(x+3)/(x-1)^5 ogf A004320 34.7336 -4*(x+4)/(x+3)/(-1+x) lgdogf A004320 10.5711 {(6+3*n)*a(n+3)+(-18-2*n)*a(n+2)+(-4-n)*a(n+1),a(0)=0,a(1)=3,a(2)=16} ogf A004321 6.166 {(2730+1761*n+378*n^2+27*n^3)*a(n+1)+(-256*n-312-58*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=12} ogf A004322 6.44313 {(4896+2598*n+459*n^2+27*n^3)*a(n+1)+(-364*n-480-70*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=15} ogf A004323 6.61633 {(7980+3597*n+540*n^2+27*n^3)*a(n+1)+(-490*n-684-82*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=18} ogf A004324 5.94878 {(12144+4758*n+621*n^2+27*n^3)*a(n+1)+(-634*n-924-94*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=21} ogf A004325 5.94497 {(17550+6081*n+702*n^2+27*n^3)*a(n+1)+(-796*n-1200-106*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=24} ogf A004326 6.0435 {(24360+7566*n+783*n^2+27*n^3)*a(n+1)+(-976*n-1512-118*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=27} ogf A004327 6.04055 {(32736+9213*n+864*n^2+27*n^3)*a(n+1)+(-1174*n-1860-130*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=30} ogf A004328 6.19824 {(42840+11022*n+945*n^2+27*n^3)*a(n+1)+(-1390*n-2244-142*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=33} ogf A004329 6.25717 {(54834+12993*n+1026*n^2+27*n^3)*a(n+1)+(-1624*n-2664-154*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=36} ogf A004330 5.63529 {(68880+15126*n+1107*n^2+27*n^3)*a(n+1)+(-1876*n-3120-166*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=39} ogf A004331 6.35731 {(-3960-4784*n-1920*n^2-256*n^3)*a(n+1)+(564*n+480+216*n^2+27*n^3)*a(n+2),a(0)=1,a(1)=8} ogf A004332 6.20893 {(10920+9392*n+2688*n^2+256*n^3)*a(n+1)+(-1032*n-1092-297*n^2-27*n^3)*a(n+2),a(0)=1,a(1)=12} ogf A004333 4.72513 {(-116280-100936*n-32816*n^2-4736*n^3-256*n^4)*a(n+1)+(10092*n+9792+3516*n^2+513*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=16} ogf A004334 4.68439 {(-255024-181800*n-48560*n^2-5760*n^3-256*n^4)*a(n+1)+(17172*n+18480+5100*n^2+621*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=20} ogf A004335 4.68439 {(-491400-297224*n-67376*n^2-6784*n^3-256*n^4)*a(n+1)+(26844*n+31200+6972*n^2+729*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=24} ogf A004336 4.42078 {(-863040-453352*n-89264*n^2-7808*n^3-256*n^4)*a(n+1)+(39492*n+48720+9132*n^2+837*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=28} ogf A004337 4.33314 {(-1413720-656328*n-114224*n^2-8832*n^3-256*n^4)*a(n+1)+(55500*n+71808+11580*n^2+945*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=32} ogf A004338 4.28494 {(-2193360-912296*n-142256*n^2-9856*n^3-256*n^4)*a(n+1)+(75252*n+101232+14316*n^2+1053*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=36} ogf A004339 3.80949 {(-3258024-1227400*n-173360*n^2-10880*n^3-256*n^4)*a(n+1)+(99132*n+137760+17340*n^2+1161*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=40} ogf A004340 3.86821 {(-4669920-1607784*n-207536*n^2-11904*n^3-256*n^4)*a(n+1)+(127524*n+182160+20652*n^2+1269*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=44} ogf A004341 3.91293 {(-6497400-2059592*n-244784*n^2-12928*n^3-256*n^4)*a(n+1)+(160812*n+235200+24252*n^2+1377*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=48} ogf A004342 3.93529 {(-8814960-2588968*n-285104*n^2-13952*n^3-256*n^4)*a(n+1)+(199380*n+297648+28140*n^2+1485*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=52} ogf A004343 4.45401 {(-120120-193750*n-116875*n^2-31250*n^3-3125*n^4)*a(n+1)+(17976*n+11440+10480*n^2+2688*n^3+256*n^4)*a(n+2),a(0)=1,a(1)=10} ogf A004344 4.04081 {(465120+533750*n+229375*n^2+43750*n^3+3125*n^4)*a(n+1)+(-44952*n-36720-19696*n^2-3712*n^3-256*n^4)*a(n+2),a(0)=1,a(1)=15} ogf A004345 4.06703 {(-1275120-1136250*n-379375*n^2-56250*n^3-3125*n^4)*a(n+1)+(88936*n+85008+31664*n^2+4736*n^3+256*n^4)*a(n+2),a(0)=1,a(1)=20} ogf A004396 34.2134 (1+x^2)/(1+x^2+x)/(x-1)^2 ogf A004396 25.1569 (x+x^3)*f(x)+(-1+x+x^3-x^4)*f(x)^2 ogf A004396 37.1884 -(-x-x^3)/(1-x-x^3+x^4) ogf A004396 17.4558 -(1+3*x+2*x^4+x^3+5*x^2)/(-1+x)/(x^2+1)/(x^2+x+1) lgdogf A004396 77.7576 1+x+x^2-x^3 ogf_with_Euler_Transform A004396 15.5515 {a(n+4)-a(n+3)-a(n+1)+a(n),a(0)=0,a(1)=1,a(2)=1,a(3)=2} ogf A004400 13.7199 1/2*(exp(-1/2)*Ei(1,x-1/2)+2-exp(-1/2)*Ei(1,-1/2))*exp(x) egf A004400 7.37767 {(-8-8*n-2*n^2)*a(n+1)+(-14-5*n)*a(n+2)+(26+14*n+2*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=2,a(2)=4,a(3)=12} ogf A004402 27.1095 -(2-x+x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004402 27.1095 -(2-x+x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004402 12.7574 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-2,a(1)=3,a(2)=-2} ogf_with_Euler_Transform A004403 27.5975 -(4-2*x+2*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004403 27.5975 -(4-2*x+2*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004403 15.1515 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-4,a(1)=6,a(2)=-4} ogf_with_Euler_Transform A004404 20.7638 -(-6+3*x-3*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A004404 12.214 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-6,a(1)=9,a(2)=-6} ogf_with_Euler_Transform A004405 21.6125 -(8-4*x+4*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004405 21.6125 -(8-4*x+4*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004405 11.6375 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-8,a(1)=12,a(2)=-8} ogf_with_Euler_Transform A004406 21.2601 -(10-5*x+5*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004406 21.2601 -(10-5*x+5*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004406 11.4174 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-10,a(1)=15,a(2)=-10} ogf_with_Euler_Transform A004407 18.4432 -(-6*x+12+6*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004407 18.4432 -(-6*x+12+6*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004407 10.2462 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-12,a(1)=18,a(2)=-12} ogf_with_Euler_Transform A004408 20.1451 -(14-7*x+7*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004408 20.1451 -(14-7*x+7*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004408 10.8186 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-14,a(1)=21,a(2)=-14} ogf_with_Euler_Transform A004409 19.317 -(16-8*x+8*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004409 19.317 -(16-8*x+8*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004409 10.3739 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-16,a(1)=24,a(2)=-16} ogf_with_Euler_Transform A004410 20.1568 -(18-9*x+9*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004410 20.1568 -(18-9*x+9*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004410 10.825 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-18,a(1)=27,a(2)=-18} ogf_with_Euler_Transform A004411 19.2492 -(20-10*x+10*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004411 19.2492 -(20-10*x+10*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004411 11.0505 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-20,a(1)=30,a(2)=-20} ogf_with_Euler_Transform A004412 18.1677 -(22-11*x+11*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004412 18.1677 -(22-11*x+11*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004412 10.4296 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-22,a(1)=33,a(2)=-22} ogf_with_Euler_Transform A004413 16.3784 -(-12*x+24+12*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004413 16.3784 -(-12*x+24+12*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004413 9.70575 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-24,a(1)=36,a(2)=-24} ogf_with_Euler_Transform A004414 17.3817 -(26-13*x+13*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004414 17.3817 -(26-13*x+13*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004414 9.97838 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-26,a(1)=39,a(2)=-26} ogf_with_Euler_Transform A004415 17.6666 -(28-14*x+14*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004415 17.6666 -(28-14*x+14*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004415 10.142 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-28,a(1)=42,a(2)=-28} ogf_with_Euler_Transform A004416 17.9516 -(30-15*x+15*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004416 17.9516 -(30-15*x+15*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004416 10.3055 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-30,a(1)=45,a(2)=-30} ogf_with_Euler_Transform A004417 16.5963 -(32-16*x+16*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004417 16.5963 -(32-16*x+16*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004417 9.52752 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-32,a(1)=48,a(2)=-32} ogf_with_Euler_Transform A004418 16.876 -(34-17*x+17*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004418 16.876 -(34-17*x+17*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004418 9.68809 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-34,a(1)=51,a(2)=-34} ogf_with_Euler_Transform A004419 16.9693 -(36-18*x+18*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004419 16.9693 -(36-18*x+18*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004419 9.74162 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-36,a(1)=54,a(2)=-36} ogf_with_Euler_Transform A004420 17.5287 -(38-19*x+19*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004420 17.5287 -(38-19*x+19*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004420 10.0628 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-38,a(1)=57,a(2)=-38} ogf_with_Euler_Transform A004421 17.8084 -(40-20*x+20*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004421 17.8084 -(40-20*x+20*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004421 10.2233 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-40,a(1)=60,a(2)=-40} ogf_with_Euler_Transform A004422 17.9949 -(42-21*x+21*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004422 17.9949 -(42-21*x+21*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004422 10.3304 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-42,a(1)=63,a(2)=-42} ogf_with_Euler_Transform A004423 18.3678 -(44-22*x+22*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004423 18.3678 -(44-22*x+22*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004423 10.5445 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-44,a(1)=66,a(2)=-44} ogf_with_Euler_Transform A004424 18.6475 -(46-23*x+23*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004424 18.6475 -(46-23*x+23*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004424 10.7051 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-46,a(1)=69,a(2)=-46} ogf_with_Euler_Transform A004425 18.1551 -(-24*x+48+24*x^2)/(1+x+x^2+x^3) ogf_with_Euler_Transform A004425 18.1551 -(-24*x+48+24*x^2)/(x^2+1+x+x^3) ogf_with_Euler_Transform A004425 10.7586 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-48,a(1)=72,a(2)=-48} ogf_with_Euler_Transform A004442 33.1954 (1-x+2*x^2)/(x+1)/(x-1)^2 ogf A004442 29.6388 -(-1+x-2*x^2)/(-x^2+1-x+x^3) ogf A004442 22.4293 -2*x*(x^2+3)/(-1+x)/(1+x)/(2*x^2-x+1) lgdogf A004442 15.6582 -2+2*x-4*x^2+(3-3*x+2*x^3)*f(x)+(-1-x^3+x+x^2)*f(x)^2 ogf A004442 17.2893 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=1,a(1)=0,a(2)=3} ogf A004443 20.0561 (2-x-2*x^2+3*x^3)/(x-1)^2/(1+x^2) ogf A004443 15.3919 -(2-x+3*x^3-2*x^2)/(-2*x^2-1+2*x-x^4+2*x^3) ogf A004443 10.3414 -(3-9*x-x^4-6*x^3+3*x^5+18*x^2)/(-1+x)/(3*x^3-2*x^2-x+2)/(x^2+1) lgdogf A004443 8.94394 2-x-2*x^2+3*x^3+(3-6*x^2+8*x^3-x^4)*f(x)+(-2+4*x-4*x^2+4*x^3-2*x^4)*f(x)^2 ogf A004443 7.97412 {(-n-3)*a(n+1)+(n+2)*a(n+2)+(-n-3)*a(n+3)+(n+2)*a(n+4),a(0)=2,a(1)=3,a(2)=0,a(3)=1} ogf A004444 16.1427 (3-x-x^2-x^3+4*x^4)/(x+1)/(1+x^2)/(x-1)^2 ogf A004444 18.91 -(3-x-x^3+4*x^4-x^2)/(-x^5-1+x+x^4) ogf A004444 9.19238 -2*(1+2*x^7-x^4+14*x^3+x^6-x^2)/(-1+x)/(1+x)/(x^2+1)/(4*x^4-x^3-x^2-x+3) lgdogf A004445 18.91 (4-3*x-4*x^4+5*x^5)/(1+x^4)/(x-1)^2 ogf A004445 14.082 -(4-3*x+5*x^5-4*x^4)/(-x^2-1+2*x+2*x^5-x^4-x^6) ogf A004445 8.70858 -(5-3*x+5*x^9+66*x^4-32*x^3-3*x^8-30*x^5)/(-1+x)/(5*x^5-4*x^4-3*x+4)/(1+x^4) lgdogf A004446 13.5072 (5-x-2*x^2-3*x^4-x^5+6*x^6)/(x+1)/(1+x^4)/(x-1)^2 ogf A004446 11.2178 -(5-x+6*x^6-x^5-3*x^4-2*x^2)/(-x^7-1+x-x^4+x^2+x^5-x^3+x^6) ogf A004446 6.01683 -2*(2+5*x+3*x^11+x^9-14*x^7-17*x^3+2*x^10-2*x^8+38*x^5-2*x^2)/(-1+x)/(1+x)/(6*x^6-x^5-3*x^4-2*x^2-x+5)/(1+x^4) lgdogf A004447 10.1823 (6-5*x+2*x^2-x^3-2*x^4+3*x^5-6*x^6+7*x^7)/(1+x^2)/(1+x^4)/(x-1)^2 ogf A004447 7.2731 -(6-5*x-x^3-6*x^6+7*x^7+3*x^5-2*x^4+2*x^2)/(-2*x^2-1+2*x-x^8-2*x^4+2*x^3-2*x^6+2*x^5+2*x^7) ogf A004448 16.1798 (7-x-x^2-x^3-x^4-x^5-x^6-x^7+8*x^8)/(x+1)/(1+x^2)/(1+x^4)/(x-1)^2 ogf A004448 20.6213 -(7-x-x^3-x^6-x^7+8*x^8-x^5-x^4-x^2)/(-x^9-1+x+x^8) ogf A004449 18.91 (8-7*x-8*x^8+9*x^9)/(1+x^8)/(x-1)^2 ogf A004449 13.7886 -(8-7*x+9*x^9-8*x^8)/(-x^2-1+2*x+2*x^9-x^8-x^10) ogf A004449 8.17101 -(9+9*x^17-7*x-126*x^9-128*x^7+258*x^8-7*x^16)/(-1+x)/(9*x^9-8*x^8-7*x+8)/(x^8+1) lgdogf A004450 12.9775 (9-x-6*x^2+10*x^10-7*x^8-x^9)/(x+1)/(1+x^8)/(x-1)^2 ogf A004450 10.5056 -(-9+x-10*x^10+x^9+7*x^8+6*x^2)/(x^11+1-x+x^8-x^2-x^9+x^3-x^10) ogf A004450 5.42501 -2*(4-4*x^16-4*x^2+5*x^19+4*x^18-x^17+7*x-62*x^11+134*x^9-3*x^3-64*x^7)/(-1+x)/(1+x)/(10*x^10-x^9-7*x^8-6*x^2-x+9)/(x^8+1) lgdogf A004451 9.19238 (10-9*x+6*x^2-5*x^3+11*x^11-10*x^10-6*x^8+7*x^9)/(1+x^2)/(1+x^8)/(x-1)^2 ogf A004451 6.42574 -(10-9*x-10*x^10+7*x^9-5*x^3+11*x^11-6*x^8+6*x^2)/(-2*x^10-1+2*x+2*x^9-2*x^2-x^8+2*x^3+2*x^11-x^4-x^12) ogf A004452 8.48528 (11-x-x^2-x^3-4*x^4-x^11+12*x^12-x^10-5*x^8-x^9)/(x+1)/(1+x^2)/(1+x^8)/(x-1)^2 ogf A004452 8.07136 -(-11+x+x^10+x^9+x^3+x^11+5*x^8+4*x^4+x^2-12*x^12)/(x^13+1-x-x^9+x^5+x^8-x^4-x^12) ogf A004453 9.06646 (12-11*x+4*x^4-12*x^12+13*x^13-3*x^5-4*x^8+5*x^9)/(1+x^4)/(1+x^8)/(x-1)^2 ogf A004454 6.75359 (-x^13+14*x^14+6*x^10-x^5-2*x^6-3*x^8-x^9-x-10*x^2+5*x^4-11*x^12+13)/(x+1)/(1+x^4)/(1+x^8)/(x-1)^2 ogf A004456 5.80572 (15-x-x^2-x^3-x^4-x^11-x^12-x^13-x^14-x^15+16*x^16-x^10-x^5-x^6-x^7-x^8-x^9)/(x+1)/(1+x^2)/(1+x^4)/(1+x^8)/(x-1)^2 ogf A004457 21.9986 (16-15*x-16*x^16+17*x^17)/(1+x^16)/(x-1)^2 ogf A004457 9.6244 -(17+17*x^33-15*x^32-510*x^17-15*x+1026*x^16-512*x^15)/(-1+x)/(17*x^17-16*x^16-15*x+16)/(x^16+1) lgdogf A004458 11.6114 (17-x-14*x^2-15*x^16-x^17+18*x^18)/(x+1)/(1+x^16)/(x-1)^2 ogf A004458 9.45502 -(-17+x+14*x^2-18*x^18+15*x^16+x^17)/(x^19+1-x+x^16-x^2-x^17+x^3-x^18) ogf A004459 8.27315 (18-17*x+14*x^2-13*x^3-14*x^16+15*x^17-18*x^18+19*x^19)/(1+x^2)/(1+x^16)/(x-1)^2 ogf A004460 7.97412 (19-x-x^2-x^3-12*x^4-13*x^16-x^17-x^18-x^19+20*x^20)/(x+1)/(1+x^2)/(1+x^16)/(x-1)^2 ogf A004460 7.52104 -(-19+x-20*x^20+x^3+12*x^4+x^2+x^18+x^19+13*x^16+x^17)/(x^21+1-x-x^17+x^5+x^16-x^4-x^20) ogf A004461 8.27315 (20-19*x+12*x^4-12*x^16+13*x^17-20*x^20-11*x^5+21*x^21)/(1+x^4)/(1+x^16)/(x-1)^2 ogf A004462 6.30335 (-x-18*x^2+13*x^4-11*x^16-x^17+14*x^18-19*x^20-x^5-10*x^6+22*x^22-x^21+21)/(x+1)/(1+x^4)/(1+x^16)/(x-1)^2 ogf A004465 8.70858 (24-23*x-8*x^16+9*x^17+8*x^8+25*x^25-24*x^24-7*x^9)/(1+x^8)/(1+x^16)/(x-1)^2 ogf A004466 29.9964 (1+8*x+x^2)/(x-1)^4 ogf A004466 14.6136 -(x+x^3+8*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A004466 17.2706 -2*(6+13*x+x^2)/(x-1)/(x^2+8*x+1) lgdogf A004466 4.82992 1219*x+9752*x^2+1219*x^3+(-1219+5256*x-4274*x^2+5256*x^3-1219*x^4)*f(x)+(-2280*x^2-380+1520*x-380*x^4+1520*x^3)*f(x)^2 ogf A004466 6.33257 {(n+3)*a(n+4)+(2+7*n)*a(n+3)+(-33-7*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=12,a(3)=43} ogf A004467 30.1804 (1+9*x+x^2)/(x-1)^4 ogf A004467 14.7033 -(-x-x^3-9*x^2)/(1-4*x+6*x^2-4*x^3+x^4) ogf A004467 16.8655 -(13+29*x+2*x^2)/(x-1)/(x^2+9*x+1) lgdogf A004467 4.81872 1387*x+12483*x^2+1387*x^3+(-1387+5933*x-4857*x^2+5933*x^3-1387*x^4)*f(x)+(-2310*x^2-385+1540*x-385*x^4+1540*x^3)*f(x)^2 ogf A004467 6.37142 {(n+3)*a(n+4)+(3+8*n)*a(n+3)+(-37-8*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=13,a(3)=47} ogf A004469 6.99225 -(-4*x+4*x^14+12*x^10-4*x^9-4*x^3-12*x^6+4*x^7-4*x^11+4*x^13+4*x^15-x^8+4*x^5+6*x^4-4*x^2-6*x^12-63*x^16)/(1-x+x^17-x^16) ogf A004470 6.93493 -(5*x+7*x^14+3*x^10+3*x^9+5*x^3+x^6+5*x^7+3*x^11+3*x^13+3*x^15-10*x^8+5*x^5-13*x^4+5*x^2-11*x^12+66*x^16)/(-1+x-x^17+x^16) ogf A004482 20.6357 (1+x-2*x^2+3*x^3)/(1+x^2+x)/(x-1)^2 ogf A004482 21.8863 -(1+x+3*x^3-2*x^2)/(-1+x-x^4+x^3) ogf A004482 11.1115 -(2-2*x+3*x^5+4*x^3-x^4+12*x^2)/(x-1)/(x^2+x+1)/(3*x^3-2*x^2+x+1) lgdogf A004482 7.36988 -226-226*x+452*x^2-678*x^3+(175-277*x+102*x^2-379*x^3+226*x^4)*f(x)+(51-51*x+51*x^4-51*x^3)*f(x)^2 ogf A004482 10.3178 {(-n-3)*a(n+1)-a(n+2)-a(n+3)+(n+2)*a(n+4),a(0)=1,a(1)=2,a(2)=0,a(3)=4} ogf A004483 23.711 (2-2*x+x^2+2*x^3)/(1+x^2+x)/(x-1)^2 ogf A004483 25.148 -(2-2*x+2*x^3+x^2)/(-1+x-x^4+x^3) ogf A004483 10.1206 -38+38*x-19*x^2-38*x^3+(5-5*x-7*x^2-33*x^3+19*x^4)*f(x)+(7-7*x^3-7*x+7*x^4)*f(x)^2 ogf A004483 13.1728 -x*(2+2*x^4-3*x^2+4*x^3+13*x)/(x-1)/(x^2+x+1)/(2*x^3+x^2-2*x+2) lgdogf A004483 11.8555 {(n+3)*a(n+1)+a(n+2)+a(n+3)+(-n-2)*a(n+4),a(0)=2,a(1)=0,a(2)=1,a(3)=5} ogf A004484 7.08086 (3+x+x^2+x^3-4*x^4+x^11+7*x^12-12*x^13+4*x^14-2*x^5-2*x^6+7*x^7+x^9)/(x+1)/(1+x^2+x)/(1-x+x^2)/(x-1)^2 ogf A004484 8.70178 -(3+x+7*x^7+4*x^14+x^9+x^3-2*x^6+x^11-12*x^13-4*x^4+x^2+7*x^12-2*x^5)/(x^6-1+x-x^7) ogf A004492 12.9775 (3-2*x+3*x^3-2*x^4-6*x^6+7*x^7)/(1+x^6+x^3)/(x-1)^2 ogf A004492 9.06646 -(-3+2*x-3*x^3+6*x^6-7*x^7+2*x^4)/(x^2+1-2*x-2*x^4-2*x^7+x^3+x^6+x^5+x^8) ogf A004492 5.17072 -(4-2*x-5*x^12-54*x^5-51*x^7+8*x^3-4*x^4-27*x^8+53*x^9-22*x^10+7*x^13+111*x^6)/(x-1)/(x^6+x^3+1)/(7*x^7-6*x^6-2*x^4+3*x^3-2*x+3) lgdogf A004493 8.37787 (4+x-2*x^2+4*x^3+x^4-2*x^5-5*x^6+x^7-2*x^8+9*x^9)/(1+x^6+x^3)/(1+x^2+x)/(x-1)^2 ogf A004493 10.0281 -(4+x+9*x^9+4*x^3-5*x^6-2*x^8+x^7+x^4-2*x^2-2*x^5)/(-x^10-1+x+x^9) ogf A004494 8.37787 (5-2*x+x^2+4*x^3-2*x^4+x^5-5*x^6-2*x^7+x^8+8*x^9)/(1+x^6+x^3)/(1+x^2+x)/(x-1)^2 ogf A004494 10.0281 -(5-2*x+8*x^9+4*x^3-5*x^6+x^8-2*x^7-2*x^4+x^2+x^5)/(-x^10-1+x+x^9) ogf A004495 12.9775 (6-5*x-3*x^3+4*x^4-3*x^6+4*x^7)/(1+x^6+x^3)/(x-1)^2 ogf A004495 9.06646 -(-6+5*x+3*x^3+3*x^6-4*x^7-4*x^4)/(x^2+1-2*x-2*x^4-2*x^7+x^3+x^6+x^5+x^8) ogf A004495 5.17072 -(7-5*x-2*x^12-54*x^5-51*x^7+59*x^3-28*x^4-4*x^9+8*x^10+4*x^13-27*x^2+111*x^6)/(x-1)/(4*x^7-3*x^6+4*x^4-3*x^3-5*x+6)/(x^6+x^3+1) lgdogf A004496 8.37787 (7+x-2*x^2-5*x^3+x^4-2*x^5+4*x^6+x^7-2*x^8+6*x^9)/(1+x^6+x^3)/(1+x^2+x)/(x-1)^2 ogf A004496 10.0281 -(7+x+6*x^9-5*x^3+4*x^6-2*x^8+x^7+x^4-2*x^2-2*x^5)/(-x^10-1+x+x^9) ogf A004497 8.37787 (8-2*x+x^2-5*x^3-2*x^4+x^5+4*x^6-2*x^7+x^8+5*x^9)/(1+x^6+x^3)/(1+x^2+x)/(x-1)^2 ogf A004497 10.0281 -(8-2*x+5*x^9-5*x^3+4*x^6+x^8-2*x^7-2*x^4+x^2+x^5)/(-x^10-1+x+x^9) ogf A004498 11.6114 (9-8*x-18*x^18+19*x^19-8*x^10+9*x^9)/(x^18+x^9+1)/(x-1)^2 ogf A004498 7.97412 -(-9+8*x-9*x^9+8*x^10+18*x^18-19*x^19)/(x^2+1-2*x-2*x^10-2*x^19+x^9+x^18+x^11+x^20) ogf A004499 6.42574 (10+x-2*x^2-6*x^3-2*x^11-6*x^12-17*x^18+x^19-2*x^20+x^10+21*x^21+10*x^9)/(1+x^2+x)/(x^18+x^9+1)/(x-1)^2 ogf A004500 6.42574 (11-2*x+x^2-7*x^3+x^11-7*x^12-16*x^18-2*x^19+x^20-2*x^10+20*x^21+11*x^9)/(1+x^2+x)/(x^18+x^9+1)/(x-1)^2 ogf A004507 11.2178 (18-17*x-9*x^18+10*x^19+10*x^10-9*x^9)/(x^18+x^9+1)/(x-1)^2 ogf A004507 7.78649 -(18-17*x-9*x^9+10*x^10-9*x^18+10*x^19)/(-x^2-1+2*x+2*x^10+2*x^19-x^9-x^18-x^11-x^20) ogf A004508 6.42574 (19+x-2*x^2-15*x^3-2*x^11+12*x^12-8*x^18+x^19-2*x^20+x^10+12*x^21-8*x^9)/(1+x^2+x)/(x^18+x^9+1)/(x-1)^2 ogf A004509 6.42574 (20-2*x+x^2-16*x^3+x^11+11*x^12-7*x^18-2*x^19+x^20-2*x^10+11*x^21-7*x^9)/(1+x^2+x)/(x^18+x^9+1)/(x-1)^2 ogf A004516 6.24388 2*(1-3*x^2+4*x^3-18*x^17+19*x^18-21*x^20+22*x^21)/(x+1)/(1+x^2)/(1-x+x^2)/(x^4-x^2+1)/(x^12-x^6+1)/(x-1)^2 ogf A004521 5.91257 (2+2*x+2*x^2+2*x^3+2*x^4+13*x^10-9*x^5+2*x^6+2*x^7+2*x^8+2*x^9)/(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004521 7.83759 -(2*x+2*x^9+2*x^3-9*x^6+13*x^11+2*x^8+2*x^7+2*x^10+2*x^4+2*x^2+2*x^5)/(-1+x-x^12+x^11) ogf A004522 14.1937 -(2*x-12*x^6+14*x^7)/(-1+2*x+2*x^7-x^2-x^6-x^8) ogf A004522 7.41226 -2*(1-9*x^11+7*x^12+27*x^5-10*x^6-15*x^4+3*x^10)/(x-1)/(x^2+1)/(7*x^6-6*x^5+1)/(x^4-x^2+1) lgdogf A004522 14.8245 2*(1-6*x^5+7*x^6)/(1+x^2)/(x^4-x^2+1)/(x-1)^2 ogf A004523 35.8352 (x+1)/(1+x^2+x)/(x-1)^2 ogf A004523 19.624 -(2+2*x+3*x^3+5*x^2)/(x-1)/(x+1)/(x^2+x+1) lgdogf A004523 32.9684 -(x^3+x^2)/(-1+x+x^3-x^4) ogf A004523 30.5263 -x^2-x^3+(1-x-x^3+x^4)*f(x) ogf A004523 117.744 2-x+x^2 ogf_with_Euler_Transform A004523 10.5668 {(2*n+5)*a(n+1)+2*a(n+2)+2*a(n+3)+(-2*n-3)*a(n+4),a(0)=0,a(1)=0,a(2)=1,a(3)=2} ogf A004524 32.0165 -2*(1-x+2*x^2)/(x^2+1)/(x-1) lgdogf A004524 52.733 1/(x-1)^2/(1+x^2) ogf A004524 128.066 2-x+x^3 ogf_with_Euler_Transform A004524 27.1655 x^3+(-1+2*x-2*x^2+2*x^3-x^4)*f(x) ogf A004524 33.2023 x^3/(1-2*x+2*x^2-2*x^3+x^4) ogf A004524 10.8007 {(-n-2)*a(n+1)+(n+1)*a(n+2)+(-n-2)*a(n+3)+(n+1)*a(n+4),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A004525 35.8584 (1-x+x^2)/(x-1)^2/(1+x^2) ogf A004525 18.6763 -(1-x-3*x^3+2*x^4+5*x^2)/(x-1)/(x^2+1)/(x^2-x+1) lgdogf A004525 24.2287 -(x-x^2+x^3)/(-1+2*x-2*x^2+2*x^3-x^4) ogf A004525 12.8066 -x+x^2-x^3+(1-3*x+3*x^2-3*x^3+x^4)*f(x)+(2*x^2+1-2*x+x^4-2*x^3)*f(x)^2 ogf A004525 68.9585 1+x^2+x^3-x^5 ogf_with_Euler_Transform A004525 10.8007 {(-n-3)*a(n+1)+(n+2)*a(n+2)+(-n-3)*a(n+3)+(n+2)*a(n+4),a(0)=0,a(1)=1,a(2)=1,a(3)=1} ogf A004526 43.2559 -(1+3*x)/(x-1)/(x+1) lgdogf A004526 37.6138 -x^2+(1-x-x^2+x^3)*f(x) ogf A004526 57.6745 1/(x+1)/(x-1)^2 ogf A004526 288.373 x+1 ogf_with_Euler_Transform A004526 50.8893 x^2/(1-x-x^2+x^3) ogf A004526 18.0233 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=0,a(1)=0,a(2)=1} ogf A004538 32.5864 (1-8*x+x^2)/(x-1)^3 ogf A004538 15.8754 -(-1-2*x-5*x^2+2*x^3)/(3*x^2+1-3*x-x^3) ogf A004538 19.3482 -(-5-14*x+x^2)/(x-1)/(x^2-8*x+1) lgdogf A004538 20.6381 -(1-8*x+x^2)/(3*x^2+1-3*x-x^3) ogf A004538 7.45954 140-1120*x+140*x^2+(109-172*x+389*x^2-140*x^3)*f(x)+(-93*x^2-31+93*x+31*x^3)*f(x)^2 ogf A004538 11.4656 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=-1,a(1)=5,a(2)=17} ogf A004643 28.4435 -(1+2*x)/(-1+10*x^2) ogf A004643 15.3749 -2*(1+10*x+10*x^2)/(2*x+1)/(10*x^2-1) lgdogf A004643 10.9398 -31-62*x+(66+70*x-310*x^2)*f(x)+(-35+350*x^2)*f(x)^2 ogf A004643 7.68745 1/30*6^(1/2)*15^(1/2)*(-arcsinh(1/3*6^(1/2))+arcsinh(1/3*6^(1/2)*(1+5*x))) revegf A004643 15.3749 1/4*(-1+(1+8*x+40*x^2)^(1/2))/(1+5*x) revogf A004643 18.3507 {-a(n+2)+10*a(n),a(0)=1,a(1)=2} ogf A004647 22.0438 -(-1-2*x-4*x^2)/(1-10*x^3) ogf A004647 22.0438 -(1+2*x+4*x^2)/(-1+10*x^3) ogf A004647 10.2346 -2*(1+4*x+20*x^4+20*x^3+15*x^2)/(4*x^2+2*x+1)/(10*x^3-1) lgdogf A004647 9.55231 -3-6*x-12*x^2+(8+10*x+20*x^2-30*x^3)*f(x)+(-5+50*x^3)*f(x)^2 ogf A004647 15.4902 {a(n+3)-10*a(n),a(0)=1,a(1)=2,a(2)=4} ogf A004652 26.7203 -(-x+x^2-x^3)/(1-2*x-x^4+2*x^3) ogf A004652 20.7082 -(1+4*x+2*x^3-x^2)/(x-1)/(x+1)/(x^2-x+1) lgdogf A004652 34.5137 -(1-x+x^2)/(x+1)/(x-1)^3 ogf A004652 63.7177 1+2*x+x^2-x^5 ogf_with_Euler_Transform A004652 10.2263 3*x-3*x^2+3*x^3+(-3-17*x+23*x^2-29*x^3+3*x^4)*f(x)+(23+46*x^3-46*x-23*x^4)*f(x)^2 ogf A004652 6.73439 {(-42-31*n-5*n^2)*a(n+1)+(42+37*n+7*n^2)*a(n+2)+(48+35*n+5*n^2)*a(n+3)+(-36-33*n-7*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=1,a(3)=3} ogf A004653 1.30412 -5*x^2+(2+4*x+18*x^2-6*x^3)*f(x)+(-2+22*x^3-5*x^2)*f(x)^2 ogf A004654 1.60483 -(11+22*x+40*x^5+88*x^3+44*x^2+20*x^4+80*x^6+50*x^7)/(-11+101*x^4+110*x^7) ogf A004654 1.5626 15+30*x+60*x^2+98*x^3+(-19+44*x^3+141*x^4)*f(x)+(44*x^4-22*x^3+4-8*x)*f(x)^2 ogf A004655 14.1048 (-1-2*x-4*x^2-8*x^3)*f(x)+(1-10*x^4)*f(x)^2 ogf A004655 20.2168 -(1+2*x)*(4*x^2+1)/(-1+10*x^4) ogf A004655 18.9533 -(1+2*x+4*x^2+8*x^3)/(-1+10*x^4) ogf A004655 8.19601 -2*(1+4*x+40*x^6+40*x^5+30*x^4+20*x^3+12*x^2)/(2*x+1)/(4*x^2+1)/(10*x^4-1) lgdogf A004655 13.4779 {-a(n+4)+10*a(n),a(0)=1,a(1)=2,a(2)=4,a(3)=8} ogf A004657 14.9507 (1-x+x^2)*(1+x^4)/(1+x^2)/(x+1)^2/(x-1)^4 ogf A004657 7.47534 -(1+4*x+2*x^9-x^8+6*x^7+14*x^5-8*x^4+14*x^3)/(x-1)/(x+1)/(1+x^2)/(x^2-x+1)/(1+x^4) lgdogf A004657 10.3895 -(1-x-x^5+x^4+x^6+x^2)/(-2*x^5-1+2*x+2*x^7-x^8-2*x^3+2*x^4) ogf A004657 26.6512 1+2*x+x^2+2*x^3-x^5-x^7 ogf_with_Euler_Transform A004663 26.0246 -(1+3*x)/(-1+10*x^2) ogf A004663 26.0246 -(3*x+1)/(-1+10*x^2) ogf A004663 14.8712 -(3+20*x+30*x^2)/(3*x+1)/(10*x^2-1) lgdogf A004663 12.1044 -1/10*10^(1/2)*(arcsinh(3)-arcsinh(3+10*x)) revegf A004663 13.3459 1/2/(3+10*x)*(-1+(1+12*x+40*x^2)^(1/2)) revogf A004663 10.2057 11+33*x+(-31-60*x+110*x^2)*f(x)+(20-200*x^2)*f(x)^2 ogf A004663 16.79 {-a(n+2)+10*a(n),a(0)=1,a(1)=3} ogf A004664 3.59981 {(128+106*n+21*n^2)*a(n+1)+(-212-275*n-131*n^2-21*n^3)*a(n+2)+(336*n+288+155*n^2+25*n^3)*a(n+3)+(-167*n-204-45*n^2-4*n^3)*a(n+4),a(0)=1,a(1)=2,a(2)=3,a(3)=5/2} egf A004667 1.19265 -(1+3*x+4*x^2)/(-1+5*x^2+6*x^3) ogf A004668 1.75953 -(1+3*x+9*x^2)/(-1+11*x^3) ogf A004669 22.0438 -(-1-3*x-9*x^2)/(1-10*x^3) ogf A004669 22.0438 -(1+3*x+9*x^2)/(-1+10*x^3) ogf A004669 10.2346 -3*(1+6*x+30*x^4+20*x^3+10*x^2)/(10*x^3-1)/(9*x^2+3*x+1) lgdogf A004669 8.95529 7+21*x+63*x^2+(13+60*x+180*x^2+70*x^3)*f(x)+(-20+200*x^3)*f(x)^2 ogf A004669 15.4902 {a(n+3)-10*a(n),a(0)=1,a(1)=3,a(2)=9} ogf A004675 6.61487 -1-6218175600*x^4+(3+12436351200*x^4)*f(x)+(-6218175600*x^4-3)*f(x)^2+f(x)^3 ogf A004694 1.42732 -(1+x+2*x^3+2*x^2+3*x^4)/(x^3-1+x^4+5*x^5) ogf A004695 16.1803 -(-1-2*x+5*x^4+4*x^3-3*x^2)/(x-1)/(x^2+x+1)/(x^2+x-1) lgdogf A004695 30.6269 1/(x-1)/(1+x^2+x)/(-1+x+x^2) ogf A004695 27.663 x^3+(-1+x+x^2+x^3-x^4-x^5)*f(x) ogf A004696 12.8043 (1+x^3+x^4)/(x-1)/(x+1)/(1+x^2)/(-1+x+x^2)/(1+x^4) ogf A004696 4.92474 -(4*x^4-8*x^7+12*x^12-2*x+2*x^5-2*x^3-3*x^2+9*x^8+10*x^9-5*x^10+2*x^11+6*x^13-1)/(x-1)/(x+1)/(1+x^2)/(x^2+x-1)/(x^4+x^3+1)/(x^4+1) lgdogf A004696 16.8478 -(x^7+x^4+x^8)/(-1+x+x^2-x^9-x^10+x^8) ogf A004697 9.06762 -(-2+2*x+7*x^6-5*x^4+4*x^3-3*x^2)/(x-1)/(x^2+x+1)/(x^2-x+1)/(x^2+x-1) lgdogf A004697 16.4649 1/(x-1)/(1+x^2+x)/(1-x+x^2)/(-1+x+x^2) ogf A004697 20.1828 x^5/(1-2*x+x^2-x^3+x^4-x^5+x^7) ogf A004698 7.92808 (x+1)*(x^7-x^5+x^3-x+1)/(x-1)/(-1+x+x^2)/(1+x+x^2+x^3+x^4)/(x^8-x^6+x^4-x^2+1) ogf A004766 41.7365 -(-9+x)/(x-1)/(x-5) lgdogf A004766 41.7365 -(5-x)/(-x^2-1+2*x) ogf A004766 56.6424 -(x-5)/(x-1)^2 ogf A004766 22.657 -1/2*(-5-2*x+(25+16*x)^(1/2))/(1+x) revogf A004766 15.2499 -205+41*x+(1-74*x+41*x^2)*f(x)+(8-16*x+8*x^2)*f(x)^2 ogf A004766 21.4323 {-a(n+2)+2*a(n+1)-a(n),a(0)=5,a(1)=9} ogf A004767 60.6899 (x+3)/(x-1)^2 ogf A004767 41.5247 -(3+x)/(-x^2-1+2*x) ogf A004767 43.8316 -(7+x)/(x+3)/(x-1) lgdogf A004767 22.542 -1/2*(-3-2*x+(9+16*x)^(1/2))/(-1+x) revogf A004767 15.47 -75-25*x+(1-58*x+25*x^2)*f(x)+(8-16*x+8*x^2)*f(x)^2 ogf A004767 21.3235 {-a(n+2)+2*a(n+1)-a(n),a(0)=3,a(1)=7} ogf A004768 45.0238 -(-17+x)/(x-1)/(-9+x) lgdogf A004768 49.7632 -(9-x)/(-x^2-1+2*x) ogf A004768 67.5357 -(x-9)/(x-1)^2 ogf A004768 27.0143 -1/2*(-9-2*x+(81+32*x)^(1/2))/(1+x) revogf A004768 16.3017 -1305+145*x+(1-274*x+145*x^2)*f(x)+(16-32*x+16*x^2)*f(x)^2 ogf A004768 24.8816 {-a(n+2)+2*a(n+1)-a(n),a(0)=9,a(1)=17} ogf A004769 52.7562 -(-11+3*x)/(x-1)^2 ogf A004769 37.9844 -(-19+3*x)/(x-1)/(3*x-11) lgdogf A004769 43.1641 -(11-3*x)/(-x^2-1+2*x) ogf A004769 25.6652 -1/2*(-11-2*x+(121+32*x)^(1/2))/(3+x) revogf A004769 16.3726 -2035+555*x+(9-322*x+185*x^2)*f(x)+(16-32*x+16*x^2)*f(x)^2 ogf A004769 24.349 {-a(n+2)+2*a(n+1)-a(n),a(0)=11,a(1)=19} ogf A004770 53.7183 (3*x+5)/(x-1)^2 ogf A004770 35.0337 -(13+3*x)/(3*x+5)/(x-1) lgdogf A004770 38.3702 -(5+3*x)/(-x^2-1+2*x) ogf A004770 22.3826 -1/2*(-5-2*x+(25+32*x)^(1/2))/(-3+x) revogf A004770 14.3888 -445-267*x+(9-226*x+89*x^2)*f(x)+(16-32*x+16*x^2)*f(x)^2 ogf A004770 21.2046 {-a(n+2)+2*a(n+1)-a(n),a(0)=5,a(1)=13} ogf A004771 61.9826 (x+7)/(x-1)^2 ogf A004771 42.4092 -(15+x)/(7+x)/(x-1) lgdogf A004771 42.4092 -(7+x)/(-x^2-1+2*x) ogf A004771 22.3826 -1/2*(-7-2*x+(49+32*x)^(1/2))/(-1+x) revogf A004771 14.1364 -791-113*x+(1-242*x+113*x^2)*f(x)+(16-32*x+16*x^2)*f(x)^2 ogf A004771 21.2046 {-a(n+2)+2*a(n+1)-a(n),a(0)=7,a(1)=15} ogf A004772 30.6305 (2+x+x^2)/(1+x^2+x)/(x-1)^2 ogf A004772 28.5181 -(-2*x-x^2-x^3)/(1-x+x^4-x^3) ogf A004772 15.6042 -(3+5*x+2*x^4+4*x^3+10*x^2)/(x-1)/(x^2+x+1)/(x^2+x+2) lgdogf A004772 9.398 30*x+15*x^2+15*x^3+(-15+127*x+56*x^2+71*x^3-15*x^4)*f(x)+(-56+56*x^3+56*x-56*x^4)*f(x)^2 ogf A004772 10.4687 {(4*n+13)*a(n+1)+4*a(n+2)+4*a(n+3)+(-4*n-9)*a(n+4),a(0)=0,a(1)=2,a(2)=3,a(3)=4} ogf A004773 28.9088 (1+x+2*x^2)/(1+x^2+x)/(x-1)^2 ogf A004773 28.9088 -(-x-x^2-2*x^3)/(1-x+x^4-x^3) ogf A004773 15.5251 -(2+6*x+4*x^4+5*x^3+7*x^2)/(x-1)/(x^2+x+1)/(2*x^2+x+1) lgdogf A004773 10.35 -16*x-16*x^2-32*x^3+(16-21*x-5*x^2-26*x^3+16*x^4)*f(x)+(5-5*x^3-5*x+5*x^4)*f(x)^2 ogf A004773 10.6121 {(-4*n-11)*a(n+1)-4*a(n+2)-4*a(n+3)+(4*n+7)*a(n+4),a(0)=0,a(1)=1,a(2)=2,a(3)=4} ogf A004774 13.24 (1+x+x^2+x^3+x^4+x^5+x^6+x^8)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004774 17.7472 -(x+x^5+x^7+x^4+x^6+x^9+x^2+x^3)/(-1+x-x^8+x^7) ogf A004775 12.967 (1+x+x^5+x^3+x^2+x^4+x^6+x^10)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004775 17.2893 -(x+x^5+x^7+x^11+x^4+x^6+x^2+x^3)/(-1+x-x^8+x^7) ogf A004776 13.6741 (1+x+x^5+x^3+x^2+2*x^4+x^6)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004776 18.536 -(x+2*x^5+x^7+x^4+x^6+x^2+x^3)/(-1+x-x^8+x^7) ogf A004777 13.6741 (1+x+x^5+x^3+x^2+x^4+2*x^6)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004777 18.536 -(x+x^5+2*x^7+x^4+x^6+x^2+x^3)/(-1+x-x^8+x^7) ogf A004794 7.23768 -(3+4*x-x^10+144*x^5+4*x^7+x^12+17*x^4-356*x^6+3*x^9+21*x^3)/(-x^12-1+x+322*x^6-322*x^7+x^13) ogf A004797 41.3732 -(4+2*x)/(-1-x) ogf_with_Euler_Transform A004797 20.0193 {-a(n+2)-a(n+1),a(0)=4,a(1)=-2} ogf_with_Euler_Transform A004798 41.3897 (x+1)^2/(-1+x+x^2)^2 ogf A004798 24.3469 -(1+2*x+x^2)/(x^2-1+2*x-x^4-2*x^3) ogf A004798 27.5931 -2*(2+2*x+x^2)/(x+1)/(x^2+x-1) lgdogf A004798 10.3474 1+2*x+x^2+(24+52*x+26*x^2-2*x^3-x^4)*f(x)+(-25*x^4+25*x^2-25+50*x-50*x^3)*f(x)^2 ogf A004798 10.095 {(-n-4)*a(n+4)+4*a(n+3)+(8+2*n)*a(n+2)+(n+3)*a(n+1),a(0)=1,a(1)=4,a(2)=10,a(3)=22} ogf A004799 31.3492 (1+2*x)^2/(-1+x+x^2)^2 ogf A004799 19.1578 -(1+4*x+4*x^2)/(x^2-1+2*x-x^4-2*x^3) ogf A004799 20.2848 -2*(3+2*x+2*x^2)/(2*x+1)/(x^2+x-1) lgdogf A004799 7.41594 -26-104*x-104*x^2+(-9-192*x-166*x^2+52*x^3+26*x^4)*f(x)+(35-70*x+35*x^4-35*x^2+70*x^3)*f(x)^2 ogf A004799 7.74924 {(-n-4)*a(n+4)+(3-n)*a(n+3)+(10+3*n)*a(n+2)+(6+2*n)*a(n+1),a(0)=1,a(1)=6,a(2)=17,a(3)=38} ogf A004812 8.7614 (-49908-4204749*x+51024*x^12-185971319*x^13+190270091*x^14)/(4252*x^12-4159)/(x-1)^2 ogf A004812 6.5129 -(49908+4204749*x-51024*x^12-190270091*x^14+185971319*x^13)/(-4159*x^2-4159+8318*x-8504*x^13+4252*x^12+4252*x^14) ogf A004822 8.57865 (-72974-13506824*x+73953*x^11-998540960*x^12+1012228988*x^13)/(6723*x^11-6634)/(x-1)^2 ogf A004822 6.30567 -(72974+13506824*x+998540960*x^12-73953*x^11-1012228988*x^13)/(-6634*x^2-6634+13268*x-13446*x^12+6723*x^11+6723*x^13) ogf A004823 8.63844 (-78540-13319075*x+79608*x^12-971751385*x^13+985251575*x^14)/(6634*x^12-6545)/(x-1)^2 ogf A004823 6.32989 -(78540+13319075*x-79608*x^12-985251575*x^14+971751385*x^13)/(-6545*x^2-6545+13090*x-13268*x^13+6634*x^12+6634*x^14) ogf A004830 6.07203 (2+21*x^23-43*x^22+22*x^21)/(x-1)/(x^2-x+1)/(x^21-x^19-x^18+x^16+x^15-x^13-x^12+x^10+x^9-x^7-x^6+x^4+x^3-x-1) lgdogf A004830 24.513 -(x-x^24+x^23)/(-1+2*x-x^2) ogf A004830 7.87919 -(x^2-x+1)*(x^21-x^19-x^18+x^16+x^15-x^13-x^12+x^10+x^9-x^7-x^6+x^4+x^3-x-1)/(x-1)^2 ogf A004919 8.47406 (6+7*x+7*x^5+7*x^3+7*x^2+7*x^4+6*x^6+x^7)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004919 10.4189 -(6*x+7*x^5+6*x^7+7*x^4+7*x^6+x^8+7*x^2+7*x^3)/(-1+x-x^8+x^7) ogf A004920 6.33187 -(11*x+11*x^10+11*x^5+11*x^7+x^12+11*x^11+11*x^4+11*x^6+11*x^8+11*x^9+11*x^2+11*x^3)/(-1+x-x^12+x^11) ogf A004923 17.5851 (46*x+x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A004923 43.9627 (46+x)/(x-1)^2 ogf A004923 19.2337 -(-23-x+(529+47*x)^(1/2))/(-1+x) revogf A004923 25.6449 -(-46*x-x^2)/(1-2*x+x^2) ogf A004923 30.7739 -(93+x)/(x+46)/(x-1) lgdogf A004923 13.0953 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=46,a(2)=93} ogf A004924 75.378 -2/(x-1) lgdogf A004924 21.5366 19*x/(19+(361+19*x)^(1/2))^2 revogf A004924 27.4102 76*x+(-1+2*x-x^2)*f(x) ogf A004924 37.689 76*x/(1-2*x+x^2) ogf A004924 60.3024 76/(x-1)^2 ogf A004924 16.2979 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=76} ogf A004925 16.0978 (122*x+x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A004925 38.6348 (122+x)/(x-1)^2 ogf A004925 23.1809 -(-122*x-x^2)/(1-2*x+x^2) ogf A004925 17.0448 -(-61-x+(3721+123*x)^(1/2))/(-1+x) revogf A004925 26.3419 -(245+x)/(x+122)/(x-1) lgdogf A004925 11.827 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=122,a(2)=245} ogf A004926 73.7735 -2/(x-1) lgdogf A004926 25.6604 199*x+(-1+2*x-x^2)*f(x) ogf A004926 34.7169 199*x/(1-2*x+x^2) ogf A004926 53.6535 199/(x-1)^2 ogf A004926 17.8845 796*x/(199+(39601+796*x)^(1/2))^2 revogf A004926 15.5313 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=199} ogf A004927 16.1625 (321*x+x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A004927 38.79 (321+x)/(x-1)^2 ogf A004927 23.274 -(-321*x-x^2)/(1-2*x+x^2) ogf A004927 26.4477 -(643+x)/(x+321)/(x-1) lgdogf A004927 13.2239 -1/2*(-321-2*x+(103041+1288*x)^(1/2))/(-1+x) revogf A004927 11.8745 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=321,a(2)=643} ogf A004928 72.3473 -2/(x-1) lgdogf A004928 16.0772 2084*x/(521+(271441+2084*x)^(1/2))^2 revogf A004928 25.1643 521*x+(-1+2*x-x^2)*f(x) ogf A004928 34.0458 521*x/(1-2*x+x^2) ogf A004928 52.6162 521/(x-1)^2 ogf A004928 15.231 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=521} ogf A004929 15.3999 (842*x+x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A004929 36.9597 (842+x)/(x-1)^2 ogf A004929 14.9837 -(-421-x+(177241+843*x)^(1/2))/(-1+x) revogf A004929 22.1758 -(-842*x-x^2)/(1-2*x+x^2) ogf A004929 24.1042 -(1685+x)/(x+842)/(x-1) lgdogf A004929 11.0879 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=842,a(2)=1685} ogf A004930 68.1878 -2/(x-1) lgdogf A004930 22.7293 1364*x+(-1+2*x-x^2)*f(x) ogf A004930 30.3057 1364*x/(1-2*x+x^2) ogf A004930 45.4586 1364/(x-1)^2 ogf A004930 16.0442 341*x/(341+(116281+341*x)^(1/2))^2 revogf A004930 13.9872 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=1364} ogf A004931 15.0163 (2206*x+x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A004931 34.7253 (2206+x)/(x-1)^2 ogf A004931 13.8901 -(-1103-x+(1216609+2207*x)^(1/2))/(-1+x) revogf A004931 21.3694 -(-2206*x-x^2)/(1-2*x+x^2) ogf A004931 23.1502 -(4413+x)/(x+2206)/(x-1) lgdogf A004931 10.8942 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=2206,a(2)=4413} ogf A004932 67.0605 -2/(x-1) lgdogf A004932 13.085 14284*x/(3571+(12752041+14284*x)^(1/2))^2 revogf A004932 22.3535 3571*x+(-1+2*x-x^2)*f(x) ogf A004932 29.8047 3571*x/(1-2*x+x^2) ogf A004932 44.707 3571/(x-1)^2 ogf A004932 13.756 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=3571} ogf A004933 14.6977 (5777*x+x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A004933 33.9884 (5777+x)/(x-1)^2 ogf A004933 20.9159 -(-5777*x-x^2)/(1-2*x+x^2) ogf A004933 21.7525 -(11555+x)/(x+5777)/(x-1) lgdogf A004933 11.3294 -1/2*(-5777-2*x+(33373729+23112*x)^(1/2))/(-1+x) revogf A004933 10.458 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=5777,a(2)=11555} ogf A004934 67.1983 -2/(x-1) lgdogf A004934 13.1119 37396*x/(9349+(87403801+37396*x)^(1/2))^2 revogf A004934 22.3994 9349*x+(-1+2*x-x^2)*f(x) ogf A004934 29.8659 9349*x/(1-2*x+x^2) ogf A004934 44.7989 9349/(x-1)^2 ogf A004934 13.7843 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=9349} ogf A004935 14.5757 (15126*x+x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A004935 32.581 (15126+x)/(x-1)^2 ogf A004935 20.514 -(-15126*x-x^2)/(1-2*x+x^2) ogf A004935 13.1875 -(-7563-x+(57198969+15127*x)^(1/2))/(-1+x) revogf A004935 21.303 -(30253+x)/(x+15126)/(x-1) lgdogf A004935 10.4505 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=15126,a(2)=30253} ogf A004940 6.50408 -(11*x+11*x^10+11*x^5+11*x^7+11*x^11+11*x^4+12*x^6+11*x^8+11*x^9+11*x^2+11*x^3)/(-1+x-x^12+x^11) ogf A004942 12.4291 (58+14*x^13+13*x^15-27*x^14)/(x-1)/(x^15-x^14-29) lgdogf A004942 25.3761 -(-29-x^14+x^15)/(x-1)^2 ogf A004942 20.3008 -(29*x-x^16+x^15)/(-1+2*x-x^2) ogf A004944 75.378 -2/(x-1) lgdogf A004944 21.5366 19*x/(19+(361+19*x)^(1/2))^2 revogf A004944 27.4102 76*x+(-1+2*x-x^2)*f(x) ogf A004944 37.689 76*x/(1-2*x+x^2) ogf A004944 60.3024 76/(x-1)^2 ogf A004944 16.2979 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=76} ogf A004945 72.4403 -2/(x-1) lgdogf A004945 25.1966 123*x+(-1+2*x-x^2)*f(x) ogf A004945 34.0895 123*x/(1-2*x+x^2) ogf A004945 52.6838 123/(x-1)^2 ogf A004945 17.5613 492*x/(123+(15129+492*x)^(1/2))^2 revogf A004945 15.2506 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=123} ogf A004946 73.7735 -2/(x-1) lgdogf A004946 25.6604 199*x+(-1+2*x-x^2)*f(x) ogf A004946 34.7169 199*x/(1-2*x+x^2) ogf A004946 53.6535 199/(x-1)^2 ogf A004946 17.8845 796*x/(199+(39601+796*x)^(1/2))^2 revogf A004946 15.5313 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=199} ogf A004947 72.7312 -2/(x-1) lgdogf A004947 25.2978 322*x+(-1+2*x-x^2)*f(x) ogf A004947 34.2264 322*x/(1-2*x+x^2) ogf A004947 17.6318 322*x/(161+(25921+322*x)^(1/2))^2 revogf A004947 52.8954 322/(x-1)^2 ogf A004947 15.3118 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=322} ogf A004948 72.3473 -2/(x-1) lgdogf A004948 16.0772 2084*x/(521+(271441+2084*x)^(1/2))^2 revogf A004948 25.1643 521*x+(-1+2*x-x^2)*f(x) ogf A004948 34.0458 521*x/(1-2*x+x^2) ogf A004948 52.6162 521/(x-1)^2 ogf A004948 15.231 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=521} ogf A004949 109.794 -2/(x-1) lgdogf A004949 24.3987 3372*x/(843+(710649+3372*x)^(1/2))^2 revogf A004949 38.1892 843*x+(-1+2*x-x^2)*f(x) ogf A004949 51.6678 843*x/(1-2*x+x^2) ogf A004949 79.8502 843/(x-1)^2 ogf A004949 23.1145 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=843} ogf A004950 68.1878 -2/(x-1) lgdogf A004950 22.7293 1364*x+(-1+2*x-x^2)*f(x) ogf A004950 30.3057 1364*x/(1-2*x+x^2) ogf A004950 45.4586 1364/(x-1)^2 ogf A004950 16.0442 341*x/(341+(116281+341*x)^(1/2))^2 revogf A004950 13.9872 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=1364} ogf A004951 69.4506 -2/(x-1) lgdogf A004951 23.1502 2207*x+(-1+2*x-x^2)*f(x) ogf A004951 30.8669 2207*x/(1-2*x+x^2) ogf A004951 46.3004 2207/(x-1)^2 ogf A004951 14.6212 8828*x/(2207+(4870849+8828*x)^(1/2))^2 revogf A004951 14.2463 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=2207} ogf A004952 67.0605 -2/(x-1) lgdogf A004952 13.085 14284*x/(3571+(12752041+14284*x)^(1/2))^2 revogf A004952 22.3535 3571*x+(-1+2*x-x^2)*f(x) ogf A004952 29.8047 3571*x/(1-2*x+x^2) ogf A004952 44.707 3571/(x-1)^2 ogf A004952 13.756 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=3571} ogf A004953 67.9767 -2/(x-1) lgdogf A004953 22.6589 5778*x+(-1+2*x-x^2)*f(x) ogf A004953 30.2119 5778*x/(1-2*x+x^2) ogf A004953 45.3178 5778/(x-1)^2 ogf A004953 15.9945 642*x/(963+(927369+642*x)^(1/2))^2 revogf A004953 13.9439 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=5778} ogf A004954 67.1983 -2/(x-1) lgdogf A004954 13.1119 37396*x/(9349+(87403801+37396*x)^(1/2))^2 revogf A004954 22.3994 9349*x+(-1+2*x-x^2)*f(x) ogf A004954 29.8659 9349*x/(1-2*x+x^2) ogf A004954 44.7989 9349/(x-1)^2 ogf A004954 13.7843 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=9349} ogf A004955 115.493 -2/(x-1) lgdogf A004955 36.9579 15127*x+(-1+2*x-x^2)*f(x) ogf A004955 48.6288 15127*x/(1-2*x+x^2) ogf A004955 71.0729 15127/(x-1)^2 ogf A004955 21.4872 60508*x/(15127+(228826129+60508*x)^(1/2))^2 revogf A004955 23.0987 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=15127} ogf A004959 8.95147 (7+7*x+7*x^5+7*x^3+7*x^2+7*x^4+6*x^6)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A004959 11.1501 -(7*x+7*x^5+6*x^7+7*x^4+7*x^6+7*x^2+7*x^3)/(-1+x-x^8+x^7) ogf A004960 6.50408 -(-12*x-11*x^10-11*x^5-11*x^7-11*x^11-11*x^4-11*x^6-11*x^8-11*x^9-11*x^2-11*x^3)/(1-x+x^12-x^11) ogf A004963 76.9348 -2/(x-1) lgdogf A004963 19.8541 188*x/(47+(2209+188*x)^(1/2))^2 revogf A004963 27.9763 47*x+(-1+2*x-x^2)*f(x) ogf A004963 38.4674 47*x/(1-2*x+x^2) ogf A004963 61.5478 47/(x-1)^2 ogf A004963 16.6345 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=47} ogf A004964 17.2292 (-77*x+x^2)*f(x)+(x^2-2*x+1)*f(x)^2 ogf A004964 27.4102 -(-153+x)/(x-1)/(x-77) lgdogf A004964 25.126 -(-77*x+x^2)/(1-2*x+x^2) ogf A004964 37.689 -(-77+x)/(x-1)^2 ogf A004964 15.4621 -1/2*(-77-2*x+(5929+304*x)^(1/2))/(1+x) revogf A004964 12.563 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=77,a(2)=153} ogf A004965 72.4403 -2/(x-1) lgdogf A004965 25.1966 123*x+(-1+2*x-x^2)*f(x) ogf A004965 34.0895 123*x/(1-2*x+x^2) ogf A004965 52.6838 123/(x-1)^2 ogf A004965 17.5613 492*x/(123+(15129+492*x)^(1/2))^2 revogf A004965 15.2506 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=123} ogf A004966 16.3941 (-200*x+x^2)*f(x)+(x^2-2*x+1)*f(x)^2 ogf A004966 16.8625 -(-100-x+(10000+199*x)^(1/2))/(1+x) revogf A004966 23.6075 -(-200*x+x^2)/(1-2*x+x^2) ogf A004966 34.7169 -(-200+x)/(x-1)^2 ogf A004966 25.6604 -(-399+x)/(x-1)/(x-200) lgdogf A004966 12.0447 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=200,a(2)=399} ogf A004967 72.7312 -2/(x-1) lgdogf A004967 25.2978 322*x+(-1+2*x-x^2)*f(x) ogf A004967 34.2264 322*x/(1-2*x+x^2) ogf A004967 17.6318 322*x/(161+(25921+322*x)^(1/2))^2 revogf A004967 52.8954 322/(x-1)^2 ogf A004967 15.3118 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=322} ogf A004968 16.0772 (-522*x+x^2)*f(x)+(x^2-2*x+1)*f(x)^2 ogf A004968 24.1158 -(-1043+x)/(x-1)/(x-522) lgdogf A004968 16.5365 -(-261-x+(68121+521*x)^(1/2))/(1+x) revogf A004968 23.1511 -(-522*x+x^2)/(1-2*x+x^2) ogf A004968 34.0458 -(-522+x)/(x-1)^2 ogf A004968 11.5756 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=522,a(2)=1043} ogf A004969 69.2994 -2/(x-1) lgdogf A004969 15.3999 3372*x/(843+(710649+3372*x)^(1/2))^2 revogf A004969 24.1042 843*x+(-1+2*x-x^2)*f(x) ogf A004969 32.6115 843*x/(1-2*x+x^2) ogf A004969 50.3996 843/(x-1)^2 ogf A004969 14.5894 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=843} ogf A004970 14.7433 (-1365*x+x^2)*f(x)+(x^2-2*x+1)*f(x)^2 ogf A004970 20.9809 -(-1365*x+x^2)/(1-2*x+x^2) ogf A004970 30.3057 -(-1365+x)/(x-1)^2 ogf A004970 21.8201 -(-2729+x)/(x-1)/(x-1365) lgdogf A004970 12.1223 -1/2*(-1365-2*x+(1863225+5456*x)^(1/2))/(1+x) revogf A004970 10.6961 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=1365,a(2)=2729} ogf A004971 69.4506 -2/(x-1) lgdogf A004971 23.1502 2207*x+(-1+2*x-x^2)*f(x) ogf A004971 30.8669 2207*x/(1-2*x+x^2) ogf A004971 46.3004 2207/(x-1)^2 ogf A004971 14.6212 8828*x/(2207+(4870849+8828*x)^(1/2))^2 revogf A004971 14.2463 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=2207} ogf A004972 14.4996 (-3572*x+x^2)*f(x)+(x^2-2*x+1)*f(x)^2 ogf A004972 13.756 -(-1786-x+(3189796+3571*x)^(1/2))/(1+x) revogf A004972 20.634 -(-3572*x+x^2)/(1-2*x+x^2) ogf A004972 29.8047 -(-3572+x)/(x-1)^2 ogf A004972 21.4594 -(-7143+x)/(x-1)/(x-3572) lgdogf A004972 10.5193 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=3572,a(2)=7143} ogf A004973 67.9767 -2/(x-1) lgdogf A004973 22.6589 5778*x+(-1+2*x-x^2)*f(x) ogf A004973 30.2119 5778*x/(1-2*x+x^2) ogf A004973 45.3178 5778/(x-1)^2 ogf A004973 15.9945 642*x/(963+(927369+642*x)^(1/2))^2 revogf A004973 13.9439 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=5778} ogf A004974 14.5294 (-9350*x+x^2)*f(x)+(x^2-2*x+1)*f(x)^2 ogf A004974 20.6764 -(-18699+x)/(x-1)/(x-9350) lgdogf A004974 13.4397 -(-4675-x+(21855625+9349*x)^(1/2))/(1+x) revogf A004974 20.6764 -(-9350*x+x^2)/(1-2*x+x^2) ogf A004974 29.8659 -(-9350+x)/(x-1)^2 ogf A004974 10.3382 {a(n+3)-2*a(n+2)+a(n+1),a(0)=0,a(1)=9350,a(2)=18699} ogf A004975 115.493 -2/(x-1) lgdogf A004975 36.9579 15127*x+(-1+2*x-x^2)*f(x) ogf A004975 48.6288 15127*x/(1-2*x+x^2) ogf A004975 71.0729 15127/(x-1)^2 ogf A004975 21.4872 60508*x/(15127+(228826129+60508*x)^(1/2))^2 revogf A004975 23.0987 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=15127} ogf A004981 39.5788 -2+(1-8*x)*f(x) lgdogf A004981 53.971 -2/(-1+8*x) lgdogf A004981 39.5788 1/(1-8*x)^(1/4) ogf A004981 13.1929 {(-n-2)*a(n+2)+(10+8*n)*a(n+1),a(0)=1,a(1)=2} ogf A004982 38.9445 -6+(1-8*x)*f(x) lgdogf A004982 53.1061 -6/(-1+8*x) lgdogf A004982 38.9445 1/(1-8*x)^(3/4) ogf A004982 12.9815 {(-n-2)*a(n+2)+(14+8*n)*a(n+1),a(0)=1,a(1)=6} ogf A004983 55.9564 (1-8*x)^(3/4) ogf A004983 45.4646 -6+(-1+8*x)*f(x) lgdogf A004983 72.7434 6/(-1+8*x) lgdogf A004983 16.1652 {(n+2)*a(n+2)+(-2-8*n)*a(n+1),a(0)=1,a(1)=-6} ogf A004984 53.0232 (1-8*x)^(1/4) ogf A004984 43.0814 -2+(-1+8*x)*f(x) lgdogf A004984 68.9302 2/(-1+8*x) lgdogf A004984 15.3178 {(n+2)*a(n+2)+(-6-8*n)*a(n+1),a(0)=1,a(1)=-2} ogf A004985 38.3828 -10+(1-8*x)*f(x) lgdogf A004985 51.1771 -10/(-1+8*x) lgdogf A004985 40.9416 1/(1-8*x)^(5/4) ogf A004985 13.3505 {(-n-2)*a(n+2)+(18+8*n)*a(n+1),a(0)=1,a(1)=10} ogf A004986 36.2534 -14+(1-8*x)*f(x) lgdogf A004986 48.3379 -14/(-1+8*x) lgdogf A004986 38.6703 1/(1-8*x)^(7/4) ogf A004986 12.6099 {(-n-2)*a(n+2)+(22+8*n)*a(n+1),a(0)=1,a(1)=14} ogf A004987 33.6579 -1+(1-9*x)*f(x)^3 ogf A004987 52.0168 -3/(-1+9*x) lgdogf A004987 38.1456 1/(1-9*x)^(1/3) ogf A004987 12.7152 {(-n-2)*a(n+2)+(12+9*n)*a(n+1),a(0)=1,a(1)=3} ogf A004988 27.0353 -1+(1-18*x+81*x^2)*f(x)^3 ogf A004988 61.4439 -6/(-1+9*x) lgdogf A004988 45.0589 1/(1-9*x)^(2/3) ogf A004988 15.0196 {(-n-2)*a(n+2)+(15+9*n)*a(n+1),a(0)=1,a(1)=6} ogf A004989 43.7837 (1-9*x)^(2/3) ogf A004989 27.1042 -1+18*x-81*x^2+f(x)^3 ogf A004989 56.9189 6/(-1+9*x) lgdogf A004989 12.6486 {(n+2)*a(n+2)+(-3-9*n)*a(n+1),a(0)=1,a(1)=-6} ogf A004990 50.1175 (1-9*x)^(1/3) ogf A004990 54.2939 1-9*x-f(x)^3 ogf A004990 65.1527 3/(-1+9*x) lgdogf A004990 14.4784 {(n+2)*a(n+2)+(-6-9*n)*a(n+1),a(0)=1,a(1)=-3} ogf A004991 24.78 -12+(1-9*x)*f(x) lgdogf A004991 33.04 -12/(-1+9*x) lgdogf A004991 26.432 1/(1-9*x)^(4/3) ogf A004991 8.61914 {(-n-2)*a(n+2)+(21+9*n)*a(n+1),a(0)=1,a(1)=12} ogf A004992 26.1663 -15+(1-9*x)*f(x) lgdogf A004992 34.8884 -15/(-1+9*x) lgdogf A004992 27.9107 1/(1-9*x)^(5/3) ogf A004992 9.10133 {(-n-2)*a(n+2)+(24+9*n)*a(n+1),a(0)=1,a(1)=15} ogf A004993 32.5779 -6+(1-36*x)*f(x) lgdogf A004993 43.4372 -6/(-1+36*x) lgdogf A004993 32.5779 1/(1-36*x)^(1/6) ogf A004993 11.3315 {(-n-2)*a(n+2)+(42+36*n)*a(n+1),a(0)=1,a(1)=6} ogf A004994 28.9921 -30+(1-36*x)*f(x) lgdogf A004994 37.9127 -30/(-1+36*x) lgdogf A004994 30.8041 1/(1-36*x)^(5/6) ogf A004994 10.4865 {(-n-2)*a(n+2)+(66+36*n)*a(n+1),a(0)=1,a(1)=30} ogf A004995 38.0241 (1-36*x)^(5/6) ogf A004995 29.5743 -30+(-1+36*x)*f(x) lgdogf A004995 44.3614 30/(-1+36*x) lgdogf A004995 11.3263 {(n+2)*a(n+2)+(-6-36*n)*a(n+1),a(0)=1,a(1)=-30} ogf A004996 34.0441 (1-36*x)^(1/6) ogf A004996 28.0363 -6+(-1+36*x)*f(x) lgdogf A004996 43.3288 6/(-1+36*x) lgdogf A004996 10.1408 {(n+2)*a(n+2)+(-30-36*n)*a(n+1),a(0)=1,a(1)=-6} ogf A004997 29.9478 -42+(1-36*x)*f(x) lgdogf A004997 39.1626 -42/(-1+36*x) lgdogf A004997 31.8196 1/(1-36*x)^(7/6) ogf A004997 10.8322 {(-n-2)*a(n+2)+(78+36*n)*a(n+1),a(0)=1,a(1)=42} ogf A004998 26.7011 -66+(1-36*x)*f(x) lgdogf A004998 34.9168 -66/(-1+36*x) lgdogf A004998 26.7011 1/(1-36*x)^(11/6) ogf A004998 9.45663 {(-n-2)*a(n+2)+(102+36*n)*a(n+1),a(0)=1,a(1)=66} ogf A005000 6.32174 -x-1+exp(x) lgdegf A005000 1.54531 {-a(n+1)+(n+2)*a(n+2),a(0)=0,a(1)=0,a(2)=1/2} lgdegf A005009 28.3433 -1/2*ln(7)+1/2*ln(7+2*x) revegf A005009 61.84 -2/(-1+2*x) lgdogf A005009 45.3493 -7+(1-2*x)*f(x) ogf A005009 68.024 -7/(2*x-1) ogf A005009 75.5822 7/(1-2*x) ogf A005009 75.5822 x/(7+2*x) revogf A005009 30.92 {a(n+1)-2*a(n),a(0)=7} ogf A005010 58.7747 -2/(-1+2*x) lgdogf A005010 43.1014 -9+(1-2*x)*f(x) ogf A005010 64.6522 -9/(2*x-1) ogf A005010 32.3261 -ln(3)+1/2*ln(9+2*x) revegf A005010 71.8357 9/(1-2*x) ogf A005010 71.8357 x/(9+2*x) revogf A005010 29.3873 {a(n+1)-2*a(n),a(0)=9} ogf A005011 61.4204 exp(5*x) lgdegf A005011 12.9306 {(-n-2)*a(n+2)+5*a(n+1),a(0)=1,a(1)=5} lgdegf A005012 50.1478 6+exp(6*x) lgdegf A005012 13.9299 {6*a(n)+(-n-1)*a(n+1),a(0)=7,a(1)=6} lgdegf A005013 24.7105 (x^2+x+1)/(x^2+x-1)/(x^2-x-1) ogf A005013 11.3747 -(-1-8*x+2*x^5+3*x^4+4*x^3-3*x^2)/(x^2+x+1)/(x^2+x-1)/(x^2-x-1) lgdogf A005013 26.5409 -(x+x^2+x^3)/(-1-x^4+3*x^2) ogf A005013 8.73909 -17*x-17*x^2-17*x^3+(17+22*x-29*x^2+22*x^3+17*x^4)*f(x)+(-22-22*x^4+66*x^2)*f(x)^2 ogf A005015 28.7927 -1/2*ln(11)+1/2*ln(11+2*x) revegf A005015 46.7881 -11+(1-2*x)*f(x) ogf A005015 68.0554 -11/(2*x-1) ogf A005015 68.0554 -2/(-1+2*x) lgdogf A005015 74.861 11/(1-2*x) ogf A005015 74.861 x/(11+2*x) revogf A005015 32.5483 {a(n+1)-2*a(n),a(0)=11} ogf A005021 18.6506 -(5-12*x+3*x^2)/(-6*x^2-1+5*x+x^3) lgdogf A005021 30.1962 -1/(-1+5*x-6*x^2+x^3) ogf A005021 9.19014 -7+(293-35*x+42*x^2-7*x^3)*f(x)+(-1716*x^2+286*x^3-286+1430*x)*f(x)^2 ogf A005021 33.3747 1/(1-5*x+6*x^2-x^3) ogf A005021 11.9645 {a(n+3)-5*a(n+2)+6*a(n+1)-a(n),a(0)=1,a(1)=5,a(2)=19} ogf A005022 19.2263 -(-6+10*x-4*x^2)/(10*x^2+1-6*x-4*x^3) ogf A005022 10.6175 -(13-56*x+8*x^4-40*x^3+74*x^2)/(x-1)/(-1+2*x)/(2*x-3)/(2*x^2-4*x+1) lgdogf A005022 18.2403 -2*(x-1)*(-3+2*x)/(2*x-1)/(2*x^2-4*x+1) ogf A005022 6.90653 8220-13700*x+5480*x^2+(17092-22550*x-1392*x^2+5480*x^3)*f(x)+(-30770*x^2-3077+18462*x+12308*x^3)*f(x)^2 ogf A005022 12.265 {a(n+3)-6*a(n+2)+10*a(n+1)-4*a(n),a(0)=6,a(1)=26,a(2)=100} ogf A005023 16.4521 -(-7+15*x+x^3-10*x^2)/(x-1)/(x^3-9*x^2+6*x-1) ogf A005023 8.22603 -(34-190*x-20*x^5+130*x^4+x^6-314*x^3+362*x^2)/(x-1)/(x^3-9*x^2+6*x-1)/(x^3-10*x^2+15*x-7) lgdogf A005023 15.752 -(7-15*x+10*x^2-x^3)/(-15*x^2-1+7*x-x^4+10*x^3) ogf A005024 13.0539 -(-8+21*x+5*x^3-20*x^2)/(1-3*x+x^2)/(5*x^2-5*x+1) ogf A005024 6.52694 -(43-296*x-200*x^5+610*x^4+25*x^6-920*x^3+746*x^2)/(x^2-3*x+1)/(5*x^2-5*x+1)/(5*x^3-20*x^2+21*x-8) lgdogf A005024 12.542 -(8-21*x+20*x^2-5*x^3)/(-21*x^2-1+8*x-5*x^4+20*x^3) ogf A005025 9.88119 -(-9+28*x-x^4-35*x^2+15*x^3)/(28*x^2+1-9*x+15*x^4-35*x^3-x^5) ogf A005025 4.78375 -(53-434*x-1106*x^5+2083*x^4+x^8-30*x^7+295*x^6-2226*x^3+1369*x^2)/(x^4-15*x^3+35*x^2-28*x+9)/(x^5-15*x^4+35*x^3-28*x^2+9*x-1) lgdogf A005025 9.88119 -(9-28*x-15*x^3+35*x^2+x^4)/(-28*x^2-1+9*x-15*x^4+35*x^3+x^5) ogf A005029 29.1889 -1/2*ln(13)+1/2*ln(13+2*x) revegf A005029 47.432 -13+(1-2*x)*f(x) ogf A005029 68.992 -13/(2*x-1) ogf A005029 68.992 -2/(-1+2*x) lgdogf A005029 75.8912 13/(1-2*x) ogf A005029 75.8912 x/(13+2*x) revogf A005029 32.9962 {a(n+1)-2*a(n),a(0)=13} ogf A005030 31.0358 -1/3*ln(5)+1/3*ln(5+3*x) revegf A005030 67.7145 -3/(-1+3*x) lgdogf A005030 49.6573 -5+(1-3*x)*f(x) ogf A005030 67.7145 -5/(-1+3*x) ogf A005030 82.7622 5/(1-3*x) ogf A005030 82.7622 x/(5+3*x) revogf A005030 33.8573 {a(n+1)-3*a(n),a(0)=5} ogf A005032 31.5851 -1/3*ln(7)+1/3*ln(7+3*x) revegf A005032 68.913 -3/(-1+3*x) lgdogf A005032 50.5362 -7+(1-3*x)*f(x) ogf A005032 68.913 -7/(-1+3*x) ogf A005032 84.227 7/(1-3*x) ogf A005032 84.227 x/(7+3*x) revogf A005032 34.4565 {a(n+1)-3*a(n),a(0)=7} ogf A005043 22.6356 -1+(1+x)*f(x)+(-x-x^2)*f(x)^2 ogf A005043 34.549 -x*(-1+x)/(1-x+x^2) revogf A005043 9.94593 {(3*n+6)*a(n+1)+(2*n+4)*a(n+2)+(-n-4)*a(n+3),a(0)=1,a(1)=0,a(2)=1} ogf A005044 24.7484 -1/(x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^3 ogf A005044 15.3611 -x*(3*x^2+x+2)*(3*x^2+2*x+1)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1) lgdogf A005044 24.0795 -x^3/(-1+x^2+x^3-x^7+x^4-x^5-x^6+x^9) ogf A005044 98.9936 x+x^2+x^3 ogf_with_Euler_Transform A005044 24.0795 {-a(n+4),a(0)=0,a(1)=1,a(2)=1,a(3)=1} ogf_with_Euler_Transform A005045 14.4381 -(1+x-x^5-x^3+x^6)/(x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^5 ogf A005045 6.25649 -(3+9*x+11*x^5+15*x^4+3*x^9-9*x^8-9*x^7-7*x^6+23*x^3+x^10+5*x^11+15*x^2)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1)/(x^6-x^5-x^3+x+1) lgdogf A005045 12.1093 -(x^5+x^7-x^2-x^8-x^3)/(1-2*x+x^3-x^11+2*x^5-2*x^6-x^8+2*x^10) ogf A005051 76.1339 -3/(3*x-1) lgdogf A005051 50.7559 -8+(1-3*x)*f(x) ogf A005051 69.2126 -8/(-1+3*x) ogf A005051 38.067 -ln(2)+1/3*ln(8+3*x) revegf A005051 84.5932 8/(1-3*x) ogf A005051 84.5932 x/(8+3*x) revogf A005051 34.6063 {a(n+1)-3*a(n),a(0)=8} ogf A005052 27.4432 -1/3*ln(10)+1/3*ln(10+3*x) revegf A005052 44.5952 -10+(1-3*x)*f(x) ogf A005052 59.4603 -10/(-1+3*x) ogf A005052 71.3524 -3/(3*x-1) lgdogf A005052 71.3524 10/(1-3*x) ogf A005052 71.3524 x/(10+3*x) revogf A005052 31.0228 {a(n+1)-3*a(n),a(0)=10} ogf A005053 35.1135 (2*x-1)/(5*x-1) ogf A005053 30.9825 -(-1+2*x)/(1-5*x) ogf A005053 27.7212 -1+2*x+(1-5*x)*f(x) ogf A005053 15.4912 1/4+5/4*x-1/4*(1+2*x+25*x^2)^(1/2) revogf A005053 30.9825 3/(5*x-1)/(2*x-1) lgdogf A005053 16.9904 {a(n+2)-5*a(n+1),a(0)=1,a(1)=3} ogf A005054 41.2181 (x-1)/(5*x-1) ogf A005054 35.7224 -(-1+x)/(1-5*x) ogf A005054 31.5197 -1+x+(1-5*x)*f(x) ogf A005054 15.7599 1/2+5/2*x-1/2*(1+6*x+25*x^2)^(1/2) revogf A005054 35.7224 4/(5*x-1)/(x-1) lgdogf A005054 17.285 {a(n+2)-5*a(n+1),a(0)=1,a(1)=4} ogf A005055 30.0484 -1/5*ln(7)+1/5*ln(7+5*x) revegf A005055 72.1163 -5/(5*x-1) lgdogf A005055 48.0775 -7+(1-5*x)*f(x) ogf A005055 72.1163 -7/(5*x-1) ogf A005055 80.1292 7/(1-5*x) ogf A005055 80.1292 x/(7+5*x) revogf A005055 32.7801 {a(n+1)-5*a(n),a(0)=7} ogf A005056 21.1357 (-1+2*x+x^2)/(x-1)/(-1+3*x)/(2*x-1) ogf A005056 21.7573 -(-1+2*x+x^2)/(11*x^2+1-6*x-6*x^3) ogf A005056 10.1335 -11+22*x+11*x^2+(10-64*x+122*x^2-66*x^3)*f(x)+(1-6*x+11*x^2-6*x^3)*f(x)^2 ogf A005056 11.2083 -2*(-2+12*x+3*x^4+12*x^3-23*x^2)/(x-1)/(3*x-1)/(2*x-1)/(x^2+2*x-1) lgdogf A005056 13.2098 {a(n+3)-6*a(n+2)+11*a(n+1)-6*a(n),a(0)=1,a(1)=4,a(2)=12} ogf A005057 27.8691 -(-7+20*x)/(5*x-1)/(2*x-1) lgdogf A005057 16.1021 -1/20*(-7*x-3+(3+14*x+3*x^2)^(1/2)*3^(1/2))/x revogf A005057 30.1915 3*x+(-1+7*x-10*x^2)*f(x) ogf A005057 40.2553 3*x/(1-7*x+10*x^2) ogf A005057 42.6233 3/(5*x-1)/(2*x-1) ogf A005057 18.5794 {a(n+2)-7*a(n+1)+10*a(n),a(0)=0,a(1)=3} ogf A005058 15.7599 -1/15*(-1-4*x+(1+8*x+x^2)^(1/2))/x revogf A005058 19.137 -2*(-4+15*x)/(5*x-1)/(3*x-1) lgdogf A005058 22.3265 2*x+(-1+8*x-15*x^2)*f(x) ogf A005058 29.7686 2*x/(1-8*x+15*x^2) ogf A005058 29.7686 2/(5*x-1)/(-1+3*x) ogf A005058 13.7394 {a(n+2)-8*a(n+1)+15*a(n),a(0)=0,a(1)=2} ogf A005059 13.9883 -1/30*(-1-8*x+(1+16*x+4*x^2)^(1/2))/x revogf A005059 18.4846 -2*(-4+15*x)/(5*x-1)/(3*x-1) lgdogf A005059 28.7538 1/(5*x-1)/(-1+3*x) ogf A005059 23.5258 x+(-1+8*x-15*x^2)*f(x) ogf A005059 32.348 x/(1-8*x+15*x^2) ogf A005059 13.271 {a(n+2)-8*a(n+1)+15*a(n),a(0)=0,a(1)=1} ogf A005060 20.492 -(-9+40*x)/(5*x-1)/(4*x-1) lgdogf A005060 15.2226 -1/40*(-9*x-1+(x^2+18*x+1)^(1/2))/x revogf A005060 31.3406 1/(5*x-1)/(4*x-1) ogf A005060 24.2178 x+(-1+9*x-20*x^2)*f(x) ogf A005060 33.2994 x/(1-9*x+20*x^2) ogf A005060 13.6613 {a(n+2)-9*a(n+1)+20*a(n),a(0)=0,a(1)=1} ogf A005061 22.3102 -(-7+24*x)/(4*x-1)/(3*x-1) lgdogf A005061 16.5733 -1/24*(-1-7*x+(1+14*x+x^2)^(1/2))/x revogf A005061 32.2259 1/(4*x-1)/(-1+3*x) ogf A005061 26.3666 x+(-1+7*x-12*x^2)*f(x) ogf A005061 36.2541 x/(1-7*x+12*x^2) ogf A005061 14.8735 {a(n+2)-7*a(n+1)+12*a(n),a(0)=0,a(1)=1} ogf A005062 19.3058 -(-11+60*x)/(6*x-1)/(5*x-1) lgdogf A005062 14.4794 -1/60*(-1-11*x+(1+22*x+x^2)^(1/2))/x revogf A005062 30.6622 1/(6*x-1)/(5*x-1) ogf A005062 22.6633 x+(-1+11*x-30*x^2)*f(x) ogf A005062 30.6622 x/(1-11*x+30*x^2) ogf A005062 13.0314 {a(n+2)-11*a(n+1)+30*a(n),a(0)=0,a(1)=1} ogf A005095 3.16637 {(-188-232*n-91*n^2-11*n^3)*a(n+1)+(993*n+958+325*n^2+34*n^3)*a(n+2)+(-720-796*n-245*n^2-23*n^3)*a(n+3)+(119*n+108+23*n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=4,a(3)=9} ogf A005102 9.85308 (-1-x-x^10+x^12-x^9+x^14+x^11-x^13-x^3+x^8-x^2+x^6+x^7)/(x-1) ogf A005102 9.69416 -(1+x+x^2-x^8-x^6+x^10-x^11+x^3-x^7-x^14-x^12+x^9+x^13)/(-1+x) ogf A005103 1.80821 3+2*x+2*x^3-8*x^4-8*x^5 ogf_with_Euler_Transform A005120 15.4619 (x^2+x+1)^2/(5*x^2+1+3*x+x^6+5*x^4+5*x^3+3*x^5) ogf A005120 8.25806 -(2*x+1)*(x^6+3*x^5+6*x^4+7*x^3+4*x^2+x+1)/(x^2+x+1)/(x^6+3*x^5+5*x^4+5*x^3+5*x^2+3*x+1) lgdogf A005126 23.6159 -(-2+4*x-x^2)/(5*x^2+1-4*x-2*x^3) ogf A005126 27.8331 -(2-4*x+x^2)/(2*x-1)/(x-1)^2 ogf A005126 16.5814 -2*(-2+7*x+x^3-7*x^2)/(x-1)/(2*x-1)/(x^2-4*x+2) lgdogf A005126 9.99135 -66+132*x-33*x^2+(43-152*x+170*x^2-66*x^3)*f(x)+(-5+20*x-25*x^2+10*x^3)*f(x)^2 ogf A005126 14.432 {a(n+3)-4*a(n+2)+5*a(n+1)-2*a(n),a(0)=2,a(1)=4,a(2)=7} ogf A005131 16.4719 -(1+x^2-x^5+2*x^4-x^3)/(-1+2*x^3-x^6) ogf A005131 13.8514 -(x^2-x+1)*(x^3-x^2-x-1)/(x-1)^2/(x^2+x+1)^2 ogf A005131 8.01922 -x*(x+1)*(x^5-5*x^4+8*x^3-7*x^2-x-2)/(x-1)/(x^2+x+1)/(x^2-x+1)/(x^3-x^2-x-1) lgdogf A005137 2.63273 -2*(-1-x^5-x^3+x^4-x^10-x^11+2*x^12)/(x+1)/(x^4-x^2+1)/(x^2+x+1)/(x^2-x+1)/(x^2+1)/(x-1)^2 ogf A005138 1.65373 x^3+(-3*x^2+3*x^3)*f(x)+(3*x-6*x^2+3*x^3)*f(x)^2+(3*x-3*x^2+x^3-1)*f(x)^3 ogf A005151 4.74341 -(1+10*x+10*x^2-98010*x^8+101000*x^6+208101*x^5-9900990*x^11+10001000*x^10-99990*x^7+2000*x^4+1091*x^3-9899010*x^12+31007101*x^9)/(-1+x) ogf A005159 34.118 -1+f(x)-3*x*f(x)^2 ogf A005159 55.8295 -x*(-1+3*x) revogf A005159 30.7062 2/(1+(1-12*x)^(1/2)) ogf A005159 17.5464 6/(1-12*x)^(1/2)/(1+(1-12*x)^(1/2)) lgdogf A005159 13.3505 {(-12*n-18)*a(n+1)+(n+3)*a(n+2),a(0)=1,a(1)=3} ogf A005165 11.6898 {(n+3)*a(n+1)+(n+2)*a(n+2)-a(n+3),a(0)=0,a(1)=1,a(2)=1} ogf A005170 2.45681 -1-x^2+2*x+(-4*x+2+2*x^3)*f(x)+(-x^4+x^2-1+2*x-2*x^3)*f(x)^2 ogf A005172 64.2869 -x+ln(1+2*x) revegf A005173 20.0401 -(1+6*x)/(x-1)/(-1+3*x)/(2*x-1) ogf A005173 19.4139 -(x+6*x^2)/(-1+6*x-11*x^2+6*x^3) ogf A005173 11.2953 -2*(6-11*x+36*x^3-24*x^2)/(x-1)/(3*x-1)/(2*x-1)/(6*x+1) lgdogf A005173 5.69948 42330*x+253980*x^2+(-42330+190117*x-848808*x^2+253980*x^3)*f(x)+(63863-383178*x+702493*x^2-383178*x^3)*f(x)^2 ogf A005173 11.0936 {a(n+3)-6*a(n+2)+11*a(n+1)-6*a(n),a(0)=0,a(1)=1,a(2)=12} ogf A005174 8.11763 -(-10*x^2-24*x^3)/(1-10*x+35*x^2-50*x^3+24*x^4) ogf A005174 4.95492 -2*(-31+175*x+432*x^4-360*x^3-165*x^2)/(12*x+5)/(x-1)/(3*x-1)/(2*x-1)/(4*x-1) lgdogf A005174 9.30558 2*(5+12*x)/(x-1)/(-1+3*x)/(2*x-1)/(4*x-1) ogf A005175 8.42549 -(-3*x^2-120*x^4-86*x^3)/(1-15*x+85*x^2-225*x^3+274*x^4-120*x^5) ogf A005175 4.64855 -(131-270*x-41892*x^4+43200*x^6-24480*x^5+35412*x^3-7085*x^2)/(x-1)/(3*x-1)/(5*x-1)/(2*x-1)/(4*x-1)/(120*x^2+86*x+3) lgdogf A005175 9.62913 -(3+86*x+120*x^2)/(x-1)/(4*x-1)/(-1+3*x)/(2*x-1)/(5*x-1) ogf A005178 22.2913 -(-x+x^3)/(1-x+x^4-5*x^2-x^3) ogf A005178 10.4266 -(1+8*x-x^4+2*x^5-4*x^3+4*x^2)/(x-1)/(x+1)/(x^4-x^3-5*x^2-x+1) lgdogf A005178 20.2015 -(x-1)*(x+1)/(1-x-5*x^2-x^3+x^4) ogf A005178 20.8531 x-x^3+(-1+x-x^4+5*x^2+x^3)*f(x) ogf A005183 19.3383 -(-1+3*x-3*x^2)/(8*x^2+1-5*x-4*x^3) ogf A005183 13.813 -(-2+6*x+6*x^3-9*x^2)/(x-1)/(2*x-1)/(1+3*x^2-3*x) lgdogf A005183 22.5613 -(1-3*x+3*x^2)/(x-1)/(2*x-1)^2 ogf A005183 18.2929 -1+3*x-3*x^2+(1-5*x+8*x^2-4*x^3)*f(x) ogf A005183 12.5341 {a(n+3)-5*a(n+2)+8*a(n+1)-4*a(n),a(0)=1,a(1)=2,a(2)=5} ogf A005189 7.4044 -(Ei(1,-1/(x-1))*exp(1)+1-Ei(1,1)*exp(1))*exp(-1/(x-1))/exp(1)/(x-1) egf A005189 4.12704 {(n^3+6*n^2+12*n+8)*a(n+1)+(-48-43*n-12*n^2-n^3)*a(n+2)+(34+17*n+2*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=1,a(2)=3,a(3)=14} ogf A005204 10.728 x^3*f(x)^2+(-1+2*x)*f(x)^3 ogf A005207 16.4856 -(1-2*x+x^3-x^2)/(1-3*x+x^2)/(x^2+x-1) ogf A005207 15.2794 -(1-2*x-x^2+x^3)/(-3*x^2-1+4*x+x^4-2*x^3) ogf A005207 8.70074 -(2-8*x-x^4+x^6-2*x^5+4*x^3+7*x^2)/(x^2-3*x+1)/(x^2+x-1)/(x^3-x^2-2*x+1) lgdogf A005207 6.80928 -3+6*x+3*x^2-3*x^3+(-13+20*x+25*x^2-10*x^3-3*x^4)*f(x)+(48*x^2+16-64*x-16*x^4+32*x^3)*f(x)^2 ogf A005212 22.2523 (x^2+1)/(x-1)^2/(x+1)^2 egf A005212 31.9876 -2*x/(x-1)/(x+1) lgdegf A005212 19.6847 1/2/x*(-1+(4*x^2+1)^(1/2)) revegf A005212 34.1201 x+(-1+x^2)*f(x) egf A005212 56.8669 x/(1-x^2) egf A005212 10.4449 {(-n^2-5*n-6)*a(n+1)+a(n+3),a(0)=0,a(1)=1,a(2)=0} ogf A005232 24.6653 (x^2-x+1)/(x^2+1)/(x+1)^2/(x-1)^4 ogf A005232 14.2799 -(1+4*x-5*x^4+6*x^5+10*x^3)/(x-1)/(x+1)/(x^2+1)/(x^2-x+1) lgdogf A005232 17.6947 -(1-x+x^2)/(2*x^7-1+2*x-2*x^5-2*x^3+2*x^4-x^8) ogf A005232 47.8797 1+2*x+x^2+x^3-x^5 ogf_with_Euler_Transform A005232 5.89823 {325*a(n+3)*n-852*a(n+3)+203*a(n+3)*n^2-420*a(n+2)-484*a(n+2)*n+208*a(n+2)*n^2+636*a(n+1)+133*a(n+1)*n-73*a(n+1)*n^2,a(0)=1,a(1)=2,a(2)=1} ogf_with_Euler_Transform A005246 21.7631 -(-1-x+3*x^2+2*x^3)/(1+x^4-4*x^2) ogf A005246 10.2597 -(1+2*x+5*x^4+2*x^6+6*x^5-4*x^3-2*x^2)/(2*x+1)/(x^2+x-1)/(x^4-4*x^2+1) lgdogf A005246 22.4431 -(2*x+1)*(x^2+x-1)/(1+x^4-4*x^2) ogf A005246 9.09089 3+3*x-9*x^2-6*x^3+(-13-10*x+42*x^2+20*x^3-3*x^4)*f(x)+(10+10*x^4-40*x^2)*f(x)^2 ogf A005247 19.466 -(-2-x+x^3+3*x^2)/(x^2+x-1)/(x^2-x-1) ogf A005247 12.004 -(1+6*x+x^6+6*x^5-8*x^3)/(x^2+x-1)/(x^2-x-1)/(x^3+3*x^2-x-2) lgdogf A005247 23.2336 -(2+x-3*x^2-x^3)/(-1-x^4+3*x^2) ogf A005247 8.37492 -34-17*x+51*x^2+17*x^3+(61+22*x-117*x^2-22*x^3+17*x^4)*f(x)+(-22-22*x^4+66*x^2)*f(x)^2 ogf A005248 36.7654 -(-2+3*x)/(x^2+1-3*x) ogf A005248 38.6036 -(3*x-2)/(1-3*x+x^2) ogf A005248 22.708 -(3-4*x+3*x^2)/(3*x-2)/(x^2-3*x+1) lgdogf A005248 16.0848 -2+3*x+(11-18*x+x^2)*f(x)+(-5+15*x-5*x^2)*f(x)^2 ogf A005248 21.4465 {a(n+2)-3*a(n+1)+a(n),a(0)=2,a(1)=3} ogf A005251 32.3341 (x-1)/(-x^2-1+2*x+x^3) ogf A005251 16.5431 -(-1+2*x+2*x^3-4*x^2)/(x-1)/(x^3-x^2+2*x-1) lgdogf A005251 28.454 -(-x+x^2)/(1-2*x+x^2-x^3) ogf A005251 13.4217 -x+x^2+(-3*x+1+2*x^2-x^3)*f(x)+(x^2+1-2*x-x^3)*f(x)^2 ogf A005251 14.227 {a(n+3)-2*a(n+2)+a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=1} ogf A005252 29.0154 (x-1)/(x^2-x+1)/(x^2+x-1) ogf A005252 14.2232 -(-1+2*x+3*x^4-4*x^3-x^2)/(x-1)/(x^2-x+1)/(x^2+x-1) lgdogf A005252 30.2244 -(-x+1)/(-x^2-1+2*x+x^4) ogf A005252 14.8038 -1+x+(2-3*x+x^2-x^4)*f(x)+(-1+x^4+2*x-x^2)*f(x)^2 ogf A005253 17.3577 -(-x+1+x^4)/(-x^2-1+2*x+x^5) ogf A005253 8.37957 -(1-2*x-x^4-2*x^5+x^8+4*x^3+x^2)/(x^4-x+1)/(x^5-x^2+2*x-1) lgdogf A005253 7.47715 2-2*x+2*x^4+(-3+5*x-2*x^2-x^4+2*x^5)*f(x)+(-x^5+x^2+1-2*x)*f(x)^2 ogf A005258 9.05344 HeunG(-123/2+55/2*5^(1/2),-33/2+15/2*5^(1/2),1,1,1,1,-1/2*(-11+5*5^(1/2))*x) ogf A005258 7.90875 {(-4-4*n-n^2)*a(n+1)+(-69-55*n-11*n^2)*a(n+2)+(n^2+6*n+9)*a(n+3),a(0)=1,a(1)=3,a(2)=19} ogf A005259 5.88397 {(-8-12*n-6*n^2-n^3)*a(n+1)+(535+639*n+255*n^2+34*n^3)*a(n+2)+(-n^3-9*n^2-27*n-27)*a(n+3),a(0)=1,a(1)=5,a(2)=73} ogf A005260 4.3477 {(-504-764*n-384*n^2-64*n^3)*a(n+1)+(-190-226*n-90*n^2-12*n^3)*a(n+2)+(n^3+9*n^2+27*n+27)*a(n+3),a(0)=1,a(1)=2,a(2)=18} ogf A005262 19.1949 -(-1-x^2-4*x^3)/(1-3*x+x^2+3*x^3-2*x^4) ogf A005262 10.8493 -(-3-3*x+12*x^4+8*x^5+13*x^3-3*x^2)/(x-1)/(2*x-1)/(x+1)/(4*x^3+x^2+1) lgdogf A005262 20.7944 -(1+4*x^3+x^2)/(2*x-1)/(x+1)/(x-1)^2 ogf A005262 6.18678 -3790-3790*x^2-15160*x^3+(4993-11370*x+4993*x^2+16182*x^3-7580*x^4)*f(x)+(-1203-3609*x^3+3609*x-1203*x^2+2406*x^4)*f(x)^2 ogf A005262 7.96383 {(16+6*n)*a(n+1)+(-3*n-2)*a(n+2)+(-6*n-13)*a(n+3)+(3*n+5)*a(n+4),a(0)=1,a(1)=3,a(2)=9,a(3)=25} ogf A005264 24.3902 -exp(-x)*(exp(x)-1-2*x) revegf A005286 31.6714 (1+2*x+x^3-3*x^2)/(x-1)^4 ogf A005286 18.4136 -(1+2*x-3*x^2+x^3)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A005286 20.8365 -(6+x^3-3*x^2)/(x-1)/(x^3-3*x^2+2*x+1) lgdogf A005286 6.88509 -351-702*x+1053*x^2-351*x^3+(109-1888*x+2832*x^2-1646*x^3+351*x^4)*f(x)+(1452*x^2+242-968*x+242*x^4-968*x^3)*f(x)^2 ogf A005286 8.51382 {(-38-21*n-n^2)*a(n+1)+(-124-60*n-8*n^2)*a(n+2)+(51*n+72+9*n^2)*a(n+3),a(0)=1,a(1)=6,a(2)=15} ogf A005287 26.0681 (-5+5*x-3*x^3+x^2+x^4)/(x-1)^5 ogf A005287 14.219 -(-5+5*x+x^2+x^4-3*x^3)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A005287 16.6392 -(x-2)*(x^3-6*x+10)/(x-1)/(x^4-3*x^3+x^2+5*x-5) lgdogf A005288 15.1244 (3+4*x-3*x^5+13*x^3-16*x^2-x^4+x^6)/(x-1)^6 ogf A005288 8.23229 -(22-12*x-17*x^4+3*x^5+35*x^3-25*x^2)/(x-1)/(x^6-3*x^5-x^4+13*x^3-16*x^2+4*x+3) lgdogf A005288 8.55725 -(3+4*x-16*x^2-3*x^5+x^6-x^4+13*x^3)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A005289 11.6139 (1+x+3*x^3+x^2)/(x^2+x+1)/(x+1)^2/(x-1)^6 ogf A005289 6.10472 -(3*x^2+2*x+1)*(7*x^4+8*x^3+9*x^2+8*x+4)/(x-1)/(x+1)/(x^2+x+1)/(3*x^3+x^2+x+1) lgdogf A005289 6.10472 -(x^2+3*x^5+x^4+x^3)/(-1+3*x-x^2-4*x^7-4*x^3+3*x^9+2*x^4+2*x^5+2*x^6-x^8-x^10) ogf A005303 18.6882 -(-2*x+x^5-4*x^2-x^3)/(1-x^2) ogf_with_Euler_Transform A005303 18.6882 -(-2*x+x^5-x^3-4*x^2)/(1-x^2) ogf_with_Euler_Transform A005303 18.6882 -(-2*x-x^3+x^5-4*x^2)/(1-x^2) ogf_with_Euler_Transform A005304 3.54041 -2*(-x+1+x^4)*(x^4+1)/(3*x^9-1+2*x+x^5+x^3-4*x^4+x^7-x^8-x^6+x^10) ogf A005307 3.81394 -(-x+1-x^2)/(-x^2+1-x+x^3) ogf_with_Euler_Transform A005307 3.81394 -(-x^2-x+1)/(-x^2+1-x+x^3) ogf_with_Euler_Transform A005308 43.2381 -x^3/(-1+x+x^2-x^3) ogf_with_Euler_Transform A005308 14.1642 {-a(n+4)+a(n+3)+a(n+2)-a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf_with_Euler_Transform A005309 1.9312 -(-2*x-x^3-4*x^2)/(1+x^4-2*x^2) ogf_with_Euler_Transform A005313 11.2394 (1-x+x^3-3*x^2)/(x+1)/(1-3*x+x^2)/(x-1)^2 ogf A005313 9.80462 -(-1+x+3*x^2-x^3)/(3*x^2+1-4*x-4*x^4+x^5+3*x^3) ogf A005313 6.22726 -(3-9*x+9*x^4+2*x^6-11*x^5+14*x^3)/(x-1)/(x+1)/(x^2-3*x+1)/(x^3-3*x^2-x+1) lgdogf A005314 25.6978 -(2-2*x+3*x^2)/(-x^2-1+2*x+x^3) lgdogf A005314 41.928 -1/(-x^2-1+2*x+x^3) ogf A005314 34.6362 -x+(1-2*x+x^2-x^3)*f(x) ogf A005314 41.928 -x/(-1+2*x-x^2+x^3) ogf A005314 15.6202 {-a(n+3)+2*a(n+2)-a(n+1)+a(n),a(0)=0,a(1)=1,a(2)=2} ogf A005317 13.9918 -x^2+(-1+6*x-8*x^2)*f(x)+(20*x^2+1-8*x-16*x^3)*f(x)^2 ogf A005317 13.483 1/2*(-4*x+1+(-(4*x-1)*(2*x-1)^2)^(1/2))/(4*x-1)/(2*x-1) ogf A005317 8.33218 {(-24-28*n-8*n^2)*a(n+1)+(18+22*n+6*n^2)*a(n+2)+(-3-4*n-n^2)*a(n+3),a(0)=1,a(1)=2,a(2)=5} ogf A005317 8.33218 {(-24-28*n-8*n^2)*a(n+1)+(18+22*n+6*n^2)*a(n+2)+(-4*n-3-n^2)*a(n+3),a(0)=1,a(1)=2,a(2)=5} ogf A005319 16.327 -(-2-3*x+2*(2*x+1)^(1/2)*(1+x)^(1/2))/x revogf A005319 30.3216 -2*(-3+x)/(x^2+1-6*x) lgdogf A005319 30.3216 4*x+(-1+6*x-x^2)*f(x) ogf A005319 42.4503 4*x/(1-6*x+x^2) ogf A005319 48.9811 4/(1-6*x+x^2) ogf A005319 17.6876 {a(n+2)-6*a(n+1)+a(n),a(0)=0,a(1)=4} ogf A005320 11.9644 -1/2*(-3-4*x+(2*x+1)^(1/2)*(3+2*x)^(1/2)*3^(1/2))/x revogf A005320 29.0565 -2*(-2+x)/(x^2+1-4*x) lgdogf A005320 29.0565 3*x+(-1+4*x-x^2)*f(x) ogf A005320 40.679 3*x/(1-4*x+x^2) ogf A005320 46.9374 3/(1+x^2-4*x) ogf A005320 16.9496 {a(n+2)-4*a(n+1)+a(n),a(0)=0,a(1)=3} ogf A005322 14.2951 -18-27*x+(6-12*x-18*x^2)*f(x)+(-2*x^2-3*x^3+x)*f(x)^2 lgdogf A005322 8.32574 {(-60-27*n-3*n^2)*a(n+1)+(-55-21*n-2*n^2)*a(n+2)+(12*n+27+n^2)*a(n+3),a(0)=1,a(1)=3,a(2)=9} ogf A005323 11.9259 -32-48*x+(8-16*x-24*x^2)*f(x)+(-2*x^2-3*x^3+x)*f(x)^2 lgdogf A005323 6.87034 {(-90-33*n-3*n^2)*a(n+1)+(-78-25*n-2*n^2)*a(n+2)+(14*n+33+n^2)*a(n+3),a(0)=1,a(1)=4,a(2)=14} ogf A005324 12.248 -50-75*x+(10-20*x-30*x^2)*f(x)+(-2*x^2-3*x^3+x)*f(x)^2 lgdogf A005324 7.03611 {(-126-39*n-3*n^2)*a(n+1)+(-105-29*n-2*n^2)*a(n+2)+(16*n+39+n^2)*a(n+3),a(0)=1,a(1)=5,a(2)=20} ogf A005325 13.4188 -6*(-1+2*x+3*x^2+(-(x+1)*(3*x-1))^(1/2))/x/(x+1)/(3*x-1) lgdogf A005325 13.6628 -72-108*x+(12-24*x-36*x^2)*f(x)+(-2*x^2-3*x^3+x)*f(x)^2 lgdogf A005325 7.99417 {(-168-45*n-3*n^2)*a(n+1)+(-136-33*n-2*n^2)*a(n+2)+(18*n+45+n^2)*a(n+3),a(0)=1,a(1)=6,a(2)=27} ogf A005337 27.6314 (15-20*x+6*x^2)/(x-1)^4 ogf A005337 15.5005 -(15-20*x+6*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A005337 4.70757 -3792645+5056860*x-1517058*x^2+(248718-1005872*x+1515408*x^2-1011372*x^3+252843*x^4)*f(x)+(275*x^4+1650*x^2+275-1100*x-1100*x^3)*f(x)^2 ogf A005337 15.888 -4*(10-12*x+3*x^2)/(x-1)/(6*x^2-20*x+15) lgdogf A005337 6.05259 {(-15*n-60)*a(n+4)+(145+35*n)*a(n+3)+(-100-26*n)*a(n+2)+(18+6*n)*a(n+1),a(0)=15,a(1)=40,a(2)=76,a(3)=124} ogf A005338 10.7233 (-8-14*x+55*x^4+7*x^6-42*x^5-3*x^2)/(x-1)/(7*x^6-11*x^5+x^2+3*x+1) lgdogf A005338 12.2024 -(1+3*x+x^2-11*x^5+7*x^6)/(-10*x^2-1+5*x-5*x^4+x^5+10*x^3) ogf A005338 21.4467 -(1+3*x-11*x^5+x^2+7*x^6)/(x-1)^5 ogf A005339 20.9791 (35-56*x-4*x^3+25*x^2+x^6)/(x-1)^6 ogf A005339 10.6461 -(35-56*x+25*x^2+x^6-4*x^3)/(-15*x^2-1+6*x-15*x^4+6*x^5+20*x^3-x^6) ogf A005339 10.9737 -2*(77-115*x+3*x^5-6*x^3+44*x^2)/(x-1)/(x^6-4*x^3+25*x^2-56*x+35) lgdogf A005340 14.3205 (-1-6*x+66*x^5-x^3-6*x^2-74*x^6+21*x^7)/(x-1)^7 ogf A005340 7.73635 -(-1-6*x-6*x^2+66*x^5-74*x^6+21*x^7-x^3)/(-x^7+1-7*x+7*x^6+21*x^2-21*x^5-35*x^3+35*x^4) ogf A005340 7.31589 -(-13-48*x+330*x^4+73*x^6-312*x^5-4*x^3-33*x^2)/(x-1)/(21*x^7-74*x^6+66*x^5-x^3-6*x^2-6*x-1) lgdogf A005357 18.6789 (-2+x^3-11*x^10+9*x^11-3*x^2)/(x-1)/(x^11+x^3+1) lgdogf A005357 44.8293 (1+x^3+x^11)/(x-1)^2 ogf A005357 21.3473 -(-x^3-x^6-x^14-3*x^26+3*x^27)/(1-2*x+x^2) ogf A005358 7.28829 (x^2+1)*(x^8-x^6+x^4-x^2+1)/(x-1)^2 ogf A005358 4.81302 2*(-1+4*x^10-5*x^9)/(x-1)/(x^2+1)/(x^8-x^6+x^4-x^2+1) lgdogf A005359 37.3595 -1+(1-x^2)*f(x) egf A005359 40.0281 -1/(x-1)/(x+1) egf A005359 35.0246 -2*x/(x-1)/(x+1) lgdegf A005359 62.2659 1/(1-x^2) egf A005359 11.6749 {(n^2+5*n+6)*a(n+1)-a(n+3),a(0)=1,a(1)=0,a(2)=2} ogf A005367 18.5462 -(-4+10*x)/(14*x^2+1-7*x-8*x^3) ogf A005367 10.4533 -(-9+56*x+80*x^3-118*x^2)/(x-1)/(4*x-1)/(2*x-1)/(5*x-2) lgdogf A005367 6.18208 -16928+42320*x+(5204-32054*x+59248*x^2-33856*x^3)*f(x)+(-3402*x^2-243+1701*x+1944*x^3)*f(x)^2 ogf A005367 17.9667 2*(-2+5*x)/(x-1)/(2*x-1)/(4*x-1) ogf A005367 10.0866 {a(n+3)-7*a(n+2)+14*a(n+1)-8*a(n),a(0)=4,a(1)=18,a(2)=70} ogf A005369 108.075 x/(1+x^2) ogf_with_Euler_Transform A005369 108.075 x/(x^2+1) ogf_with_Euler_Transform A005369 36.0251 {a(n+2)+a(n),a(0)=0,a(1)=1} ogf_with_Euler_Transform A005373 5.19565 -(-2+8*x+2*x^2+(-(x^2+4*x-1)*(x-3)^2)^(1/2))/(x^2+4*x-1)/(x+1)^2 egf A005373 15.8344 -x*(-2+x)/(2+2*x+x^2) revegf A005373 6.27399 5+(-4+16*x+4*x^2)*f(x)+(8*x^2+6*x^3-1+2*x+x^4)*f(x)^2 egf A005377 19.9948 (x^2+1)*(x^4-x^2+1)/(x-1)^2 ogf A005377 22.4941 -(-x^4-x^10)/(1-2*x+x^2) ogf A005377 12.2695 2*(-1+2*x^6-3*x^5)/(x-1)/(x^2+1)/(x^4-x^2+1) lgdogf A005377 53.9859 2+x^5-x^11 ogf_with_Euler_Transform A005377 5.29273 {2*a(n+2)-a(n+3)-a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=1,a(5)=2,a(6)=3,a(7)=4,a(8)=5,a(9)=6,a(10)=8} ogf A005379 9.00341 -(-x^2-x^8-x^14-x^16-x^22+x^26-x^6-x^21-x^17-x^3-x^13-x^11-x^9-x^5-x^25+x^23-x^19)/(1-x-x^21+x^22) ogf A005380 34.8398 -(2-x)/(-x^2-1+2*x) ogf_with_Euler_Transform A005380 17.8907 {-a(n+2)+2*a(n+1)-a(n),a(0)=2,a(1)=3} ogf_with_Euler_Transform A005386 22.2317 -(-1+x)/(-4*x^2+1-4*x+x^3) ogf A005386 13.1369 -(3+8*x+2*x^3-7*x^2)/(x-1)/(x+1)/(x^2-5*x+1) lgdogf A005386 24.0844 -(x-1)/(x+1)/(x^2-5*x+1) ogf A005386 6.56846 323-323*x+(-5792+6761*x+1292*x^2-323*x^3)*f(x)+(-21876*x^2+5469-21876*x+5469*x^3)*f(x)^2 ogf A005386 10.7042 {-a(n+3)+4*a(n+2)+4*a(n+1)-a(n),a(0)=1,a(1)=3,a(2)=16} ogf A005387 10.1638 {n*a(n)+(n+2-n^2)*a(n+1)+(-3*n-2-n^2)*a(n+2),a(0)=2,a(1)=1} lgdegf A005389 23.2222 -(-1+2*x+x^2)/(10*x^2+1-8*x+x^4) ogf A005389 11.4325 -2*(3-11*x+3*x^4+x^5-2*x^3+14*x^2)/(x^2+2*x-1)/(x^4+10*x^2-8*x+1) lgdogf A005389 8.84656 29-58*x-29*x^2+(326-478*x-645*x^2-29*x^4)*f(x)+(-355+2840*x-3550*x^2-355*x^4)*f(x)^2 ogf A005403 15.0654 -(-1-2*x+x^5+x^3+2*x^4)/(x+1)/(x^2+x-1)/(x^3+x-1) ogf A005403 15.3793 -(1+2*x-2*x^4-x^3-x^5)/(2*x^2-1+x-2*x^5-x^4-x^6) ogf A005403 6.71096 -(3+4*x-13*x^4-3*x^6-10*x^5-10*x^3+x^10+x^2+4*x^9+4*x^7+6*x^8)/(x+1)/(x^2+x-1)/(x^3+x-1)/(x^5+2*x^4+x^3-2*x-1) lgdogf A005404 6.68667 -(-3*x^5+4*x^9+x^11-x^3+x^2-4*x^4-2*x^6+4*x^8+3*x^10+x^7+2*x+1)/(x+1)/(x^3+x-1)/(x^4+x-1)/(x^2+x-1)/(x^2+x+1) ogf A005408 67.0344 (x+1)/(x-1)^2 ogf A005408 45.8656 -(1+x)/(-x^2-1+2*x) ogf A005408 48.4137 -(3+x)/(x-1)/(x+1) lgdogf A005408 25.6308 -1/2*(-1-2*x+(1+8*x)^(1/2))/(-1+x) revogf A005408 41.4975 1+x+(-x^2-1+2*x)*f(x) ogf A005408 290.482 3-x ogf_with_Euler_Transform A005408 23.5526 {-a(n+2)+2*a(n+1)-a(n),a(0)=1,a(1)=3} ogf A005408 37.889 {a(n+2),a(0)=3,a(1)=-1} ogf_with_Euler_Transform A005409 21.1763 (1-2*x+x^3+2*x^2)/(x-1)/(-1+2*x+x^2) ogf A005409 12.4975 -(-1-2*x+x^4+2*x^3+4*x^2)/(x-1)/(x^2+2*x-1)/(x^3+2*x^2-2*x+1) lgdogf A005409 21.7813 -(1-2*x+2*x^2+x^3)/(-x^2-1+3*x-x^3) ogf A005409 9.07554 -27+54*x-54*x^2-27*x^3+(49-125*x+71*x^2+49*x^3)*f(x)+(-22+66*x-22*x^2-22*x^3)*f(x)^2 ogf A005409 12.4975 {-a(n+4)+3*a(n+3)-a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=4,a(3)=11} ogf A005410 1.44518 -1-x+x^3+(3+x-x^2-x^3)*f(x)+(-3+x+2*x^2-x^3)*f(x)^2+(x^3-x-x^2+1)*f(x)^3 ogf A005418 24.1158 -(-1+3*x^2)/(1-2*x-2*x^2+4*x^3) ogf A005418 25.7789 -(-1+3*x^2)/(2*x-1)/(2*x^2-1) ogf A005418 15.5748 -2*(1-x+6*x^4-3*x^2)/(2*x-1)/(3*x^2-1)/(2*x^2-1) lgdogf A005418 10.9939 37-111*x^2+(-35+74*x+68*x^2-148*x^3)*f(x)+(4*x^2-8*x^3-2+4*x)*f(x)^2 ogf A005418 13.8442 {a(n+3)-2*a(n+2)-2*a(n+1)+4*a(n),a(0)=1,a(1)=2,a(2)=3} ogf A005425 45.817 exp(1/2*x*(x+4)) egf A005425 91.6341 x+2-f(x) lgdegf A005425 183.268 x+2] lgdegf A005425 14.0975 {(-n-2)*a(n+1)+a(n+3)-2*a(n+2),a(0)=1,a(1)=2,a(2)=5} ogf A005425 14.0975 {(-n-2)*a(n+1)-2*a(n+2)+a(n+3),a(0)=1,a(1)=2,a(2)=5} ogf A005429 18.3426 -12*(2+9*x+2*x^2)/(4*x-1)/(4*x^2+10*x+1) lgdogf A005429 7.41116 {(n+3)*a(n+4)+(-12+6*n)*a(n+3)+(-144-36*n)*a(n+2)+(-24-16*n)*a(n+1),a(0)=0,a(1)=2,a(2)=48,a(3)=540} ogf A005430 16.7226 -4*x^2+(1-12*x+48*x^2-64*x^3)*f(x)^2 ogf A005430 60.2014 -6/(4*x-1) lgdogf A005430 35.4126 2*x/(1-4*x)^(3/2) ogf A005430 37.6259 2/(-4*x+1)^(3/2) ogf A005430 13.6821 {(n+1)*a(n+2)+(-6-4*n)*a(n+1),a(0)=0,a(1)=2} ogf A005431 5.54518 {(8*n^2+16*n^3)*a(n)+(24+48*n+34*n^2+8*n^3)*a(n+1)+(-5*n-6-n^2)*a(n+2),a(0)=1,a(1)=1} ogf A005442 29.9351 -(2*x+1)/(x^2-1+x) lgdegf A005442 41.4487 -1/(-1+x+x^2) egf A005442 44.9027 -1/(x^2+x-1) egf A005442 12.8293 -4+(9-4*x-4*x^2)*f(x)+(5*x^2-5+5*x)*f(x)^2 egf A005442 8.83332 {(5*n+n^2+6)*a(n+1)+(n+3)*a(n+2)-a(n+3),a(0)=1,a(1)=1,a(2)=4} ogf A005443 27.5848 (x^2+1)/(x^2+x-1)^2 egf A005443 29.1172 -(2*x+1)/(x^2-1+x) lgdegf A005443 40.3162 -x/(-1+x+x^2) egf A005443 16.3784 1/2/x*(-1-x+(2*x+5*x^2+1)^(1/2)) revegf A005443 30.83 x+(-1+x+x^2)*f(x) egf A005443 8.31921 {(-5*n-6-n^2)*a(n+1)+(-n-3)*a(n+2)+a(n+3),a(0)=0,a(1)=1,a(2)=2} ogf A005443 8.31921 {(-6-5*n-n^2)*a(n+1)+(-n-3)*a(n+2)+a(n+3),a(0)=0,a(1)=1,a(2)=2} ogf A005448 27.9137 -(-1-x-x^2)/(3*x^2+1-3*x-x^3) ogf A005448 33.7291 -(x+2)^2/(x-1)/(x^2+x+1) lgdogf A005448 44.9721 -(x^2+x+1)/(x-1)^3 ogf A005448 16.5204 -1/3*(-2*(9*x+1)^(1/3)+(9*x+1)^(2/3)+1-3*x)/(1+x) revogf A005448 14.4553 1+x+x^2+(-2+2*x-4*x^2+x^3)*f(x)+(1-3*x+3*x^2-x^3)*f(x)^2 ogf A005448 161.9 4-x^2 ogf_with_Euler_Transform A005448 26.9833 {a(n+3),a(0)=4,a(1)=0,a(2)=-1} ogf_with_Euler_Transform A005448 15.2736 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=4,a(2)=10} ogf A005449 27.7795 -(2*x+x^2)/(-1+3*x-3*x^2+x^3) ogf A005449 40.2803 -(7+2*x)/(x+2)/(x-1) lgdogf A005449 57.5433 -(x+2)/(x-1)^3 ogf A005449 10.4624 190*x+95*x^2+(-95+123*x-366*x^2+95*x^3)*f(x)+(81-243*x+243*x^2-81*x^3)*f(x)^2 ogf A005449 15.4924 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=2,a(2)=7} ogf A005460 9.60263 -(-1-2*x)/(10*x^2+1-5*x-x^5-10*x^3+5*x^4) egf A005460 24.6067 -(2*x+1)/(x-1)^5 egf A005460 17.8958 -(7+8*x)/(2*x+1)/(x-1) lgdegf A005460 4.578 {(-20-14*n-2*n^2)*a(n+1)+(73+32*n+3*n^2)*a(n+2)+(-3*n-9)*a(n+3),a(0)=1,a(1)=7,a(2)=50} ogf A005461 19.0968 -(6*x^2+8*x+1)/(-1+x)^5/(x^2-2*x+1) egf A005461 30.3813 -(6*x^2+8*x+1)/(x-1)^7 egf A005461 18.0645 -15*(1+4*x+2*x^2)/(x-1)/(6*x^2+8*x+1) lgdegf A005461 13.1056 {(-24-10*n-n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=15} ogf A005462 5.49632 -(31+292*x+144*x^3+478*x^2)/(x-1)/(24*x^3+58*x^2+22*x+1) lgdegf A005462 2.5229 {(-896-772*n-190*n^2-14*n^3)*a(n+1)+(2284+1401*n+268*n^2+15*n^3)*a(n+2)+(-89*n-132-15*n^2)*a(n+3),a(0)=1,a(1)=31,a(2)=602} ogf A005463 2.11124 {(-1024-384*n-32*n^2)*a(n+1)+(4056+1172*n+76*n^2)*a(n+2)+(96-22*n+3*n^2)*a(n+3)+(-3*n-12)*a(n+4),a(0)=1,a(1)=63,a(2)=1932,a(3)=46620} ogf A005475 26.2821 -(11+4*x)/(2*x+3)/(x-1) lgdogf A005475 19.4996 -(3*x+2*x^2)/(-1+3*x-3*x^2+x^3) ogf A005475 37.7805 -(3+2*x)/(x-1)^3 ogf A005475 6.36303 -11172*x-7448*x^2+(3724-5097*x+15222*x^2-3724*x^3)*f(x)+(-2025+6075*x-6075*x^2+2025*x^3)*f(x)^2 ogf A005475 11.4054 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=3,a(2)=11} ogf A005476 19.2632 -(-2*x-3*x^2)/(1-3*x+3*x^2-x^3) ogf A005476 37.3225 -(3*x+2)/(x-1)^3 ogf A005476 24.8817 -3*(2*x+3)/(3*x+2)/(x-1) lgdogf A005476 6.2859 10374*x+15561*x^2+(-5187+9211*x-25086*x^2+5187*x^3)*f(x)+(3175-9525*x+9525*x^2-3175*x^3)*f(x)^2 ogf A005476 11.4839 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=2,a(2)=9} ogf A005488 4.15888 3-x^2+x^3 ogf_with_Euler_Transform A005491 19.6182 (1+x+3*x^3+x^2)/(x-1)^4 ogf A005491 11.0053 -(-1-x-x^2-3*x^3)/(6*x^2+1-4*x+x^4-4*x^3) ogf A005491 10.4934 -(5+5*x+3*x^3+11*x^2)/(x-1)/(3*x^3+x^2+x+1) lgdogf A005491 4.10198 -109-109*x-109*x^2-327*x^3+(-14-559*x+531*x^2-805*x^3+109*x^4)*f(x)+(123-492*x+738*x^2-492*x^3+123*x^4)*f(x)^2 ogf A005491 4.38076 {(-762-503*n-61*n^2)*a(n+1)+(180+748*n+134*n^2)*a(n+2)+(-209*n+30-73*n^2)*a(n+3),a(0)=1,a(1)=5,a(2)=15} ogf A005492 12.2207 -(-4+5*x-17*x^2-7*x^4-x^3)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A005492 11.6196 -(15+14*x+7*x^4+30*x^3+54*x^2)/(x-1)/(7*x^4+x^3+17*x^2-5*x+4) lgdogf A005492 21.4787 -(4-5*x+x^3+17*x^2+7*x^4)/(x-1)^5 ogf A005493 83.8744 2+exp(x) lgdegf A005493 19.7351 {-a(n)+(n+1)*a(n+1),a(0)=3,a(1)=1} lgdegf A005494 80.7534 3+exp(x) lgdegf A005494 19.0008 {-a(n)+(n+1)*a(n+1),a(0)=4,a(1)=1} lgdegf A005513 9.4427 (1-x-x^5+x^3+x^2+2*x^4+2*x^6+x^8)/(x^2-x+1)/(x^2+x+1)^2/(x+1)^3/(x-1)^6 ogf A005517 22.0094 (-1-2*x-3*x^2+x^4)/(-1+5*x^3) ogf A005517 10.2947 (2+6*x+15*x^4+5*x^6+16*x^3+15*x^2)/(x^4-3*x^2-2*x-1)/(5*x^3-1) lgdogf A005517 22.0094 -(-1-2*x-3*x^2+x^4)/(1-5*x^3) ogf A005517 9.67078 2+4*x+6*x^2-2*x^4+(-3-2*x-3*x^2+10*x^3+x^4)*f(x)+(-5*x^3+1)*f(x)^2 ogf A005517 12.2744 {a(n+5)-5*a(n+2),a(0)=1,a(1)=2,a(2)=3,a(3)=5,a(4)=9} ogf A005522 12.2181 -(-3+9*x+4*x^4-x^2-10*x^3)/(7*x^2+1-5*x-3*x^4-x^3+x^5) ogf A005522 12.2181 -(-3+9*x-10*x^3-x^2+4*x^4)/(x-1)/(1-3*x+x^2)/(x^2+x-1) ogf A005522 5.99796 -(6-40*x+35*x^4+31*x^6-98*x^3-14*x^5-20*x^7+97*x^2+4*x^8)/(x-1)/(x^2-3*x+1)/(x^2+x-1)/(4*x^4-10*x^3-x^2+9*x-3) lgdogf A005554 18.1311 1+2*x+x^2+(-1+x^2)*f(x)+x^2*f(x)^2 ogf A005554 5.98502 {(3*n+3*n^2)*a(n)+(20*n+15+5*n^2)*a(n+1)+(20+9*n+n^2)*a(n+2)+(-8*n-15-n^2)*a(n+3),a(0)=1,a(1)=2,a(2)=3} ogf A005557 19.4406 (42-120*x-70*x^3+135*x^2+14*x^4)/(x-1)^6 ogf A005557 10.6524 -(42-120*x+14*x^4+135*x^2-70*x^3)/(-15*x^2-1+6*x-x^6-15*x^4+20*x^3+6*x^5) ogf A005557 10.5084 -2*(66-165*x+14*x^4-77*x^3+165*x^2)/(x-1)/(14*x^4-70*x^3+135*x^2-120*x+42) lgdogf A005557 12.7479 {(36+15*n+n^2)*a(n+1)+(-10*n-16-n^2)*a(n+2),a(0)=42,a(1)=132} ogf A005563 63.5142 (x-3)/(x-1)^3 ogf A005563 28.4719 -(3*x-x^2)/(-1+3*x-3*x^2+x^3) ogf A005563 41.2842 -2*(x-4)/(x-1)/(x-3) lgdogf A005563 12.1424 27*x-9*x^2+(-9+51*x-35*x^2+9*x^3)*f(x)+(-24*x^2-8+24*x+8*x^3)*f(x)^2 ogf A005563 15.8785 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=3,a(2)=8} ogf A005564 42.9569 (6-4*x+x^2)/(x-1)^4 ogf A005564 22.0589 -(6-4*x+x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A005564 24.7327 -2*(10-5*x+x^2)/(x-1)/(x^2-4*x+6) lgdogf A005564 5.8718 -783858+522572*x-130643*x^2+(-73315-386600*x+749865*x^2-522572*x^3+130643*x^4)*f(x)+(33993-135972*x+33993*x^4+203958*x^2-135972*x^3)*f(x)^2 ogf A005564 8.50188 {(6*n+24)*a(n+4)+(-50-10*n)*a(n+3)+(20+5*n)*a(n+2)+(-n-3)*a(n+1),a(0)=6,a(1)=20,a(2)=45,a(3)=84} ogf A005565 25.3929 (-20+25*x+3*x^3-14*x^2)/(x-1)^5 ogf A005565 14.0568 -(-20+25*x-14*x^2+3*x^3)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A005565 14.3124 -3*(-25+24*x+2*x^3-11*x^2)/(x-1)/(3*x^3-14*x^2+25*x-20) lgdogf A005565 9.3712 {(21+10*n+n^2)*a(n+1)+(29+7*n)*a(n+2)+(-9*n-18-n^2)*a(n+3),a(0)=20,a(1)=75,a(2)=189} ogf A005566 7.52365 {(80*n+16*n^2+96)*a(n+1)+(8*n+28)*a(n+2)+(-n^2-9*n-20)*a(n+3),a(0)=1,a(1)=2,a(2)=6} ogf A005567 9.35333 -(-10+20*x-8*x^2)/(33*x^2+1-9*x+66*x^4-36*x^5+8*x^6-63*x^3) ogf A005567 9.8544 -(-35+112*x+32*x^3-112*x^2)/(x-1)/(2*x-1)/(4*x^2-10*x+5) lgdogf A005567 16.2308 2*(5-10*x+4*x^2)/(x-1)^3/(2*x-1)^3 ogf A005567 5.8707 {(-80-26*n-2*n^2)*a(n+1)+(82+33*n+3*n^2)*a(n+2)+(-9*n-18-n^2)*a(n+3),a(0)=10,a(1)=70,a(2)=308} ogf A005568 12.7763 {(16*n^2+64*n+60)*a(n+1)+(-7*n-12-n^2)*a(n+2),a(0)=1,a(1)=2} ogf A005569 3.8435 {(-420-428*n-144*n^2-16*n^3)*a(n+1)+(-4902-3499*n-820*n^2-63*n^3)*a(n+2)+(324*n+504+64*n^2+4*n^3)*a(n+3),a(0)=4,a(1)=34,a(2)=308} ogf A005570 41.8867 (-17+x)/(x-1)^3 ogf A005570 24.1654 -(-17+x)/(3*x^2+1-3*x-x^3) ogf A005570 28.5591 -2*(x-25)/(x-1)/(x-17) lgdogf A005570 4.98651 -415865985+24462705*x+(48846961-74822483*x+73388115*x^2-24462705*x^3)*f(x)+(-4303104*x^2-1434368+4303104*x+1434368*x^3)*f(x)^2 ogf A005570 11.4236 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=17,a(1)=50,a(2)=99} ogf A005571 14.0441 -(76-16*x+4*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A005571 16.9355 -2*(36-5*x+x^2)/(x-1)/(x^2-4*x+19) lgdogf A005571 26.1731 4*(19-4*x+x^2)/(x-1)^4 ogf A005571 5.59037 {(-19*n-76)*a(n+4)+(141+23*n)*a(n+3)+(-20-5*n)*a(n+2)+(n+3)*a(n+1),a(0)=76,a(1)=288,a(2)=700,a(3)=1376} ogf A005572 9.5224 -((6*x-1)^(1/2)*(2*x-1)^(1/2)+1)/(6*x-1)^(1/2)/(2*x-1)^(1/2)/x lgdogf A005572 22.7073 1+(-1+4*x)*f(x)+x^2*f(x)^2 ogf A005572 13.4179 1/2*(-4*x+1+(6*x-1)^(1/2)*(2*x-1)^(1/2))/x^2 ogf A005572 45.4145 x/(1+4*x+x^2) revogf A005572 8.31533 {(-12*n-24)*a(n+1)+(8*n+28)*a(n+2)+(-n-5)*a(n+3),a(0)=1,a(1)=4,a(2)=17} ogf A005573 11.3865 -1/2*((6*x-1)^(1/2)-(2*x-1)^(1/2))/(6*x-1)^(1/2)/x ogf A005573 5.52743 -1/2*(6*x-1+12*x*(6*x-1)^(1/2)*(2*x-1)^(1/2)-(6*x-1)^(1/2)*(2*x-1)^(1/2))/(6*x-1)^(3/2)/(2*x-1)^(1/2)/x lgdogf A005573 17.2523 1+(-1+6*x)*f(x)+(-x+6*x^2)*f(x)^2 ogf A005573 27.1107 x*(1+x)/(1+6*x+6*x^2) revogf A005573 8.01867 {(-12*n-24)*a(n+1)+(8*n+26)*a(n+2)+(-n-4)*a(n+3),a(0)=1,a(1)=5,a(2)=26} ogf A005578 22.6108 -(-1+x+x^2)/(-x^2+1-2*x+2*x^3) ogf A005578 13.0447 -(1+2*x^4+4*x^3-5*x^2)/(x-1)/(2*x-1)/(x+1)/(x^2+x-1) lgdogf A005578 22.6108 -(x^2+x-1)/(x-1)/(2*x-1)/(x+1) ogf A005578 10.767 3-3*x-3*x^2+(-2+5*x+2*x^2-6*x^3)*f(x)+(-1+2*x+x^2-2*x^3)*f(x)^2 ogf A005578 13.0447 {a(n+3)-2*a(n+2)-a(n+1)+2*a(n),a(0)=1,a(1)=1,a(2)=2} ogf A005581 21.3162 -(-2*x^2+x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A005581 37.5571 -(-7+3*x)/(x-1)/(x-2) lgdogf A005581 56.3357 -(x-2)/(x-1)^4 ogf A005581 20.2231 2*x^2-x^3+(-1+4*x-6*x^2+4*x^3-x^4)*f(x) ogf A005581 11.7716 {(-2*n-2)*a(n+3)+(7+3*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=2} ogf A005581 11.7716 {(-2-2*n)*a(n+3)+(7+3*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=2} ogf A005582 59.9884 (x-2)/(x-1)^5 ogf A005582 37.1357 -(-9+4*x)/(x-1)/(x-2) lgdogf A005582 18.136 -(2*x-x^2)/(-1+5*x-5*x^4-10*x^2+10*x^3+x^5) ogf A005582 11.4684 {(-4-2*n)*a(n+3)+(12+3*n)*a(n+2)+(-4-n)*a(n+1),a(0)=0,a(1)=2,a(2)=9} ogf A005583 34.4679 -(-11+5*x)/(x-1)/(x-2) lgdogf A005583 16.4846 -(2-x)/(-15*x^2-1+6*x+6*x^5-x^6+20*x^3-15*x^4) ogf A005583 54.1638 -(x-2)/(x-1)^6 ogf A005583 10.9898 {(2*n+6)*a(n+3)+(-17-3*n)*a(n+2)+(6+n)*a(n+1),a(0)=2,a(1)=11,a(2)=36} ogf A005584 46.047 (x-2)/(x-1)^7 ogf A005584 27.2096 -(-13+6*x)/(x-1)/(x-2) lgdogf A005584 11.2946 -(-2+x)/(21*x^2+1-7*x-21*x^5+7*x^6-35*x^3+35*x^4-x^7) ogf A005584 8.67552 {(2*n+6)*a(n+3)+(-19-3*n)*a(n+2)+(7+n)*a(n+1),a(0)=2,a(1)=13,a(2)=49} ogf A005585 51.8104 (x+1)/(x-1)^6 ogf A005585 14.6421 -(1+x)/(-15*x^2-1+6*x+6*x^5-x^6+20*x^3-15*x^4) ogf A005585 33.6767 -(5*x+7)/(x-1)/(x+1) lgdogf A005585 224.512 7-x ogf_with_Euler_Transform A005585 11.4158 {(-n-3)*a(n+3)+7*a(n+2)+(6+n)*a(n+1),a(0)=1,a(1)=7,a(2)=27} ogf A005585 29.2841 {a(n+2),a(0)=7,a(1)=-1} ogf_with_Euler_Transform A005586 37.7041 (5-6*x+2*x^2)/(x-1)^4 ogf A005586 18.4136 -(-5*x+6*x^2-2*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A005586 21.994 -2*(7-7*x+2*x^2)/(x-1)/(2*x^2-6*x+5) lgdogf A005586 8.16273 {(15+5*n)*a(n+4)+(-36-11*n)*a(n+3)+(22+8*n)*a(n+2)+(-4-2*n)*a(n+1),a(0)=0,a(1)=5,a(2)=14,a(3)=28} ogf A005587 25.2272 (-14+28*x+5*x^3-20*x^2)/(x-1)^5 ogf A005587 14.4823 -(-42+72*x+10*x^3-45*x^2)/(x-1)/(5*x^3-20*x^2+28*x-14) lgdogf A005587 13.034 -(14*x-5*x^4-28*x^2+20*x^3)/(-1+5*x-10*x^2+10*x^3-5*x^4+x^5) ogf A005587 13.72 {(18+11*n+n^2)*a(n+1)+(-6-7*n-n^2)*a(n+2),a(0)=0,a(1)=14} ogf A005592 21.0508 -(-2+2*x-x^2)/(4*x^2+1-4*x-x^3) ogf A005592 21.7525 -(2-2*x+x^2)/(1-3*x+x^2)/(x-1) ogf A005592 11.6531 -(6-14*x+x^4-4*x^3+10*x^2)/(x-1)/(x^2-3*x+1)/(x^2-2*x+2) lgdogf A005592 7.76877 62-62*x+31*x^2+(809-716*x+296*x^2+31*x^3)*f(x)+(-420+1680*x-1680*x^2+420*x^3)*f(x)^2 ogf A005592 12.3128 {a(n+3)-4*a(n+2)+4*a(n+1)-a(n),a(0)=2,a(1)=6,a(2)=17} ogf A005593 13.2635 -(-2+5*x+x^4-x^2-2*x^3)/(7*x^2+1-5*x-3*x^4-x^3+x^5) ogf A005593 13.2635 -(-2+5*x-2*x^3-x^2+x^4)/(x-1)/(1-3*x+x^2)/(x^2+x-1) ogf A005593 6.56735 -(5-26*x-25*x^4-4*x^7+12*x^5+4*x^6-10*x^3+42*x^2+x^8)/(x-1)/(x^2-3*x+1)/(x^2+x-1)/(x^4-2*x^3-x^2+5*x-2) lgdogf A005609 19.4399 -(-64+112*x)/(28*x^2+1-29*x) ogf A005609 12.6586 -(109-224*x+196*x^2)/(x-1)/(28*x-1)/(7*x-4) lgdogf A005609 10.8864 -1/56*(-64-29*x+(4096+3264*x+729*x^2)^(1/2))/(4+x) revogf A005609 20.1599 -16*(-4+7*x)/(28*x-1)/(x-1) ogf A005609 6.71998 136192-238336*x+(185840-267232*x-59584*x^2)*f(x)+(-2937+85173*x-82236*x^2)*f(x)^2 ogf A005609 12.3709 {a(n+2)-29*a(n+1)+28*a(n),a(0)=64,a(1)=1744} ogf A005610 23.0921 -(-7+12*x)/(6*x-1)/(x-1) lgdogf A005610 14.5845 -1/12*(-7*x-2+(25*x^2+28*x+4)^(1/2))/x revogf A005610 32.6006 -2/(-1+7*x-6*x^2) ogf A005610 10.2631 -48+(-50-168*x+144*x^2)*f(x)+(37-259*x+222*x^2)*f(x)^2 ogf A005610 36.9473 2/(6*x-1)/(x-1) ogf A005610 13.8553 {-a(n+2)+7*a(n+1)-6*a(n),a(0)=2,a(1)=14} ogf A005616 13.8935 -x+ln(x+2)+ln(1+x)-ln(2) revegf A005618 23.0921 -(-4+12*x)/(6*x^2+1-7*x) ogf A005618 13.1955 -1/12*(-4-7*x+(16+8*x+25*x^2)^(1/2))/(x+2) revogf A005618 14.5845 -2*(2-6*x+9*x^2)/(x-1)/(6*x-1)/(3*x-1) lgdogf A005618 22.1684 -4*(-1+3*x)/(6*x-1)/(x-1) ogf A005618 8.65953 -528+1584*x+(520-2088*x+792*x^2)*f(x)+(-582*x^2-97+679*x)*f(x)^2 ogf A005618 14.2105 {a(n+2)-7*a(n+1)+6*a(n),a(0)=4,a(1)=16} ogf A005619 3.69532 -(16-288*x+320*x^2)/(-112*x^2-1+33*x+80*x^3) ogf A005619 3.96571 -16*(1-18*x+20*x^2)/(x-1)/(80*x^2-32*x+1) ogf A005665 31.2875 (2*x+1)/(x-1)/(2*x^2+2*x-1) ogf A005665 18.7725 -(-5+8*x^3+6*x^2)/(x-1)/(2*x+1)/(2*x^2+2*x-1) lgdogf A005665 33.7905 -(x+2*x^2)/(-1+3*x-2*x^3) ogf A005665 31.2875 -x-2*x^2+(1-3*x+2*x^3)*f(x) ogf A005665 18.3644 {-a(n+3)+3*a(n+2)-2*a(n),a(0)=0,a(1)=1,a(2)=5} ogf A005666 18.1858 (x+2)/(x-1)/(2*x^2+2*x-1) ogf A005666 18.1858 -(-2*x-x^2)/(1-3*x+2*x^3) ogf A005666 10.3329 -(-7+4*x^3+12*x^2)/(x-1)/(x+2)/(2*x^2+2*x-1) lgdogf A005666 7.70587 -8*x-4*x^2+(4-26*x-7*x^2+8*x^3)*f(x)+(7-21*x+14*x^3)*f(x)^2 ogf A005666 10.1032 {a(n+3)-3*a(n+2)+2*a(n),a(0)=0,a(1)=2,a(2)=7} ogf A005667 35.7446 (-1+3*x)/(x^2-1+6*x) ogf A005667 20.4255 -(-3-2*x+3*x^2)/(3*x-1)/(x^2+6*x-1) lgdogf A005667 35.7446 -(1-3*x)/(x^2-1+6*x) ogf A005667 11.1702 -289+867*x+(659-2844*x-289*x^2)*f(x)+(370*x^2-370+2220*x)*f(x)^2 ogf A005667 19.8581 1/2/(-3+x)*(-1-6*x+(40*x^2+1)^(1/2)) revogf A005667 19.3214 {-a(n+2)+6*a(n+1)+a(n),a(0)=1,a(1)=3} ogf A005668 39.3613 -1/(x^2-1+6*x) ogf A005668 27.5529 -2*(3+x)/(x^2+6*x-1) lgdogf A005668 29.0031 -x+(1-6*x-x^2)*f(x) ogf A005668 39.3613 -x/(x^2-1+6*x) ogf A005668 15.3072 1/2/x*(-1-6*x+(1+12*x+40*x^2)^(1/2)) revogf A005668 14.8935 {-a(n+2)+6*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A005672 12.2569 -(-1-6*x+8*x^3+6*x^2)/(2*x^2-1)/(x^2+x-1) lgdogf A005672 7.61413 -x^3+(1-x-3*x^2+4*x^3+2*x^4)*f(x)+(6*x^2-2+2*x-4*x^4-4*x^3)*f(x)^2 ogf A005672 17.3287 -x^3/(-1+x+3*x^2-2*x^3-2*x^4) ogf A005672 23.9301 1/(2*x^2-1)/(x^2+x-1) ogf A005673 10.0873 -(2+4*x+10*x^4-15*x^2)/(x-1)/(2*x^2-1)/(x^2+x-1) lgdogf A005673 17.2926 -1/(x-1)/(2*x^2-1)/(x^2+x-1) ogf A005673 11.5284 -x^4*f(x)+(1-2*x-2*x^2+5*x^3-2*x^5)*f(x)^2 ogf A005673 16.6963 x^4/(1-2*x-2*x^2+5*x^3-2*x^5) ogf A005674 8.62802 -(3+2*x+20*x^4+8*x^3-24*x^2)/(2*x-1)/(2*x^2-1)/(x^2+x-1) lgdogf A005674 16.1056 -1/(2*x-1)/(2*x^2-1)/(x^2+x-1) ogf A005674 12.3889 -x^4+(1-3*x-x^2+8*x^3-2*x^4-4*x^5)*f(x) ogf A005674 13.8048 -x^4/(-1+3*x+x^2-8*x^3+2*x^4+4*x^5) ogf A005676 11.3179 (1-3*x+3*x^2-x^3)*f(x)^2+(-6*x^2-1+4*x-x^4+x^5+4*x^3)*f(x)^3 ogf A005676 18.8631 (x-1)^3/(-6*x^2-1+4*x-x^4+x^5+4*x^3) ogf A005676 10.1354 -(-1+4*x-6*x^4+4*x^3-6*x^2+2*x^5)/(x-1)/(x^5-x^4+4*x^3-6*x^2+4*x-1) lgdogf A005676 14.7624 -(3*x+x^3-1-3*x^2)/(6*x^2+1-4*x+x^4-x^5-4*x^3) ogf A005682 17.3631 -2*(-1+2*x^3+3*x^5)/(x^3+x^2-1)/(x^3-x^2+2*x-1) lgdogf A005682 48.004 1/(1-2*x+x^4+x^6) ogf A005682 27.2023 1/(x^3+x^2-1)/(-x^2-1+2*x+x^3) ogf A005683 21.7272 -(-1+x^2+x^5+x^3+x^4)/(1-2*x+x^4+x^6) ogf A005683 16.0781 -(-1+x^5+x^3+x^2+x^4)/(x^3+x^2-1)/(-x^2-1+2*x+x^3) ogf A005683 7.80493 -(2-2*x+x^4+x^6-4*x^3-x^2+4*x^5+4*x^7+x^10+2*x^9+2*x^8)/(x^3+x^2-1)/(x^3-x^2+2*x-1)/(x^5+x^4+x^3+x^2-1) lgdogf A005684 6.33011 -2*(-1+5*x^4-6*x^3+3*x^2+4*x^7)/(x^2-x+1)/(x^2+x-1)/(x^4+x^2-1) lgdogf A005684 12.0847 1/(x^2-x+1)/(x^2+x-1)/(x^4+x^2-1) ogf A005685 9.81954 -(-1+x^5-x^3+x^2+2*x^4+x^6+x^7)/(x^2-x+1)/(x^2+x-1)/(x^4+x^2-1) ogf A005685 10.1415 -(1-x^6-x^2-x^7-x^5+x^3-2*x^4)/(-2*x^3-1+2*x-2*x^5+3*x^4-x^8) ogf A005686 24.1618 (-x-x^2)*f(x)^2+(1-x^2-x^5)*f(x)^3 ogf A005686 39.1192 -(-x-x^2)/(1-x^2-x^5) ogf A005686 19.5596 -(1+2*x+5*x^4+x^2+4*x^5)/(x+1)/(x^5+x^2-1) lgdogf A005686 43.237 -(x+1)/(-1+x^2+x^5) ogf A005687 11.6107 -2*(-1-5*x^4-2*x^3+3*x^2+6*x^5+5*x^9)/(x^5+x^2-1)/(x^5-x^2+2*x-1) lgdogf A005687 24.3449 1/(-1+x^2+x^5)/(-x^2-1+2*x+x^5) ogf A005687 20.9637 1/(1-2*x+2*x^3-x^4-2*x^5+2*x^6+x^10) ogf A005688 9.94392 -(-1+2*x^5+x^9-x^3+x^2+x^6+x^8+x^7)/(-1+x^2+x^5)/(-x^2-1+2*x+x^5) ogf A005688 9.23364 -(-1+x^6+x^9+x^2+x^7+2*x^5-x^3+x^8)/(1-2*x+2*x^3-x^4-2*x^5+2*x^6+x^10) ogf A005689 13.3816 -(1+x^2+x^5+x^3+x^4)/(x^6-1+2*x-x^2) ogf A005689 12.0434 -(1+x^5+x^3+x^2+x^4)/(x^3+x-1)/(x^3-x+1) ogf A005689 6.25634 -(2+3*x^6+x^2+4*x^7+x^10+2*x^9+3*x^8)/(x^3+x-1)/(x^5+x^4+x^3+x^2+1)/(x^3-x+1) lgdogf A005690 11.0987 -1/(-1+2*x-2*x^3+x^4+2*x^6-2*x^7-x^12) ogf A005690 6.02498 -2*(-1+7*x^6-2*x^3+3*x^2-6*x^5+6*x^11)/(x^3+x-1)/(x^3-x+1)/(x^6+x^2-1) lgdogf A005690 12.7803 1/(x^3+x-1)/(x^3-x+1)/(x^6+x^2-1) ogf A005691 9.70226 -(-1+x^9+x^11-x^3+x^2+2*x^6+x^8+x^10+x^7)/(x^3+x-1)/(x^3-x+1)/(x^6+x^2-1) ogf A005700 8.88733 {(16*n^2+64*n+60)*a(n+1)+(-n^2-9*n-20)*a(n+2),a(0)=1,a(1)=1} ogf A005701 45.7236 (x-3)/(x-1)^5 ogf A005701 15.2412 -(-3+x)/(10*x^2+1-5*x-x^5-10*x^3+5*x^4) ogf A005701 25.8438 -2*(-7+2*x)/(x-1)/(x-3) lgdogf A005701 8.61459 {(3*n+9)*a(n+3)+(-22-4*n)*a(n+2)+(5+n)*a(n+1),a(0)=3,a(1)=14,a(2)=40} ogf A005705 13.2682 -1/(-1+2*x-x^2+x^4-2*x^5+x^6+x^16-2*x^17+x^18-x^20+2*x^21-x^22) ogf A005705 7.26866 -2*(1+x+x^2+3*x^3+x^4+x^5+x^6+3*x^7+x^8+x^9+x^10+3*x^11+x^12+x^13+x^14+11*x^15)/(x-1)/(x+1)/(1+x^2)/(1+x^4)/(1+x^8) lgdogf A005705 19.4394 1/(x^4+1)/(x^8+1)/(x+1)^2/(x^2+1)^2/(x-1)^4 ogf A005705 83.5896 2+x^3+x^15 ogf_with_Euler_Transform A005706 83.5245 2+x^4+x^24 ogf_with_Euler_Transform A005708 42.1692 -(1+6*x^5)/(-1+x+x^6) lgdogf A005708 68.1195 -1/(-1+x+x^6) ogf A005709 32.8025 -(1+7*x^6)/(-1+x+x^7) lgdogf A005709 52.9886 -1/(-1+x+x^7) ogf A005710 39.2951 -(1+8*x^7)/(-1+x+x^8) lgdogf A005710 63.4767 -1/(-1+x+x^8) ogf A005711 21.2519 -(1+8*x^7+2*x^8+x^16)/(x^9+x-1)/(1+x^8) lgdogf A005711 43.6224 -(1+x^8)/(-1+x+x^9) ogf A005711 43.6224 -(x^8+1)/(-1+x+x^9) ogf A005712 44.7005 (x^2-x-1)/(x-1)^5 ogf A005712 17.6723 -(-1-x+x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A005712 24.5132 -(-6-2*x+3*x^2)/(x-1)/(x^2-x-1) lgdogf A005712 9.15553 {(-4-n)*a(n+4)+6*a(n+3)+(2*n+6)*a(n+2)+(-4-n)*a(n+1),a(0)=1,a(1)=6,a(2)=19,a(3)=45} ogf A005714 10.8123 -(-1-3*x+4*x^2-x^3)/(21*x^2+1-7*x-x^7+35*x^4-21*x^5-35*x^3+7*x^6) ogf A005714 27.0307 -(1+3*x+x^3-4*x^2)/(x-1)^7 ogf A005714 14.9532 -(10+10*x+4*x^3-17*x^2)/(x-1)/(x^3-4*x^2+3*x+1) lgdogf A005714 7.39788 {(90+33*n+3*n^2)*a(n+1)+(-114-61*n-7*n^2)*a(n+2)+(22*n+30+4*n^2)*a(n+3),a(0)=1,a(1)=10,a(2)=45} ogf A005715 31.5826 (x-2)*(x^2-2)/(x-1)^8 ogf A005715 15.7913 -(30-18*x+5*x^3-9*x^2)/(x-1)/(x-2)/(x^2-2) lgdogf A005715 9.21158 -(4-2*x-2*x^2+x^3)/(-28*x^2-1+8*x+8*x^7-70*x^4+56*x^5+56*x^3-x^8-28*x^6) ogf A005715 6.83746 {(126+39*n+3*n^2)*a(n+1)+(-161-72*n-7*n^2)*a(n+2)+(26*n+42+4*n^2)*a(n+3),a(0)=4,a(1)=30,a(2)=126} ogf A005716 7.85703 -(-1-6*x+9*x^2-3*x^3)/(-x^9+1-9*x-36*x^7+36*x^2-126*x^5-84*x^3+126*x^4+84*x^6+9*x^8) ogf A005716 23.5711 -(1+6*x+3*x^3-9*x^2)/(x-1)^9 ogf A005716 13.1998 -3*(5+10*x+6*x^3-18*x^2)/(x-1)/(3*x^3-9*x^2+6*x+1) lgdogf A005716 6.80403 {(-126-39*n-3*n^2)*a(n+1)+(140+69*n+7*n^2)*a(n+2)+(-22*n-30-4*n^2)*a(n+3),a(0)=1,a(1)=15,a(2)=90} ogf A005717 16.4705 1+(-1+2*x+3*x^2)*f(x)+(3*x^4-x^2+2*x^3)*f(x)^2 ogf A005717 8.41825 {(-36-21*n-3*n^2)*a(n+1)+(-28-15*n-2*n^2)*a(n+2)+(8*n+15+n^2)*a(n+3),a(0)=1,a(1)=2,a(2)=6} ogf A005718 26.378 -(12-10*x+3*x^2)/(x-1)/(x^2-3*x+3) lgdogf A005718 44.8427 -(3-3*x+x^2)/(x-1)^5 ogf A005718 9.44056 {(3*n+12)*a(n+4)+(-30-6*n)*a(n+3)+(18+4*n)*a(n+2)+(-4-n)*a(n+1),a(0)=3,a(1)=12,a(2)=31,a(3)=65} ogf A005719 37.7616 (2+x^3-2*x^2)/(x-1)^6 ogf A005719 19.3413 -(12-4*x+3*x^3-5*x^2)/(x-1)/(x^3-2*x^2+2) lgdogf A005719 7.69898 {(1076+417*n+37*n^2)*a(n+1)+(-444-496*n-68*n^2)*a(n+2)+(109*n+48+31*n^2)*a(n+3),a(0)=2,a(1)=12,a(2)=40} ogf A005720 11.9807 -(-1-3*x+5*x^2-2*x^3)/(21*x^2+1-7*x-x^7+35*x^4-21*x^5-35*x^3+7*x^6) ogf A005720 28.6682 -(1+3*x+2*x^3-5*x^2)/(x-1)^7 ogf A005720 16.7231 -(10+8*x+8*x^3-19*x^2)/(x-1)/(2*x^3-5*x^2+3*x+1) lgdogf A005720 7.57272 {(-2070-659*n-49*n^2)*a(n+1)+(1170+855*n+95*n^2)*a(n+2)+(-214*n-228-46*n^2)*a(n+3),a(0)=1,a(1)=10,a(2)=44} ogf A005725 14.6615 1+(3-2*x)*f(x)+(-4+16*x^3+11*x+8*x^2)*f(x)^3 ogf A005727 78.3919 ln(x+1)+1 lgdegf A005727 19.0683 {-n*a(n)+(-1-n)*a(n+1),a(0)=1,a(1)=1} lgdegf A005732 46.5407 (-1-x+x^3)/(x-1)^7 ogf A005732 14.6971 -(-1-x+x^3)/(21*x^2+1-7*x+35*x^4-21*x^5-35*x^3-x^7+7*x^6) ogf A005732 22.6414 -(-8-6*x+4*x^3+3*x^2)/(x-1)/(x^3-x-1) lgdogf A005732 8.81825 {(-250-75*n-5*n^2)*a(n+1)+(-38+71*n+9*n^2)*a(n+2)+(-2*n+30-4*n^2)*a(n+3),a(0)=1,a(1)=8,a(2)=35} ogf A005744 19.4504 -(-4-6*x+3*x^3-x^2)/(x-1)/(x+1)/(x^2-x-1) lgdogf A005744 18.5457 -(-x-x^2+x^3)/(1-3*x+2*x^2+x^5+2*x^3-3*x^4) ogf A005744 33.2278 -(x^2-x-1)/(x+1)/(x-1)^4 ogf A005744 5.2122 {(546+2633*n+817*n^2)*a(n+1)+(-46920-19711*n-2381*n^2)*a(n+2)+(-23838-7325*n-817*n^2)*a(n+3)+(23628+15019*n+2381*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=4,a(3)=9} ogf A005745 9.98308 -(-1-2*x-2*x^5+x^3-3*x^2+2*x^4-x^6+x^8-x^7)/(x^2+x+1)^2/(x+1)^2/(x-1)^8 ogf A005745 5.32931 -(1+x^6+2*x^5-x^8+x^7+2*x+3*x^2-x^3-2*x^4)/(-4*x^2-1+4*x+3*x^8+2*x^4+4*x^9-2*x^3-2*x^11+3*x^6+4*x^13+4*x^5+2*x^10-4*x^12-12*x^7-x^14) ogf A005758 74.4679 12/(1-x) ogf_with_Euler_Transform A005758 28.3687 {a(n+1)-a(n),a(0)=12} ogf_with_Euler_Transform A005770 9.08391 (1-3*x+x^3+2*x^2)/(4*x-1)/(2*x-1)/(1-3*x+x^2)^2 ogf A005770 4.54196 -(-9+79*x-259*x^4+24*x^6+28*x^5+391*x^3-258*x^2)/(4*x-1)/(2*x-1)/(x^2-3*x+1)/(x^3+2*x^2-3*x+1) lgdogf A005770 6.671 -(1-3*x+2*x^2+x^3)/(-55*x^2-1+12*x-125*x^4+54*x^5+120*x^3-8*x^6) ogf A005773 14.4395 -1/2*(1-3*x+(-(x+1)*(-1+3*x))^(1/2))/(-1+3*x) ogf A005773 20.9606 -x+(-1+3*x)*f(x)+(1-3*x)*f(x)^2 ogf A005773 12.0329 {-3*a(n)*n+(-2*n-4)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=1} ogf A005774 20.0912 -x+(1-3*x)*f(x)+(x^2-3*x^3)*f(x)^2 ogf A005774 7.59001 {(-18-15*n-3*n^2)*a(n+1)+(-24-14*n-2*n^2)*a(n+2)+(10+7*n+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=3} ogf A005775 8.9263 -20+36*x+81*x^2+(5-28*x+54*x^3+21*x^2)*f(x)+(-5*x^2+x+3*x^3+9*x^4)*f(x)^2 lgdogf A005775 7.08283 {(-60-27*n-3*n^2)*a(n+1)+(-60-22*n-2*n^2)*a(n+2)+(11*n+24+n^2)*a(n+3),a(0)=1,a(1)=4,a(2)=14} ogf A005783 8.1556 -(7*x^5+3*x^9-3*x^11-x^2+3*x^4-6*x^6+x^12+x^8+x^10-3*x^7+3)/(x^2+x+1)^2/(x+1)^2/(x-1)^7 ogf A005789 10.4955 {(27*n^2+135*n+168)*a(n+1)+(-n^2-9*n-20)*a(n+2),a(0)=1,a(1)=5} ogf A005790 8.08672 {(-4784*n-256*n^3-1920*n^2-3960)*a(n+1)+(n^3+15*n^2+74*n+120)*a(n+2),a(0)=1,a(1)=14} ogf A005798 31.3105 -(8-8*x)/(x^2+1+x+x^3) ogf_with_Euler_Transform A005802 8.20638 {(9*n^2+36*n+36)*a(n+1)+(-10*n^2-62*n-93)*a(n+2)+(n^2+10*n+25)*a(n+3),a(0)=1,a(1)=1,a(2)=2} ogf A005803 22.0242 -(-4*x+1+5*x^2)/(2*x-1)/(x-1)^2 ogf A005803 20.0809 -(4*x-1-5*x^2)/(5*x^2+1-4*x-2*x^3) ogf A005803 18.4527 -1+4*x-5*x^2+(5*x^2+1-4*x-2*x^3)*f(x) ogf A005803 16.256 -2*x^2*(5*x-3)/(x-1)/(2*x-1)/(5*x^2-4*x+1) lgdogf A005803 12.6435 {a(n+3)-4*a(n+2)+5*a(n+1)-2*a(n),a(0)=1,a(1)=0,a(2)=0} ogf A005807 13.8266 -1-1/2*x-1/2*x^2+1/2*((x^2+4)*(1+x)^2)^(1/2) revogf A005807 23.3988 2+x+(-1+x)*f(x)+x^2*f(x)^2 ogf A005807 6.33717 {(-14*n-12-4*n^2)*a(n+1)+(168+109*n+17*n^2)*a(n+2)+(-32*n-60-4*n^2)*a(n+3),a(0)=2,a(1)=3,a(2)=7} ogf A005809 25.5938 -1-3*f(x)+(4-27*x)*f(x)^3 ogf A005809 19.3893 hypergeom([1/3,2/3],[1/2],27/4*x) ogf A005809 10.1563 {(60+81*n+27*n^2)*a(n+1)+(-14*n-12-4*n^2)*a(n+2),a(0)=1,a(1)=3} ogf A005810 6.8523 {(840+1712*n+1152*n^2+256*n^3)*a(n+1)+(-222*n-120-135*n^2-27*n^3)*a(n+2),a(0)=1,a(1)=4} ogf A005815 4.6824 15*x+240*x^2-1-x^5+(3-45*x+2*x^5-720*x^2)*f(x)+(-x^5-3+45*x+720*x^2)*f(x)^2+(-15*x-240*x^2+1)*f(x)^3 ogf A005817 7.95808 {(-80*n-16*n^2-96)*a(n+1)+(-8*n-36)*a(n+2)+(n^2+13*n+42)*a(n+3),a(0)=1,a(1)=1,a(2)=2} ogf A005818 29.2556 -(-7+3*x)/(x-1)/(2*x-3)/(x+1) lgdogf A005818 33.9365 -(3+x-2*x^2)/(-x^2-1+2*x) ogf A005818 36.8875 -(x+1)*(-3+2*x)/(x-1)^2 ogf A005818 14.3799 -111-37*x+74*x^2+(25-78*x+45*x^2)*f(x)+(4-8*x+4*x^2)*f(x)^2 ogf A005818 18.4437 {-a(n+3)+2*a(n+2)-a(n+1),a(0)=3,a(1)=7,a(2)=9} ogf A005822 4.62976 -(x-1)*(x+1)*(x^4+x^3-x^2+x+1)/(-4*x^6+1+x^8-4*x^2-x^4) ogf A005824 16.0909 (x+x^2-2*x^3)*f(x)+(-1-2*x^4+5*x^2)*f(x)^2 ogf A005824 10.9003 -(1+6*x-6*x^4+8*x^5-8*x^3+5*x^2)/(x-1)/(2*x+1)/(2*x^4-5*x^2+1) lgdogf A005824 22.5273 -(2*x+1)*(x-1)/(1-5*x^2+2*x^4) ogf A005824 21.8006 -(x-2*x^3+x^2)/(-1-2*x^4+5*x^2) ogf A005825 19.0592 (-1-2*x+4*x^2)/(2*x^2-1)/(1-5*x+2*x^2) ogf A005825 9.65664 -(-7+8*x-64*x^4+32*x^5+24*x^3+10*x^2)/(2*x^2-1)/(4*x^2-2*x-1)/(2*x^2-5*x+1) lgdogf A005825 7.31564 -512*x-1024*x^2+2048*x^3+(512-2577*x-34*x^2+5188*x^3-2048*x^4)*f(x)+(17+170*x^3-85*x-68*x^4)*f(x)^2 ogf A005826 14.6824 (-1+4*x^3-6*x^2)/(2*x^2-1)/(1-5*x+2*x^2) ogf A005827 18.3638 -(1-2*x+2*x^3-2*x^2)/(2*x^2-1)/(1-5*x+2*x^2) ogf A005827 9.50599 -(3-4*x-4*x^4+8*x^6-16*x^5+36*x^3-14*x^2)/(2*x^2-1)/(2*x^2-5*x+1)/(2*x^3-2*x^2-2*x+1) lgdogf A005827 6.56918 -1979+3958*x+3958*x^2-3958*x^3+(-9714+13491*x+23386*x^2-3596*x^3-7916*x^4)*f(x)+(11693+116930*x^3-58465*x-46772*x^4)*f(x)^2 ogf A005827 6.56918 -1979+3958*x-3958*x^3+3958*x^2+(-9714+13491*x-7916*x^4-3596*x^3+23386*x^2)*f(x)+(11693+116930*x^3-58465*x-46772*x^4)*f(x)^2 ogf A005833 10.4366 -(-1+x+x^5+x^3-x^4)/(x-1)/(x^2+x+1)/(x^4-x^3+2*x-1) ogf A005833 12.6731 -(-x^6+x+x^5-x^4-x^2)/(-1+2*x+x^6-x^4-x^7) ogf A005833 4.51075 -(1-8*x^4-11*x^6+2*x^11+14*x^5-4*x^10+6*x^7+4*x^3-3*x^2+6*x^9-4*x^8)/(x-1)/(x^2+x+1)/(x^4-x^3+2*x-1)/(x^5-x^4+x^3+x-1) lgdogf A005834 9.04829 -(-2+2*x+2*x^5+2*x^3-x^2-2*x^4)/(x-1)/(x^2+x+1)/(x^4-x^3+2*x-1) ogf A005834 10.5563 -(2*x^6-2*x-2*x^5+2*x^4-x^3+2*x^2)/(1-2*x+x^7-x^6+x^4) ogf A005843 96.6054 -2/(x-1) lgdogf A005843 36.8021 2*x+(-x^2+2*x-1)*f(x) ogf A005843 33.6019 2*x/(1+(2*x+1)^(1/2))^2 revogf A005843 51.5229 2*x/(1-2*x+x^2) ogf A005843 85.8715 2/(x-1)^2 ogf A005843 21.4679 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=2} ogf A005855 2.29922 (x-1)*(x+1)*(x^5+x^3+x^2+x+1)/(x^4+x^2-1) ogf A005856 1.23706 -(x^2+x-1)*(x^4+x^3+x^2+x-1)/(x-1)/(3*x^6+x^5+x^4+x^3-x^2-2*x+1) ogf A005856 1.2567 -1+(3-3*x)*f(x)+(-3+6*x-3*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 ogf A005859 1.61898 -1+(3-3*x)*f(x)+(-3+6*x-3*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 ogf A005860 1.17105 1+x-2*x^2-2*x^3-2*x^4-x^5+(-2+5*x^2-x+x^4)*f(x)+(1-x^4-3*x^2+2*x^3)*f(x)^2 ogf A005861 1.88441 -(x^5+x^3-1)*(x^5-x^4+x^2-x+1)/(x-1)/(x^7-x^6+x^5+x^3-x^2+x-1) ogf A005861 1.8545 -1+(3-3*x)*f(x)+(-3+6*x-3*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 ogf A005862 2.79722 -(-1+x^5+x^4)/(x-1)/(x^2+1)/(-1+x^2+x^5) ogf A005862 1.77601 -1+(3-3*x)*f(x)+(-3+6*x-3*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 ogf A005863 1.7434 -1+(3-3*x)*f(x)+(-3+6*x-3*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 ogf A005864 1.3717 (-17+17*x-28*x^5-26*x^3+43*x^2+36*x^4-168*x^6+236*x^8+88*x^7)/(2*x-1)/(88*x^6-28*x^4-26*x^2+17) ogf A005866 1.61898 -1+(3-3*x)*f(x)+(-3+6*x-3*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 ogf A005868 14.8273 -(1+x^10-x^5)/(x^5-1+x^2+x^4-x^9-x^6-x^7+x^11) ogf A005868 8.74431 -(x^2-x+1)*(x^8+x^7-x^5-x^4-x^3+x+1)/(x^2+1)/(x^4+x^3+x^2+x+1)/(x+1)^2/(x-1)^3 ogf A005869 28.5483 {-a(n+1)-a(n),a(0)=3} ogf_with_Euler_Transform A005875 30.6691 -(6-3*x+3*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A005875 17.7881 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=6,a(1)=-9,a(2)=6} ogf_with_Euler_Transform A005876 17.4188 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=4,a(1)=-5,a(2)=4} ogf_with_Euler_Transform A005877 12.0956 {a(n+3)+a(n+2)+a(n+1)+a(n),a(0)=2,a(1)=-1,a(2)=2} ogf_with_Euler_Transform A005878 41.4313 {-a(n+1)-a(n),a(0)=3} ogf_with_Euler_Transform A005879 39.3248 {-a(n+1)-a(n),a(0)=4} ogf_with_Euler_Transform A005880 27.2101 {-a(n+1)-a(n),a(0)=4} ogf_with_Euler_Transform A005881 27.0188 {-a(n+3)-a(n),a(0)=1,a(1)=-1,a(2)=2} ogf_with_Euler_Transform A005882 28.0979 {a(n+2)+a(n+1)+a(n),a(0)=1,a(1)=1} ogf_with_Euler_Transform A005883 45.5293 {-a(n+1)-a(n),a(0)=2} ogf_with_Euler_Transform A005884 18.1511 {a(n+3)+a(n+2)+a(n+1)+a(n),a(0)=2,a(1)=-1,a(2)=2} ogf_with_Euler_Transform A005886 27.5704 {-a(n+1)-a(n),a(0)=3} ogf_with_Euler_Transform A005891 25.5849 -(-1-3*x-x^2)/(3*x^2+1-3*x-x^3) ogf A005891 26.4377 -(6+8*x+x^2)/(x-1)/(x^2+3*x+1) lgdogf A005891 39.6565 -(x^2+3*x+1)/(x-1)^3 ogf A005891 10.718 -13-39*x-13*x^2+(19-21*x+45*x^2-13*x^3)*f(x)+(-6+18*x-18*x^2+6*x^3)*f(x)^2 ogf A005891 14.9647 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=6,a(2)=16} ogf A005892 22.1995 -(-1-9*x-4*x^2)/(3*x^2+1-3*x-x^3) ogf A005892 33.2992 -(1+9*x+4*x^2)/(x-1)^3 ogf A005892 5.72331 -1684069-15156621*x-6736276*x^2+(1985713-2337411*x+6258783*x^2-1684069*x^3)*f(x)+(-904932*x^2-301644+904932*x+301644*x^3)*f(x)^2 ogf A005892 20.3495 -2*(x+6)*(2*x+1)/(x-1)/(4*x^2+9*x+1) lgdogf A005892 13.5664 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=12,a(2)=37} ogf A005893 23.5676 -(-1-x-x^2-x^3)/(3*x^2+1-3*x-x^3) ogf A005893 35.3514 -(x+1)*(x^2+1)/(x-1)^3 ogf A005893 24.3041 -4*(1+x+x^2)/(x-1)/(x+1)/(x^2+1) lgdogf A005893 155.546 4-x^3 ogf_with_Euler_Transform A005893 9.72163 7+7*x+7*x^2+7*x^3+(31+59*x+17*x^2+45*x^3)*f(x)+(-38+114*x-114*x^2+38*x^3)*f(x)^2 ogf A005893 21.0197 {a(n+4),a(0)=4,a(1)=0,a(2)=0,a(3)=-1} ogf_with_Euler_Transform A005893 12.3449 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=4,a(2)=10,a(3)=20} ogf A005894 33.1465 (x+1)*(x^2+1)/(x-1)^4 ogf A005894 17.8481 -(1+x+x^2+x^3)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A005894 18.3178 -(5+5*x+5*x^2+x^3)/(x-1)/(x+1)/(x^2+1) lgdogf A005894 7.64919 -9-9*x-9*x^2-9*x^3+(-7-52*x+38*x^2-52*x^3+9*x^4)*f(x)+(96*x^2+16-64*x+16*x^4-64*x^3)*f(x)^2 ogf A005894 139.215 5-x^3 ogf_with_Euler_Transform A005894 6.75802 {(-12-8*n-n^2)*a(n+1)+(-3+10*n+2*n^2)*a(n+2)+(-2*n+3-n^2)*a(n+3),a(0)=1,a(1)=5,a(2)=15,a(3)=35,a(4)=69} ogf A005894 18.8129 {a(n+4),a(0)=5,a(1)=0,a(2)=0,a(3)=-1} ogf_with_Euler_Transform A005897 19.9242 -(-1-5*x-x^3-5*x^2)/(3*x^2+1-3*x-x^3) ogf A005897 28.3537 -(x+1)*(x^2+4*x+1)/(x-1)^3 ogf A005897 7.5224 -301-1505*x-1505*x^2-301*x^3+(431-253*x+1553*x^2-171*x^3)*f(x)+(-390*x^2-130+390*x+130*x^3)*f(x)^2 ogf A005897 18.4299 -4*(x+2)*(2*x+1)/(x-1)/(x+1)/(x^2+4*x+1) lgdogf A005897 11.7015 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=8,a(2)=26,a(3)=56} ogf A005898 28.6642 (x+1)*(x^2+4*x+1)/(x-1)^4 ogf A005898 16.6652 -(-1-5*x-x^3-5*x^2)/(6*x^2+1-4*x+x^4-4*x^3) ogf A005898 16.2865 -(9+25*x+x^3+13*x^2)/(x-1)/(x+1)/(x^2+4*x+1) lgdogf A005898 5.55508 -4631-23155*x-23155*x^2-4631*x^3+(3335-25004*x+21306*x^2-19820*x^3+4631*x^4)*f(x)+(1296-5184*x+7776*x^2-5184*x^3+1296*x^4)*f(x)^2 ogf A005898 8.53101 {(2*n+n^2)*a(n+1)+(-39-10*n-2*n^2)*a(n+2)+(8*n+15+n^2)*a(n+3),a(0)=1,a(1)=9,a(2)=35} ogf A005899 21.9563 -(1+3*x+x^3+3*x^2)/(-3*x^2-1+3*x+x^3) ogf A005899 50.7739 -(x+1)^3/(x-1)^3 ogf A005899 14.2523 -1-3*x-3*x^2-x^3+(2+6*x^2)*f(x)+(-1+3*x-3*x^2+x^3)*f(x)^2 ogf A005899 58.0273 -6/(x-1)/(x+1) lgdogf A005899 162.476 6-3*x ogf_with_Euler_Transform A005899 35.3209 {a(n+2),a(0)=6,a(1)=-3} ogf_with_Euler_Transform A005899 12.8949 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=6,a(2)=18,a(3)=38} ogf A005900 49.2667 (x+1)^2/(x-1)^4 ogf A005900 18.9487 -(x+x^3+2*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A005900 36.95 -2*(3+x)/(x-1)/(x+1) lgdogf A005900 6.59822 251*x+502*x^2+251*x^3+(-251+1284*x-946*x^2+1284*x^3-251*x^4)*f(x)+(-1680*x^2-280+1120*x-280*x^4+1120*x^3)*f(x)^2 ogf A005900 147.8 6-2*x ogf_with_Euler_Transform A005900 12.7414 {(n+2)*a(n+3)-6*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=6} ogf A005901 19.8726 -(-1-9*x-x^3-9*x^2)/(3*x^2+1-3*x-x^3) ogf A005901 28.2803 -(x+1)*(x^2+8*x+1)/(x-1)^3 ogf A005901 18.8535 -12*(1+3*x+x^2)/(x-1)/(x+1)/(x^2+8*x+1) lgdogf A005901 7.65924 -371-3339*x-3339*x^2-371*x^3+(445-447*x+1779*x^2-297*x^3)*f(x)+(-74+222*x-222*x^2+74*x^3)*f(x)^2 ogf A005901 11.4889 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=12,a(2)=42,a(3)=92} ogf A005902 27.9515 (x+1)*(x^2+8*x+1)/(x-1)^4 ogf A005902 16.2508 -(1+9*x+x^3+9*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A005902 15.5286 -(13+45*x+x^3+21*x^2)/(x-1)/(x+1)/(x^2+8*x+1) lgdogf A005902 8.03203 {(-4-4*n-n^2)*a(n+1)+(25+10*n+2*n^2)*a(n+2)+(-6*n-9-n^2)*a(n+3),a(0)=1,a(1)=13,a(2)=55} ogf A005903 20.6627 -(-1-29*x-x^3-29*x^2)/(3*x^2+1-3*x-x^3) ogf A005903 29.8461 -(x+1)*(x^2+28*x+1)/(x-1)^3 ogf A005903 7.00735 -12733-369257*x-369257*x^2-12733*x^3+(13415-18421*x+57977*x^2-12051*x^3)*f(x)+(-2046*x^2-682+2046*x+682*x^3)*f(x)^2 ogf A005903 19.1868 -4*(8+29*x+8*x^2)/(x-1)/(x+1)/(x^2+28*x+1) lgdogf A005903 12.2098 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=32,a(2)=122,a(3)=272} ogf A005904 29.0816 (x+1)*(x^2+28*x+1)/(x-1)^4 ogf A005904 16.8027 -(1+29*x+x^3+29*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A005904 16.0877 -(33+145*x+x^3+61*x^2)/(x-1)/(x+1)/(x^2+28*x+1) lgdogf A005904 7.48636 {(-72-62*n-13*n^2)*a(n+1)+(255+130*n+26*n^2)*a(n+2)+(-68*n-87-13*n^2)*a(n+3),a(0)=1,a(1)=33,a(2)=155} ogf A005905 20.9277 -(-1-13*x-x^3-13*x^2)/(3*x^2+1-3*x-x^3) ogf A005905 30.2289 -(x+1)*(x^2+12*x+1)/(x-1)^3 ogf A005905 7.69982 -2429-31577*x-31577*x^2-2429*x^3+(2743-3205*x+11369*x^2-2115*x^3)*f(x)+(-942*x^2-314+942*x+314*x^3)*f(x)^2 ogf A005905 19.4329 -4*(4+13*x+4*x^2)/(x-1)/(x+1)/(x^2+12*x+1) lgdogf A005905 12.5566 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=16,a(2)=58,a(3)=128} ogf A005906 30.6936 (1+12*x+10*x^2)/(x-1)^4 ogf A005906 17.2184 -(1+12*x+10*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A005906 18.1014 -4*(4+14*x+5*x^2)/(x-1)/(10*x^2+12*x+1) lgdogf A005906 7.20361 {(n+4)*a(n+4)+(17+11*n)*a(n+3)+(-60-2*n)*a(n+2)+(-30-10*n)*a(n+1),a(0)=1,a(1)=16,a(2)=68,a(3)=180} ogf A005907 12.9894 -(-1-x+x^4-x^5+2*x^2+x^6)/(-x^6+1-2*x+x^4+x^7) ogf A005907 10.4827 -(-1-x-x^5+2*x^2+x^4+x^6)/(x-1)/(x^2+x+1)/(x^4-x^3+2*x-1) ogf A005907 4.49259 -(3-2*x^11-14*x^7-4*x^5-8*x^3+4*x^2-4*x^9+11*x^8-4*x+8*x^6+x^12+8*x^4+4*x^10)/(x-1)/(1+x+x^2)/(x^4-x^3+2*x-1)/(x^6-x^5+x^4+2*x^2-x-1) lgdogf A005908 14.1585 -(-1+x+x^3+x^2)/(x-1)/(x^4+2*x^3+2*x^2+x-1) ogf A005908 8.22723 -(1-x^4+4*x^6+2*x^7+6*x^5-2*x^2)/(x-1)/(x^3+x^2+x-1)/(x^4+2*x^3+2*x^2+x-1) lgdogf A005908 16.9115 -(x^3-x+x^4+x^2)/(1-2*x+x^4-x^2+x^5) ogf A005908 7.33512 2*x-2*x^2-2*x^3-2*x^4+(-2+5*x+x^2-x^3-3*x^4-2*x^5)*f(x)+(-1-x^5+2*x-x^4+x^2)*f(x)^2 ogf A005909 13.979 -(-2*x+2*x^4+x^3+x^2)/(1-2*x+x^4-x^2+x^5) ogf A005909 12.7364 -(-2+x+2*x^3+x^2)/(x-1)/(x^4+2*x^3+2*x^2+x-1) ogf A005909 6.98949 -(3+2*x-5*x^4+5*x^6+4*x^7+6*x^5-5*x^2)/(x-1)/(2*x^3+x^2+x-2)/(x^4+2*x^3+2*x^2+x-1) lgdogf A005910 22.4676 (1+34*x+6*x^3+55*x^2)/(x-1)^4 ogf A005910 13.863 -(1+34*x+6*x^3+55*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A005910 12.0659 -2*(19+106*x+3*x^3+64*x^2)/(x-1)/(6*x^3+55*x^2+34*x+1) lgdogf A005910 4.62099 {(-2441922-2230943*n-504991*n^2)*a(n+1)+(5208012+2662540*n+738974*n^2)*a(n+2)+(-1244621*n-1628016-233983*n^2)*a(n+3),a(0)=1,a(1)=38,a(2)=201} ogf A005911 20.4307 -(-1-45*x-x^3-45*x^2)/(3*x^2+1-3*x-x^3) ogf A005911 29.511 -(x+1)*(x^2+44*x+1)/(x-1)^3 ogf A005911 18.5302 -12*(4+15*x+4*x^2)/(x-1)/(x+1)/(x^2+44*x+1) lgdogf A005911 7.7359 -1481-66645*x-66645*x^2-1481*x^3+(1531-2193*x+6693*x^2-1431*x^3)*f(x)+(-150*x^2-50+150*x+50*x^3)*f(x)^2 ogf A005911 12.0727 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=48,a(2)=186,a(3)=416} ogf A005912 27.4325 (1+52*x+8*x^3+93*x^2)/(x-1)^4 ogf A005912 16.9264 -(1+52*x+8*x^3+93*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A005912 14.4644 -2*(28+171*x+4*x^3+105*x^2)/(x-1)/(8*x^3+93*x^2+52*x+1) lgdogf A005912 5.37528 {(-22325406-19748505*n-4292901*n^2)*a(n+1)+(26548176+16172888*n+5420332*n^2)*a(n+2)+(-5920793*n-7615500-1127431*n^2)*a(n+3),a(0)=1,a(1)=56,a(2)=311} ogf A005913 11.2328 -(-1-x+x^3+2*x^2+x^4)/(x-1)/(x^4+2*x^3+2*x^2+x-1) ogf A005913 13.7601 -(1+x-x^4-x^3-2*x^2)/(x^2-1+2*x-x^4-x^5) ogf A005913 5.85538 -(3-2*x-x^4+7*x^6+2*x^7+2*x^5-4*x^3+2*x^2+x^8)/(x-1)/(x^4+2*x^3+2*x^2+x-1)/(x^4+x^3+2*x^2-x-1) lgdogf A005914 20.6384 -(-1-11*x-x^3-11*x^2)/(3*x^2+1-3*x-x^3) ogf A005914 29.811 -(x+1)*(x^2+10*x+1)/(x-1)^3 ogf A005914 19.1642 -2*(7+22*x+7*x^2)/(x-1)/(x+1)/(x^2+10*x+1) lgdogf A005914 8.38434 -427-4697*x-4697*x^2-427*x^3+(494-544*x+2018*x^2-360*x^3)*f(x)+(-201*x^2-67+201*x+67*x^3)*f(x)^2 ogf A005914 12.383 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=14,a(2)=50,a(3)=110} ogf A005915 32.8265 (1+10*x+7*x^2)/(x-1)^4 ogf A005915 18.0546 -(1+10*x+7*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A005915 19.0048 -2*(7+22*x+7*x^2)/(x-1)/(7*x^2+10*x+1) lgdogf A005915 5.51285 -49393-493930*x-345751*x^2+(43045-261052*x+251922*x^2-197572*x^3+49393*x^4)*f(x)+(6348-25392*x+6348*x^4+38088*x^2-25392*x^3)*f(x)^2 ogf A005915 7.52275 {(n+4)*a(n+4)+(13+9*n)*a(n+3)+(-50-3*n)*a(n+2)+(-21-7*n)*a(n+1),a(0)=1,a(1)=14,a(2)=57,a(3)=148} ogf A005916 7.98599 (1-x+x^5+x^11-x^13+x^14)/(x^2+1)/(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/(x+1)^2/(x-1)^4 ogf A005917 27.2899 (x+1)*(x^2+10*x+1)/(x-1)^4 ogf A005917 15.7675 -(1+11*x+x^3+11*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A005917 15.4247 -(15+55*x+x^3+25*x^2)/(x-1)/(x+1)/(x^2+10*x+1) lgdogf A005917 5.76859 -1991-21901*x-21901*x^2-1991*x^3+(1757-10538*x+9372*x^2-8198*x^3+1991*x^4)*f(x)+(1404*x^2+234-936*x+234*x^4-936*x^3)*f(x)^2 ogf A005917 7.46881 {(-18-17*n-4*n^2)*a(n+1)+(93+40*n+8*n^2)*a(n+2)+(-23*n-33-4*n^2)*a(n+3),a(0)=1,a(1)=15,a(2)=65} ogf A005918 22.1809 -(-1-2*x-x^3-2*x^2)/(3*x^2+1-3*x-x^3) ogf A005918 22.7971 -(5+8*x+5*x^2)/(x-1)/(x+1)/(x^2+x+1) lgdogf A005918 34.1956 -(x^2+x+1)*(x+1)/(x-1)^3 ogf A005918 8.82467 -91-182*x-182*x^2-91*x^3+(335+215*x+761*x^2+153*x^3)*f(x)+(-732*x^2-244+732*x+244*x^3)*f(x)^2 ogf A005918 117.242 5-x-x^2 ogf_with_Euler_Transform A005918 25.6467 {-a(n+3),a(0)=5,a(1)=-1,a(2)=-1} ogf_with_Euler_Transform A005918 13.0269 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=5,a(2)=14,a(3)=29} ogf A005919 19.6985 -(-1-6*x-x^3-6*x^2)/(3*x^2+1-3*x-x^3) ogf A005919 28.0325 -(x+1)*(x^2+5*x+1)/(x-1)^3 ogf A005919 7.59214 -203-1218*x-1218*x^2-203*x^3+(271-201*x+1017*x^2-135*x^3)*f(x)+(-204*x^2-68+204*x+68*x^3)*f(x)^2 ogf A005919 18.2211 -3*(3+8*x+3*x^2)/(x-1)/(x+1)/(x^2+5*x+1) lgdogf A005919 11.569 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=9,a(2)=30,a(3)=65} ogf A005920 36.1862 (1+5*x+3*x^2)/(x-1)^4 ogf A005920 19.4849 -(1+5*x+3*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A005920 21.1086 -3*(x+3)*(2*x+1)/(x-1)/(3*x^2+5*x+1) lgdogf A005920 8.25988 {(n+4)*a(n+4)+(3+4*n)*a(n+3)+(-25-2*n)*a(n+2)+(-9-3*n)*a(n+1),a(0)=1,a(1)=9,a(2)=33,a(3)=82} ogf A005921 25.2954 -(1+2*x+x^2)/(x^2-1+x) egf A005921 30.9166 -(x+1)^2/(x^2+x-1) egf A005921 25.2954 -(x+3)/(x+1)/(x^2+x-1) lgdegf A005921 10.3055 -2-4*x-2*x^2+(-5-16*x-9*x^2)*f(x)+(7-7*x-7*x^2)*f(x)^2 egf A005921 12.6477 {-a(n+3)+a(n+2)+a(n+1),a(0)=1,a(1)=3,a(2)=5} egf A005922 11.0798 -(-1-4*x+x^4+2*x^3-2*x^2)/(-x^2+1-2*x+x^4+2*x^3) egf A005922 15.642 -(x+1)*(x^3+x^2-3*x-1)/(x^2+x-1)^2 egf A005922 10.428 2*(3+6*x+x^3+3*x^2)/(x+1)/(x^2+x-1)/(x^3+x^2-3*x-1) lgdegf A005922 6.732 {(6+5*n+n^2)*a(n)+(3+4*n+n^2)*a(n+1)+(-2-3*n-n^2)*a(n+2),a(0)=1,a(1)=6,a(2)=15} egf A005928 43.5572 -(-3-3*x-2*x^2)/(-1+x^3) ogf_with_Euler_Transform A005928 45.451 -(-3-3*x-2*x^2)/(x^3-1) ogf_with_Euler_Transform A005928 27.5098 {-a(n+3)+a(n),a(0)=-3,a(1)=-3,a(2)=-2} ogf_with_Euler_Transform A005943 6.85013 -1+(3-6*x)*f(x)+(-3+12*x-12*x^2)*f(x)^2+(-6*x+12*x^2-8*x^3+1)*f(x)^3 ogf A005945 32.0059 (1+11*x+6*x^2)/(x-1)^4 ogf A005945 16.765 -(-x-11*x^2-6*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A005945 18.5297 -3*(5+15*x+4*x^2)/(x-1)/(6*x^2+11*x+1) lgdogf A005945 7.49074 {(n+3)*a(n+4)+(5+10*n)*a(n+3)+(-50-5*n)*a(n+2)+(-12-6*n)*a(n+1),a(0)=0,a(1)=1,a(2)=15,a(3)=60} ogf A005968 19.5279 (-1+2*x+x^2)/(x-1)/(x^2+4*x-1)/(x^2-x-1) ogf A005968 9.52578 -(-2-4*x-2*x^4+3*x^6+12*x^5-44*x^3+29*x^2)/(x-1)/(x^2+2*x-1)/(x^2+4*x-1)/(x^2-x-1) lgdogf A005969 12.2402 (x+1)*(x^2-5*x+1)/(x^2+3*x+1)/(x^2-7*x+1)/(x-1)^2 ogf A005969 10.1656 -(-1+4*x+4*x^2-x^3)/(-10*x^2+1-6*x-10*x^4-6*x^5+30*x^3+x^6) ogf A005969 5.9977 -(2+14*x+199*x^4-25*x^6+17*x^5+3*x^7+179*x^3-89*x^2)/(x-1)/(x+1)/(x^2+3*x+1)/(x^2-7*x+1)/(x^2-5*x+1) lgdogf A005970 16.2905 (-1-7*x+4*x^2)/(x-1)/(x+1)/(1-3*x+x^2) ogf A005970 8.36539 -(-10+8*x-33*x^4+8*x^5+38*x^3-3*x^2)/(x-1)/(x+1)/(x^2-3*x+1)/(4*x^2-7*x-1) lgdogf A005970 18.7588 -(1+7*x-4*x^2)/(-1+3*x-3*x^3+x^4) ogf A005970 4.83624 54933+384531*x-219732*x^2+(-195923-822131*x+563960*x^2-164799*x^3+54933*x^4)*f(x)+(140990-422970*x+422970*x^3-140990*x^4)*f(x)^2 ogf A005971 11.9314 (-1-24*x+8*x^3+23*x^2)/(x-1)/(x^2+4*x-1)/(x^2-x-1) ogf A005971 5.68163 -(-28+40*x-380*x^4+85*x^6-4*x^5+16*x^7+360*x^3-113*x^2)/(x-1)/(x^2+4*x-1)/(x^2-x-1)/(8*x^3+23*x^2-24*x-1) lgdogf A005971 11.4725 -(1+24*x-23*x^2-8*x^3)/(3*x^2-1+4*x+2*x^4+x^5-9*x^3) ogf A005972 8.88081 (1+76*x-79*x^3-164*x^2+16*x^4)/(x^2+3*x+1)/(x^2-7*x+1)/(x-1)^2 ogf A005972 7.64737 -(-1-76*x+164*x^2+79*x^3-16*x^4)/(-10*x^2+1-6*x-10*x^4-6*x^5+30*x^3+x^6) ogf A005985 12.5937 -(1+2*x+4*x^3-4*x^2)/(x-1)/(2*x+1)/(x+1)/(2*x-1)^2 ogf A005985 11.2444 -(x+2*x^2-4*x^3+4*x^4)/(-1+2*x+5*x^2-10*x^3-4*x^4+8*x^5) ogf A005985 6.69878 -2*(-2-5*x+14*x^4+16*x^6-20*x^5+16*x^3-10*x^2)/(x-1)/(2*x+1)/(2*x-1)/(x+1)/(4*x^3-4*x^2+2*x+1) lgdogf A005986 30.9161 -(-2+x^2)/(1-x-x^2+x^3) ogf_with_Euler_Transform A005986 14.814 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=2,a(1)=2,a(2)=3} ogf_with_Euler_Transform A005987 24.3757 -(-1+x^4-x^3)/(-x^4+1-x^2+x^6) ogf_with_Euler_Transform A005987 24.3757 -(-1-x^3+x^4)/(-x^4+1-x^2+x^6) ogf_with_Euler_Transform A005990 38.57 -(3*x+1)/(x-1)^5 egf A005990 77.14 -4/(x-1) lgdegf A005990 8.01455 9*x+(-9+50*x-54*x^2+36*x^3-9*x^4)*f(x)+(-14+56*x-84*x^2+56*x^3-14*x^4)*f(x)^2 egf A005990 24.6848 x/(1-4*x+6*x^2-4*x^3+x^4) egf A005990 12.8567 {(-8-6*n-n^2)*a(n+1)+(n+1)*a(n+2),a(0)=0,a(1)=1} ogf A005993 31.6118 (x^2+1)/(x+1)^2/(x-1)^4 ogf A005993 17.7335 -(1+x^2)/(-x^6-1+2*x+x^2-4*x^3+x^4+2*x^5) ogf A005993 18.1768 -2*(1+4*x+x^2+2*x^3)/(x-1)/(x+1)/(1+x^2) lgdogf A005993 80.7858 2+3*x-x^3 ogf_with_Euler_Transform A005993 4.60172 {(-38685-9352*n-323*n^2)*a(n+1)+(202980+72495*n+6122*n^2)*a(n+2)+(69603+20304*n+323*n^2)*a(n+3)+(-48653*n-96660-6122*n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=6,a(3)=10} ogf A005993 19.6506 {a(n+4),a(0)=2,a(1)=3,a(2)=0,a(3)=-1} ogf_with_Euler_Transform A005994 15.7234 -(1+x^2)/(-3*x^6-1+3*x-x^2-5*x^3+5*x^4+x^5+x^7) ogf A005994 18.475 -(3+9*x+3*x^2+5*x^3)/(x-1)/(x+1)/(1+x^2) lgdogf A005994 30.7917 -(x^2+1)/(x+1)^2/(x-1)^5 ogf A005994 82.1112 3+3*x-x^3 ogf_with_Euler_Transform A005994 5.39416 {(-1002-305*n-23*n^2)*a(n+1)+(486+261*n+27*n^2)*a(n+2)+(624+271*n+23*n^2)*a(n+3)+(-195*n-348-27*n^2)*a(n+4),a(0)=1,a(1)=3,a(2)=9,a(3)=19} ogf A005994 19.973 {a(n+4),a(0)=3,a(1)=3,a(2)=0,a(3)=-1} ogf_with_Euler_Transform A005995 32.4621 (1+3*x^2)/(x+1)^3/(x-1)^6 ogf A005995 15.3123 -(-1-3*x^2)/(1-3*x+8*x^3-6*x^4-6*x^5+8*x^6-3*x^8+x^9) ogf A005995 18.4444 -3*(1+5*x+7*x^3+3*x^2)/(x-1)/(x+1)/(3*x^2+1) lgdogf A005995 5.55859 {(-4872-1161*n-69*n^2)*a(n+1)+(4176+1585*n+125*n^2)*a(n+2)+(2664+1053*n+69*n^2)*a(n+3)+(-917*n-1668-125*n^2)*a(n+4),a(0)=1,a(1)=3,a(2)=12,a(3)=28} ogf A005996 12.7535 -(2+2*x+2*x^2)/(-x^6-1+2*x+x^2-4*x^3+x^4+2*x^5) ogf A005996 13.9398 -(3+10*x+4*x^3+7*x^2)/(x-1)/(x+1)/(x^2+x+1) lgdogf A005996 22.2005 2*(x^2+x+1)/(x+1)^2/(x-1)^4 ogf A005996 4.13388 {(-2070-904*n-98*n^2)*a(n+1)+(-6588-2163*n-163*n^2)*a(n+2)+(-846+186*n+98*n^2)*a(n+3)+(1315*n+2652+163*n^2)*a(n+4),a(0)=2,a(1)=6,a(2)=16,a(3)=30} ogf A005996 19.9804 {a(n+3),a(0)=3,a(1)=2,a(2)=-1} ogf_with_Euler_Transform A005997 26.1554 (1+x^3+x+3*x^2)/(x+1)^2/(x-1)^4 ogf A005997 16.5473 -(1+x+3*x^2+x^3)/(-x^6-1+2*x+x^2-4*x^3+x^4+2*x^5) ogf A005997 15.0152 -(3*x^2+2*x+3)*(1+x^2+4*x)/(x-1)/(x+1)/(x^3+3*x^2+x+1) lgdogf A005997 6.23707 {(-304-136*n-15*n^2)*a(n+1)+(-270-63*n-2*n^2)*a(n+2)+(48+72*n+15*n^2)*a(n+3)+(25*n+68+2*n^2)*a(n+4),a(0)=1,a(1)=3,a(2)=10,a(3)=20} ogf A005998 22.7312 (1+2*x^3+2*x^2+x^4)/(x+1)^2/(x-1)^4 ogf A005998 15.0112 -(1+2*x^2+2*x^3+x^4)/(-x^6-1+2*x+x^2-4*x^3+x^4+2*x^5) ogf A005998 12.4311 -2*(1+5*x+4*x^4+x^5+8*x^3+5*x^2)/(x-1)/(x+1)/(x^4+2*x^3+2*x^2+1) lgdogf A005999 16.0633 (x^2+x+1)*(x^3+x^2-x+1)/(x+1)^2/(x-1)^4 ogf A005999 9.21278 -(1+x^2+4*x)*(x^4+2*x^3+3*x^2+2)/(x-1)/(x+1)/(x^2+x+1)/(x^3+x^2-x+1) lgdogf A005999 11.3903 -(1+x^5+x^2+x^3+2*x^4)/(-x^6-1+2*x+x^2-4*x^3+x^4+2*x^5) ogf A006000 54.6522 (1+2*x^2)/(x-1)^4 ogf A006000 26.5454 -(1+2*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A006000 8.29543 -3277-6554*x^2+(10-13108*x+3277*x^4-13108*x^3+13128*x^2)*f(x)+(3267-13068*x^3-13068*x+19602*x^2+3267*x^4)*f(x)^2 ogf A006000 33.1817 -4*(x^2+x+1)/(x-1)/(2*x^2+1) lgdogf A006000 10.9304 {(n+4)*a(n+4)+(-7-n)*a(n+3)+2*a(n+2)*n+(-6-2*n)*a(n+1),a(0)=1,a(1)=4,a(2)=12,a(3)=28} ogf A006001 12.9318 (-1-2*x^3)*f(x)+(1-4*x+6*x^2-4*x^3+x^4)*f(x)^2 ogf A006001 34.992 (1+2*x^3)/(x-1)^4 ogf A006001 16.9961 -(-1-2*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A006001 18.5895 -2*(2+x^3+3*x^2)/(x-1)/(2*x^3+1) lgdogf A006001 6.46592 {(-10-7*n-n^2)*a(n+1)+(4+10*n+2*n^2)*a(n+2)+(-3*n-n^2)*a(n+3),a(0)=1,a(1)=4,a(2)=10,a(3)=22} ogf A006002 46.0344 (x+2)/(x-1)^4 ogf A006002 17.0985 -(-2*x-x^2)/(1-4*x+6*x^2-4*x^3+x^4) ogf A006002 29.9224 -3*(3+x)/(x+2)/(x-1) lgdogf A006002 4.78758 39878*x+19939*x^2+(-19939+108808*x-19939*x^4+79756*x^3-105108*x^2)*f(x)+(-14526*x^4-14526+58104*x+58104*x^3-87156*x^2)*f(x)^2 ogf A006002 9.06739 {(2*n+4)*a(n+3)+(-10-n)*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=2,a(2)=9} ogf A006002 9.06739 {(4+2*n)*a(n+3)+(-10-n)*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=2,a(2)=9} ogf A006003 44.1925 (x^2+x+1)/(x-1)^4 ogf A006003 20.3046 -(-x-x^2-x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A006003 25.0424 -(5+5*x+2*x^2)/(x-1)/(x^2+x+1) lgdogf A006003 7.51272 41*x+41*x^3+41*x^2+(-41+239*x-41*x^4+239*x^3-171*x^2)*f(x)+(-75+300*x-450*x^2+300*x^3-75*x^4)*f(x)^2 ogf A006003 150.254 5-x^2 ogf_with_Euler_Transform A006003 10.017 {(-3-n)*a(n+4)+5*a(n+3)+5*a(n+2)+(n+2)*a(n+1),a(0)=0,a(1)=1,a(2)=5,a(3)=15} ogf A006004 42.8211 (1+x^3+x^2)/(x-1)^4 ogf A006004 21.9892 -(1+x^2+x^3)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A006004 22.6 -(4+2*x+x^3+5*x^2)/(x-1)/(x^3+x^2+1) lgdogf A006004 6.45715 -6505-6505*x^3-6505*x^2+(-8669-26020*x+6505*x^4-41194*x^3+23856*x^2)*f(x)+(15174-60696*x^3-60696*x+91044*x^2+15174*x^4)*f(x)^2 ogf A006004 8.13601 {(-390-293*n-49*n^2)*a(n+1)+(-240+204*n+68*n^2)*a(n+2)+(-n+168-19*n^2)*a(n+3),a(0)=1,a(1)=4,a(2)=11} ogf A006007 26.2991 -(5+2*x+3*x^2)/(x-1)/(1+x^2) lgdogf A006007 17.9604 -(x+x^3)/(-1+5*x-5*x^4-10*x^2+10*x^3+x^5) ogf A006007 46.0235 -(x^2+1)/(x-1)^5 ogf A006007 105.197 5+x-x^3 ogf_with_Euler_Transform A006007 8.76638 {(n+3)*a(n+4)+(-7-n)*a(n+3)+(n-1)*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=1,a(2)=5,a(3)=16} ogf A006008 24.9869 -(5+2*x^3+3*x^2)/(x-1)/(x+1)/(x^2-x+1) lgdogf A006008 39.5626 -(x+1)*(x^2-x+1)/(x-1)^5 ogf A006008 23.1586 -(x+x^4)/(-1+5*x-5*x^4-10*x^2+10*x^3+x^5) ogf A006008 105.5 5+x^2-x^5 ogf_with_Euler_Transform A006008 9.78869 {(10+7*n+n^2)*a(n+1)+(4-2*n^2-8*n)*a(n+2)+(-2+n+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=5,a(3)=15,a(4)=36} ogf A006009 15.069 -(-4-4*x-4*x^2)/(x^2+1-3*x-5*x^4-x^5+3*x^6+5*x^3-x^7) ogf A006009 18.5734 -(4+12*x+5*x^3+9*x^2)/(x-1)/(x+1)/(x^2+x+1) lgdogf A006009 28.5234 -4*(x^2+x+1)/(x+1)^2/(x-1)^5 ogf A006009 5.43303 {(-2202-865*n-83*n^2)*a(n+1)+(-6970-2035*n-131*n^2)*a(n+2)+(-1432+57*n+83*n^2)*a(n+3)+(1131*n+2428+131*n^2)*a(n+4),a(0)=4,a(1)=16,a(2)=48,a(3)=108} ogf A006009 26.6219 {a(n+3),a(0)=4,a(1)=2,a(2)=-1} ogf_with_Euler_Transform A006010 11.4059 -(-1-2*x-6*x^2-2*x^3-x^4)/(x^2+1-3*x-5*x^4-x^5+3*x^6+5*x^3-x^7) ogf A006010 17.9643 -(1+2*x+2*x^3+6*x^2+x^4)/(x+1)^2/(x-1)^5 ogf A006010 9.98018 -(5+25*x+11*x^4+3*x^5+40*x^3+36*x^2)/(x-1)/(x+1)/(x^4+2*x^3+6*x^2+2*x+1) lgdogf A006011 16.0983 -(-3*x^2-3*x^3)/(1-5*x+10*x^2-x^5-10*x^3+5*x^4) ogf A006011 34.3918 -2*(3+2*x)/(x-1)/(x+1) lgdogf A006011 47.2887 -3*(x+1)/(x-1)^5 ogf A006011 13.0452 {(n+1)*a(n+3)-6*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=0,a(2)=3} ogf A006012 26.4508 -(-1+2*x)/(2*x^2+1-4*x) ogf A006012 27.6531 -(2*x-1)/(2*x^2-4*x+1) ogf A006012 16.0097 -2*(1-2*x+2*x^2)/(2*x-1)/(2*x^2-4*x+1) lgdogf A006012 11.9288 -3+6*x+(10-26*x+6*x^2)*f(x)+(-14*x^2-7+28*x)*f(x)^2 ogf A006012 16.0097 {a(n+2)-4*a(n+1)+2*a(n),a(0)=1,a(1)=2} ogf A006013 23.2922 1-f(x)+2*x*f(x)^2-x^2*f(x)^3 ogf A006013 72.4647 x*(x-1)^2 revogf A006013 10.0336 {(27*n^2+108*n+105)*a(n+1)+(-4*n^2-22*n-30)*a(n+2),a(0)=1,a(1)=2} ogf A006021 1.78322 -(1+2*x+3*x^5+x^3+3*x^2+4*x^4+2*x^6+4*x^8)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A006027 12.3668 -1+(1+x+x^2)*f(x)+(-2*x-x^2)*f(x)^2+x^2*f(x)^3 ogf A006040 10.0954 {(-4*n-n^2-4)*a(n+1)+(n^2+10+6*n)*a(n+2)-a(n+3),a(0)=1,a(1)=2,a(2)=9} ogf A006041 5.523 {(n^3+6*n+5*n^2)*a(n)+(-n^3-6*n^2-12*n-9)*a(n+1)+(n+2)*a(n+2),a(0)=0,a(1)=2} ogf A006043 44.4634 -2/(-1+3*x)^3 ogf A006043 57.8024 -9/(3*x-1) lgdogf A006043 25.1315 2/(1-9*x+27*x^2-27*x^3) ogf A006043 9.79703 4+(-4+18*x+54*x^3-54*x^2)*f(x)+(27*x^2-27*x^3+1-9*x)*f(x)^2 ogf A006043 9.79703 {a(n+3)-9*a(n+2)+27*a(n+1)-27*a(n),a(0)=2,a(1)=18,a(2)=108} ogf A006044 66.5979 -16/(4*x-1) lgdogf A006044 9.15721 36+(96*x-1536*x^4+1536*x^3-576*x^2)*f(x)+(-1-256*x^4+16*x-96*x^2+256*x^3)*f(x)^2 ogf A006044 66.5979 6/(4*x-1)^4 ogf A006044 15.9256 {(-n-2)*a(n+2)+(20+4*n)*a(n+1),a(0)=6,a(1)=96} ogf A006051 16.714 -(1-26*x+x^2)/(-195*x^2-1+195*x+x^3) ogf A006051 18.2335 -(1-26*x+x^2)/(x-1)/(x^2-194*x+1) ogf A006051 9.25701 -(169-388*x+x^4-52*x^3+4878*x^2)/(x-1)/(x^2-194*x+1)/(x^2-26*x+1) lgdogf A006051 9.55088 {-a(n+3)+195*a(n+2)-195*a(n+1)+a(n),a(0)=1,a(1)=169,a(2)=32761} ogf A006053 24.4401 -(-1-4*x+3*x^2)/(-2*x^2+1-x+x^3) lgdogf A006053 46.0048 1/(1-x-2*x^2+x^3) ogf A006053 15.04 x^2+(-1+x-x^3+4*x^2)*f(x)+(4*x^2-2+2*x-2*x^3)*f(x)^2 ogf A006053 41.1622 x^2/(1-x-2*x^2+x^3) ogf A006053 15.6416 {a(n+3)-a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=0,a(2)=1} ogf A006054 23.3829 -(-2-2*x+3*x^2)/(-x^2+1-2*x+x^3) lgdogf A006054 44.0149 1/(1-2*x+x^3-x^2) ogf A006054 29.9301 x^2+(-1+2*x+x^2-x^3)*f(x) ogf A006054 39.3817 x^2/(1-2*x-x^2+x^3) ogf A006054 14.9651 {a(n+3)-2*a(n+2)-a(n+1)+a(n),a(0)=0,a(1)=0,a(2)=1} ogf A006060 11.6653 -(-1-58*x-x^2)/(195*x^2+1-195*x-x^3) ogf A006060 12.7258 -(1+58*x+x^2)/(x-1)/(x^2-194*x+1) ogf A006060 6.77338 {a(n+3)-195*a(n+2)+195*a(n+1)-a(n),a(0)=1,a(1)=253,a(2)=49141} ogf A006061 13.5037 -(-1-22*x-x^2)/(99*x^2+1-99*x-x^3) ogf A006061 14.3477 -(1+22*x+x^2)/(x-1)/(x^2-98*x+1) ogf A006061 7.17384 -(121-196*x+x^4+44*x^3-2274*x^2)/(x-1)/(x^2+22*x+1)/(x^2-98*x+1) lgdogf A006061 7.6521 {a(n+3)-99*a(n+2)+99*a(n+1)-a(n),a(0)=1,a(1)=121,a(2)=11881} ogf A006062 8.96074 -(-1-2*x-x^2)/(35*x^2+1-35*x-x^3) ogf A006062 6.42835 -(37-105*x+x^3+3*x^2)/(x-1)/(x+1)/(x^2-34*x+1) lgdogf A006062 10.952 -(x+1)^2/(x-1)/(x^2-34*x+1) ogf A006062 2.68822 -2590-5180*x-2590*x^2+(83437+71044*x-2590*x^3+171497*x^2)*f(x)+(-2829645*x^2-80847+2829645*x+80847*x^3)*f(x)^2 ogf A006062 5.09835 {a(n+3)-35*a(n+2)+35*a(n+1)-a(n),a(0)=1,a(1)=37,a(2)=1261} ogf A006071 17.7246 (1+x+x^5+6*x^3+4*x^2-5*x^4)/(x+1)/(x-1)^4 ogf A006071 12.3171 -(-1-x-x^5-4*x^2-6*x^3+5*x^4)/(2*x^2+1-3*x-3*x^4+2*x^3+x^5) ogf A006071 10.2353 2*(-2-8*x-x^4+x^5-5*x^3-17*x^2)/(x-1)/(x+1)/(x^5-5*x^4+6*x^3+4*x^2+x+1) lgdogf A006077 8.10026 {(108+108*n+27*n^2)*a(n+1)+(-57-45*n-9*n^2)*a(n+2)+(n^2+6*n+9)*a(n+3),a(0)=1,a(1)=3,a(2)=9} ogf A006083 17.1819 -(-1-2*x+3*x^6-x^2-2*x^3+x^4+x^10-x^8)/(-x^3+1+x^9-x^6) ogf A006083 12.7703 -(-1-2*x-2*x^3-x^2+x^4+3*x^6-x^8+x^10)/(x+1)/(x^2-x+1)/(x-1)^2/(x^2+x+1)^2 ogf A006084 8.46808 -(-x-x^5-5*x^6-9*x^2+x^16-x^3-x^7+5*x^15-x^4-x^20+x^10-x^9-x^8+x^12-8*x^11+x^18-x^17+x^13-x^14)/(1-2*x^9+x^18) ogf A006089 5.23531 -(16+176*x-576*x^2)/(-663*x^2-1+46*x-7711*x^4+6606*x^5-2025*x^6+3748*x^3) ogf A006089 7.96203 -16*(-1-11*x+36*x^2)/(-1+25*x)/(9*x-1)^2/(x-1)^3 ogf A006089 4.71824 -3*(-19+257*x+10800*x^4-7749*x^3+1319*x^2)/(x-1)/(25*x-1)/(9*x-1)/(36*x^2-11*x-1) lgdogf A006090 10.1041 -6*(1+5*x+5*x^4+10*x^3+10*x^2)/(2*x+1)/(x^2+x+1)/(1+3*x^2+3*x) lgdogf A006090 17.4015 1/(1+6*x+15*x^2+20*x^3+15*x^4+6*x^5) ogf A006090 17.4015 1/(1-6*x+15*x^2-20*x^3+15*x^4-6*x^5) ogf A006090 18.9834 1/(2*x+1)/(x^2+x+1)/(3*x+1+3*x^2) ogf A006095 16.9415 -(7-28*x+24*x^2)/(x-1)/(2*x-1)/(4*x-1) lgdogf A006095 26.824 -1/(x-1)/(2*x-1)/(4*x-1) ogf A006095 21.4592 x^2+(-1+7*x-14*x^2+8*x^3)*f(x) ogf A006095 26.824 x^2/(1-7*x+14*x^2-8*x^3) ogf A006095 11.705 {a(n+3)-7*a(n+2)+14*a(n+1)-8*a(n),a(0)=0,a(1)=0,a(2)=1} ogf A006096 10.8466 -(-15+140*x+256*x^3-360*x^2)/(x-1)/(8*x-1)/(2*x-1)/(4*x-1) lgdogf A006096 18.503 -1/(-1+15*x-70*x^2+120*x^3-64*x^4) ogf A006096 5.4233 -1024+(-12627-15360*x+65536*x^4-122880*x^3+71680*x^2)*f(x)+(955570*x^2-1638120*x^3+13651-204765*x+873664*x^4)*f(x)^2 ogf A006096 20.2937 1/(x-1)/(8*x-1)/(2*x-1)/(4*x-1) ogf A006097 8.18313 -(31-620*x+5120*x^4-7936*x^3+3720*x^2)/(x-1)/(4*x-1)/(2*x-1)/(8*x-1)/(16*x-1) lgdogf A006097 15.3683 -1/(x-1)/(4*x-1)/(2*x-1)/(8*x-1)/(16*x-1) ogf A006097 14.0022 1/(1-31*x+310*x^2-1240*x^3+1984*x^4-1024*x^5) ogf A006100 11.4055 -(13-78*x+81*x^2)/(x-1)/(3*x-1)/(9*x-1) lgdogf A006100 17.7926 -1/(x-1)/(-1+3*x)/(9*x-1) ogf A006100 4.99791 -891+(8542-11583*x-24057*x^3+34749*x^2)*f(x)+(-7651+99463*x-298389*x^2+206577*x^3)*f(x)^2 ogf A006100 18.5339 1/(1-13*x+39*x^2-27*x^3) ogf A006100 7.41357 {a(n+3)-13*a(n+2)+39*a(n+1)-27*a(n),a(0)=1,a(1)=13,a(2)=130} ogf A006101 10.9129 -1/(-1+40*x-390*x^2+1080*x^3-729*x^4) ogf A006101 6.61928 -4*(-10+195*x+729*x^3-810*x^2)/(x-1)/(3*x-1)/(27*x-1)/(9*x-1) lgdogf A006101 12.2356 1/(x-1)/(-1+3*x)/(27*x-1)/(9*x-1) ogf A006102 8.35039 -(121-7260*x+295245*x^4-352836*x^3+98010*x^2)/(x-1)/(81*x-1)/(3*x-1)/(9*x-1)/(27*x-1) lgdogf A006102 16.5066 -1/(x-1)/(81*x-1)/(-1+3*x)/(9*x-1)/(27*x-1) ogf A006102 14.1957 1/(1-121*x+3630*x^2-32670*x^3+88209*x^4-59049*x^5) ogf A006105 16.2483 -1/(x-1)/(4*x-1)/(16*x-1) ogf A006105 9.9075 -3*(7-56*x+64*x^2)/(x-1)/(4*x-1)/(16*x-1) lgdogf A006105 4.14497 -3520+(74513-73920*x-225280*x^3+295680*x^2)*f(x)+(-70993+1490853*x-5963412*x^2+4543552*x^3)*f(x)^2 ogf A006105 16.9253 1/(1-21*x+84*x^2-64*x^3) ogf A006105 6.77013 {a(n+3)-21*a(n+2)+84*a(n+1)-64*a(n),a(0)=1,a(1)=21,a(2)=357} ogf A006106 5.27566 -(-85+2856*x+16384*x^3-16320*x^2)/(x-1)/(4*x-1)/(64*x-1)/(16*x-1) lgdogf A006106 8.79276 -1/(-1+85*x-1428*x^2+5440*x^3-4096*x^4) ogf A006106 10.3914 1/(x-1)/(4*x-1)/(64*x-1)/(16*x-1) ogf A006110 12.6513 -1/(-1+63*x-1302*x^2+11160*x^3-41664*x^4+64512*x^5-32768*x^6) ogf A006110 15.7496 1/(x-1)/(4*x-1)/(2*x-1)/(8*x-1)/(16*x-1)/(32*x-1) ogf A006111 14.6383 -(31-310*x+375*x^2)/(x-1)/(25*x-1)/(5*x-1) lgdogf A006111 23.6464 -1/(x-1)/(-1+25*x)/(5*x-1) ogf A006111 23.6464 1/(1-31*x+155*x^2-125*x^3) ogf A006111 9.91623 {a(n+3)-31*a(n+2)+155*a(n+1)-125*a(n),a(0)=1,a(1)=31,a(2)=806} ogf A006112 7.53626 -1/(-1+156*x-4030*x^2+19500*x^3-15625*x^4) ogf A006112 4.65475 -4*(-39+2015*x+15625*x^3-14625*x^2)/(x-1)/(125*x-1)/(25*x-1)/(5*x-1) lgdogf A006112 9.04351 1/(x-1)/(125*x-1)/(-1+25*x)/(5*x-1) ogf A006124 18.0777 -(-3+2*x-6*x^2)/(3*x^2+1-3*x-x^3) ogf A006124 27.1166 -(3-2*x+6*x^2)/(x-1)^3 ogf A006124 17.546 -(7+8*x+6*x^2)/(x-1)/(6*x^2-2*x+3) lgdogf A006124 5.37446 -55089+36726*x-110178*x^2+(57318-81059*x-18363*x^3+132999*x^2)*f(x)+(-38955*x^2-12985+38955*x+12985*x^3)*f(x)^2 ogf A006124 11.2559 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=3,a(1)=7,a(2)=18} ogf A006127 31.173 (x^2+x-1)/(2*x-1)/(x-1)^2 ogf A006127 25.1395 -(-1+x+x^2)/(5*x^2+1-4*x-2*x^3) ogf A006127 17.7119 -(3-9*x+2*x^3+6*x^2)/(x-1)/(2*x-1)/(x^2+x-1) lgdogf A006127 10.824 17-17*x-17*x^2+(-16+67*x+34*x^3-86*x^2)*f(x)+(-5*x^2-1+4*x+2*x^3)*f(x)^2 ogf A006127 14.432 {a(n+3)-4*a(n+2)+5*a(n+1)-2*a(n),a(0)=1,a(1)=3,a(2)=6} ogf A006130 33.3318 -(1+6*x)/(3*x^2-1+x) lgdogf A006130 44.4423 -1/(-1+3*x^2+x) ogf A006130 44.4423 -1/(-1+x+3*x^2) ogf A006130 13.6048 -18+(37-18*x-54*x^2)*f(x)+(57*x^2-19+19*x)*f(x)^2 ogf A006130 20.2011 1/6/x*(-1-x+(1+2*x+13*x^2)^(1/2)) revogf A006130 18.0172 {-a(n+2)+a(n+1)+3*a(n),a(0)=1,a(1)=1} ogf A006131 34.1781 -(1+8*x)/(4*x^2-1+x) lgdogf A006131 45.5708 -1/(-1+x+4*x^2) ogf A006131 13.4032 -28+(57-28*x-112*x^2)*f(x)+(116*x^2-29+29*x)*f(x)^2 ogf A006131 20.714 1/8/x*(-1-x+(1+2*x+17*x^2)^(1/2)) revogf A006131 18.4746 {-a(n+2)+a(n+1)+4*a(n),a(0)=1,a(1)=1} ogf A006134 22.4212 -1+(1-6*x+9*x^2-4*x^3)*f(x)^2 ogf A006134 28.2702 -1/(-4*x+1)^(1/2)/(x-1) ogf A006134 27.0922 -3*(2*x-1)/(4*x-1)/(x-1) lgdogf A006134 9.42339 {(-n-3)*a(n+3)+(13+5*n)*a(n+2)+(-10-4*n)*a(n+1),a(0)=1,a(1)=3,a(2)=9} ogf A006137 18.4084 -(-1-3*x-5*x^2)/(3*x^2+1-3*x-x^3) ogf A006137 27.6126 -(1+3*x+5*x^2)/(x-1)^3 ogf A006137 17.3565 -(6+16*x+5*x^2)/(x-1)/(1+5*x^2+3*x) lgdogf A006137 5.67736 -13309-39927*x-66545*x^2+(18169-25347*x-13309*x^3+64227*x^2)*f(x)+(-4860+14580*x-14580*x^2+4860*x^3)*f(x)^2 ogf A006137 11.4618 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=6,a(2)=20} ogf A006138 24.5851 -(2+6*x+3*x^2)/(x+1)/(3*x^2+x-1) lgdogf A006138 41.4065 -(x+1)/(-1+3*x^2+x) ogf A006138 43.7068 -(x+1)/(3*x^2-1+x) ogf A006138 14.3041 -21-21*x+(58+16*x-63*x^2)*f(x)+(111*x^2-37+37*x)*f(x)^2 ogf A006138 20.1724 1/2/(3*x+1)*(-1-x+(1+6*x+13*x^2)^(1/2)) revogf A006138 21.2628 {-a(n+2)+a(n+1)+3*a(n),a(0)=1,a(1)=2} ogf A006139 17.7063 (-2*x+(8*x^2+1)^(1/2))/(1+4*x^2)*x revogf A006139 25.0839 -2*(2*x+1)/(4*x^2-1+4*x) lgdogf A006139 26.1745 1+(-1+4*x+4*x^2)*f(x)^2 ogf A006139 28.6673 1/(1-4*x-4*x^2)^(1/2) ogf A006139 8.85315 {(n+3)*a(n+3)+(-10-4*n)*a(n+2)+(-4*n-8)*a(n+1),a(0)=1,a(1)=2,a(2)=8} ogf A006149 6.67283 {(-1136*n-64*n^3-480*n^2-840)*a(n+1)+(n^3+18*n^2+107*n+210)*a(n+2),a(0)=1,a(1)=1} ogf A006152 21.7889 -(-2+x)/(x^2-x+1)/(x-1)^2 lgdegf A006152 5.50224 1418-709*x+(-505+2025*x-709*x^4+2127*x^3-2836*x^2)*f(x)+(-408*x^2-102+306*x-102*x^4+306*x^3)*f(x)^2 lgdegf A006152 14.3348 exp(-1/(x-1))/(x-1)^2*(x^2-x+1)/exp(1) egf A006152 7.67213 {(6*n+5*n^2+n^3)*a(n)+(-9-9*n-2*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=2} ogf A006157 50.2361 (x+1)/(x-1)^4 egf A006157 21.0667 -(1+x)/(-6*x^2-1+4*x+4*x^3-x^4) egf A006157 32.6535 -(5+3*x)/(x-1)/(x+1) lgdegf A006157 5.83097 -7423-7423*x+(2175-34940*x+7423*x^4-29692*x^3+44538*x^2)*f(x)+(5248-20992*x^3-20992*x+31488*x^2+5248*x^4)*f(x)^2 egf A006157 7.96426 {(-8-6*n-n^2)*a(n+1)+(40+19*n+2*n^2)*a(n+2)+(-2*n-6)*a(n+3),a(0)=1,a(1)=5,a(2)=28} ogf A006172 2.47495 -(-2-3*x-17*x^3+19*x^2+4*x^4)/(x-1)/(1-3*x+x^2)/(x^2-x-1) ogf A006183 44.9359 (-3+x)/(x-1) lgdegf A006183 33.702 2*exp(x)/(x-1)^2 egf A006183 9.4602 {(-n-2)*a(n+1)+(n+5)*a(n+2)-a(n+3),a(0)=2,a(1)=6,a(2)=22} ogf A006190 31.7665 -(3+2*x)/(x^2-1+3*x) lgdogf A006190 42.3553 -1/(-1+3*x+x^2) ogf A006190 33.4384 -x+(1-3*x-x^2)*f(x) ogf A006190 42.3553 -x/(-1+3*x+x^2) ogf A006190 18.1523 1/2/x*(-3*x-1+(1+6*x+13*x^2)^(1/2)) revogf A006190 17.1711 {-a(n+2)+3*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A006192 16.7315 (x-1)*(x+1)/(x^2-x+1)/(-1+3*x+x^2) ogf A006192 17.2385 -(-1+x^2)/(1-4*x+3*x^2-2*x^3-x^4) ogf A006192 8.75186 -2*(-2+4*x+x^4+x^5-2*x^3-5*x^2)/(x-1)/(x+1)/(x^2-x+1)/(x^2-1+3*x) lgdogf A006192 6.05182 -41+41*x^2+(-250-164*x-41*x^4-82*x^3+414*x^2)*f(x)+(873*x^2-582*x^3+291-1164*x-291*x^4)*f(x)^2 ogf A006198 10.4159 (-4*x^2+8*x-6+(-(2*x-3)^2*(2*x-1)^3)^(1/2))/(4*x^2-6*x+3)/(2*x-1) lgdegf A006198 7.96512 9+8*x+8*x^3-20*x^2+(-12+40*x+16*x^3-40*x^2)*f(x)+(40*x^2+3-18*x+16*x^4-40*x^3)*f(x)^2 lgdegf A006198 6.6376 {(n+3)*a(n+1)+(9+10*n+2*n^2)*a(n+2)+(-37-18*n-2*n^2)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=1,a(2)=6,a(3)=41} ogf A006199 9.56943 1/2*(-1-7*x-4*x^2+(2*x+1)^(3/2)*x+(2*x+1)^(3/2))/(x+1)/(2*x+1)/x lgdegf A006199 6.00435 {(-3-n)*a(n+1)+(3+2*n^2+8*n)*a(n+2)+(27+16*n+2*n^2)*a(n+3)+(n+3)*a(n+4),a(0)=0,a(1)=1,a(2)=-3,a(3)=21} ogf A006200 3.59386 {(-5-n)*a(n+1)+(-18-14*n-2*n^2)*a(n+2)+(54+22*n+2*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=6,a(2)=55,a(3)=610} ogf A006221 24.5077 (x+1)*(5*x^2+92*x+5)/(x-1)^4 ogf A006221 12.9475 -(117+485*x+5*x^3+209*x^2)/(x-1)/(x+1)/(5*x^2+92*x+5) lgdogf A006221 14.6004 -(5+97*x+5*x^3+97*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A006221 6.5354 {(216+190*n+41*n^2)*a(n+1)+(-843-410*n-82*n^2)*a(n+2)+(220*n+291+41*n^2)*a(n+3),a(0)=5,a(1)=117,a(2)=535} ogf A006222 20.3651 -(-3-16*x-3*x^2)/(3*x^2+1-3*x-x^3) ogf A006222 18.7139 -(25+38*x+3*x^2)/(x-1)/(3*x^2+16*x+3) lgdogf A006222 30.1049 -(3+16*x+3*x^2)/(x-1)^3 ogf A006222 7.28856 -3420-18240*x-3420*x^2+(1461-1708*x-1140*x^3+3741*x^2)*f(x)+(-321*x^2-107+321*x+107*x^3)*f(x)^2 ogf A006222 12.8225 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=3,a(1)=25,a(2)=69} ogf A006223 8.0041 -1/(2*x-1)/(2*x^2-4*x+1)/(2*x^4-16*x^3+20*x^2-8*x+1) ogf A006223 4.16213 -2*(7-78*x+630*x^4+28*x^6-252*x^5-660*x^3+330*x^2)/(2*x-1)/(2*x^2-4*x+1)/(2*x^4-16*x^3+20*x^2-8*x+1) lgdogf A006223 7.70765 1/(1-14*x+78*x^2-220*x^3+330*x^4-252*x^5+84*x^6-8*x^7) ogf A006228 33.6378 -1+(1-x^2)*f(x)^2 lgdegf A006228 25.9928 1/(-(x-1)*(x+1))^(1/2) lgdegf A006228 5.24626 {(-4-6*n-4*n^2-n^3)*a(n+1)+(-20-21*n-8*n^2-n^3)*a(n+2)+(n+2)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=2} ogf A006230 11.8997 -(-1-7*x-6*x^2)/(11*x^2+1-6*x-6*x^3) ogf A006230 6.39387 -(13-10*x+36*x^4+84*x^3-95*x^2)/(x-1)/(3*x-1)/(2*x-1)/(6*x+1)/(x+1) lgdogf A006230 11.5781 -(x+1)*(1+6*x)/(x-1)/(-1+3*x)/(2*x-1) ogf A006230 3.69301 -39162-274134*x-234972*x^2+(58913-96715*x-234972*x^3+549288*x^2)*f(x)+(-217261*x^2-19751+118506*x+118506*x^3)*f(x)^2 ogf A006230 7.5156 {a(n+3)-6*a(n+2)+11*a(n+1)-6*a(n),a(0)=1,a(1)=13,a(2)=73} ogf A006231 6.32518 {(-12-7*n-n^2)*a(n+1)+(28+15*n+2*n^2)*a(n+2)+(-19-9*n-n^2)*a(n+3)+(n+3)*a(n+4),a(0)=0,a(1)=1,a(2)=5,a(3)=20} ogf A006234 27.0106 -(1-2*x)/(-9*x^2-1+6*x) ogf A006234 32.697 -(2*x-1)/(-1+3*x)^2 ogf A006234 17.7498 -1/2*(-1-6*x+(1+4*x)^(1/2))/(2+9*x) revogf A006234 23.009 -2*(-2+3*x)/(3*x-1)/(2*x-1) lgdogf A006234 12.1813 -5+10*x+(2-24*x+45*x^2)*f(x)+(3-18*x+27*x^2)*f(x)^2 ogf A006234 15.9293 {-a(n+2)+6*a(n+1)-9*a(n),a(0)=1,a(1)=4} ogf A006235 15.4757 (1+2*x+2*x^3-10*x^2+x^4)/(x-1)^2/(1+x^2-4*x)^2 ogf A006235 10.6251 -(1+2*x+2*x^3-10*x^2+x^4)/(-35*x^2-1+10*x-x^6-35*x^4+52*x^3+10*x^5) ogf A006235 8.4748 -2*(6-15*x-30*x^4+x^6+3*x^5+52*x^3-9*x^2)/(x-1)/(x^2-4*x+1)/(x^4+2*x^3-10*x^2+2*x+1) lgdogf A006235 4.62262 {(60+47*n+12*n^2+n^3)*a(n+1)+(-190*n-200-55*n^2-5*n^3)*a(n+2)+(155*n+150+50*n^2+5*n^3)*a(n+3)+(-26*n-24-9*n^2-n^3)*a(n+4),a(0)=1,a(1)=12,a(2)=75,a(3)=384} ogf A006238 19.8883 -(1-x^2)/(-1+15*x-32*x^2+15*x^3-x^4) ogf A006238 9.54639 -(15-66*x-15*x^4+2*x^5-4*x^3+60*x^2)/(x-1)/(x+1)/(x^4-15*x^3+32*x^2-15*x+1) lgdogf A006238 18.3584 -(x-1)*(x+1)/(1-15*x+32*x^2-15*x^3+x^4) ogf A006238 5.68238 1259-1259*x^2+(-104587+18885*x-1259*x^4+18885*x^3+63040*x^2)*f(x)+(103328-1549920*x^3-1549920*x+3306496*x^2+103328*x^4)*f(x)^2 ogf A006244 21.5086 -(1-8*x+x^2)/(-99*x^2-1+99*x+x^3) ogf A006244 22.8962 -(1-8*x+x^2)/(x-1)/(x^2-98*x+1) ogf A006244 11.6358 -(91-196*x+x^4-16*x^3+696*x^2)/(x-1)/(x^2-8*x+1)/(x^2-98*x+1) lgdogf A006244 6.01511 -3436+27488*x-3436*x^2+(410877-3599692*x-3436*x^3+747605*x^2)*f(x)+(-40336659*x^2-407441+40336659*x+407441*x^3)*f(x)^2 ogf A006244 12.0302 {-a(n+3)+99*a(n+2)-99*a(n+1)+a(n),a(0)=1,a(1)=91,a(2)=8911} ogf A006248 1.76449 1+(2*x-3)*f(x)+(3-4*x+x^2)*f(x)^2+(-1-x^2+2*x)*f(x)^3 ogf A006253 27.4432 -(-1+x)/(-3*x^2+1-3*x+x^3) ogf A006253 29.7302 -(x-1)/(x+1)/(1+x^2-4*x) ogf A006253 8.3944 -111+111*x+(1429-1651*x+111*x^3-333*x^2)*f(x)+(-1318-1318*x^3+3954*x+3954*x^2)*f(x)^2 ogf A006253 16.2165 -2*(1+3*x+x^3-3*x^2)/(x-1)/(x+1)/(x^2-4*x+1) lgdogf A006253 13.4627 {-a(n+3)+3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=2,a(2)=9} ogf A006256 12.4766 -1+9*f(x)+(-24+162*x)*f(x)^2+(-216*x+16+729*x^2)*f(x)^3 ogf A006256 6.41319 {(2916*n+729*n^2+2835)*a(n+1)+(-216*n^2-1026*n-1230)*a(n+2)+(16*n^2+88*n+120)*a(n+3),a(0)=1,a(1)=6,a(2)=39} ogf A006261 22.2479 (x^2-x+1)*(1-3*x+3*x^2)/(x-1)^6 ogf A006261 10.4498 -(1-4*x-6*x^3+7*x^2+3*x^4)/(-15*x^2-1+6*x-x^6-15*x^4+20*x^3+6*x^5) ogf A006261 11.8911 -2*(1-3*x+3*x^4-3*x^3+5*x^2)/(x-1)/(x^2-x+1)/(3*x^2-3*x+1) lgdogf A006261 7.11016 {(2*n+4)*a(n+1)+(-3*n+4)*a(n+2)+(n-3)*a(n+3),a(0)=1,a(1)=2,a(2)=4,a(3)=8,a(4)=16,a(5)=32,a(6)=63} ogf A006298 72.7805 -(23+18*x)/(x+1)/(4*x-1) lgdogf A006298 72.7805 21*(x+1)/(-4*x+1)^(11/2) ogf A006298 75.9449 21*(x+1)/(1-4*x)^(11/2) ogf A006298 23.6045 {(-n-3)*a(n+3)+(29+3*n)*a(n+2)+(22+4*n)*a(n+1),a(0)=21,a(1)=483,a(2)=6468} ogf A006300 9.95038 40-372*x-3600*x^2+(-2+60*x-2880*x^3-192*x^2)*f(x)+(20*x^2-576*x^4-48*x^3-x)*f(x)^2 lgdogf A006300 5.43954 {(-2880*n^2-22176*n-42336)*a(n+1)+(-240*n^2-1488*n-2448)*a(n+2)+(100*n^2+830*n+1650)*a(n+3)+(-5*n^2-46*n-96)*a(n+4),a(0)=1,a(1)=20,a(2)=307,a(3)=4280} ogf A006318 27.3643 -1+(1-x)*f(x)-x*f(x)^2 ogf A006318 12.286 -1/2*(-x-1+(1-6*x+x^2)^(1/2))/(1-6*x+x^2)^(1/2)/x lgdogf A006318 20.0671 -1/2*(x-1+(1-6*x+x^2)^(1/2))/x ogf A006318 43.001 -x*(x-1)/(1+x) revogf A006318 5.9021 {(n+n^2)*a(n)+(-11*n-6-5*n^2)*a(n+1)+(-42-29*n-5*n^2)*a(n+2)+(7*n+12+n^2)*a(n+3),a(0)=1,a(1)=2,a(2)=6} ogf A006319 20.118 1-2*x+x^2+(-1+2*x-x^2)*f(x)+x*f(x)^2 ogf A006319 12.2754 1/2*(x+1)*((1-6*x+x^2)^(1/2)+x-1)/x/(x-1)/(1-6*x+x^2)^(1/2) lgdogf A006319 20.6928 1/2*(x-1)*(x-1+(1-6*x+x^2)^(1/2))/x ogf A006319 5.24817 {(-5*n+3*n^2+2*n^3)*a(n)+(-25*n-45*n^2-14*n^3)*a(n+1)+(48+133*n+81*n^2+14*n^3)*a(n+2)+(-31*n-12-15*n^2-2*n^3)*a(n+3),a(0)=1,a(1)=1,a(2)=4} ogf A006320 12.1867 -1+(1-6*x-x^3+6*x^2)*f(x)-x^3*f(x)^2 ogf A006320 4.98547 -1/2*((1-6*x+x^2)^(1/2)-3*(1-6*x+x^2)^(1/2)*x+(1-6*x+x^2)^(1/2)*x^2-1+6*x+x^3-6*x^2)/x^3 ogf A006320 8.9535 -3/2*(-x-1+(1-6*x+x^2)^(1/2))/(1-6*x+x^2)^(1/2)/x lgdogf A006320 4.13888 {(3*n+n^2)*a(n)+(-28-21*n-5*n^2)*a(n+1)+(-82-39*n-5*n^2)*a(n+2)+(9*n+18+n^2)*a(n+3),a(0)=1,a(1)=6,a(2)=30} ogf A006321 6.99214 139+(-136+1112*x-139*x^4+1112*x^3-2224*x^2)*f(x)+(-3+24*x+136*x^4+24*x^3-48*x^2)*f(x)^2+3*x^4*f(x)^3 ogf A006321 12.486 2*(-1+6*x-x^2+((x+1)^2*(1-6*x+x^2))^(1/2))/x/(1-6*x+x^2) lgdogf A006321 6.47421 {(-4*n-n^2)*a(n)+(45+26*n+5*n^2)*a(n+1)+(108+44*n+5*n^2)*a(n+2)+(-10*n-21-n^2)*a(n+3),a(0)=1,a(1)=8,a(2)=48} ogf A006322 15.1695 -(-1-3*x-x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A006322 21.3321 -(4+x)*(3*x+2)/(x-1)/(x^2+3*x+1) lgdogf A006322 34.1314 -(x^2+3*x+1)/(x-1)^5 ogf A006322 7.58475 {(n+4)*a(n+4)+(2*n-2)*a(n+3)+(-18-2*n)*a(n+2)+(-4-n)*a(n+1),a(0)=1,a(1)=8,a(2)=31,a(3)=85} ogf A006323 14.8891 -(-1-5*x-x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A006323 19.7061 -(10+22*x+3*x^2)/(x-1)/(x^2+5*x+1) lgdogf A006323 33.5004 -(x^2+5*x+1)/(x-1)^5 ogf A006323 7.2827 {(n+4)*a(n+4)+(2+4*n)*a(n+3)+(-30-4*n)*a(n+2)+(-4-n)*a(n+1),a(0)=1,a(1)=10,a(2)=41,a(3)=115} ogf A006324 16.4842 -(-1-6*x-x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A006324 37.0894 -(1+6*x+x^2)/(x-1)^5 ogf A006324 21.8173 -(11+26*x+3*x^2)/(x-1)/(x^2+6*x+1) lgdogf A006324 8.06292 {(n+4)*a(n+4)+(4+5*n)*a(n+3)+(-36-5*n)*a(n+2)+(-4-n)*a(n+1),a(0)=1,a(1)=11,a(2)=46,a(3)=130} ogf A006325 14.7731 -(-2*x^3-x^2-x^4)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A006325 36.194 -(7+3*x)/(x+1)/(x-1) lgdogf A006325 45.2425 -(x+1)^2/(x-1)^5 ogf A006325 144.776 7-2*x ogf_with_Euler_Transform A006325 12.4807 {(n+1)*a(n+3)-7*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=1} ogf A006325 12.4807 {(n+1)*a(n+3)-7*a(n+2)+(-n-2)*a(n+1),a(0)=0,a(1)=0,a(2)=1} ogf A006327 38.2813 (x+2)/(x-1)/(x^2+x-1) ogf A006327 34.9525 -(-2*x-x^2)/(1-2*x+x^3) ogf A006327 20.613 -(-5+2*x^3+6*x^2)/(x+2)/(x-1)/(x^2+x-1) lgdogf A006327 11.1654 110*x+55*x^2+(-55+342*x-55*x^3+116*x^2)*f(x)+(-116-116*x^3+232*x)*f(x)^2 ogf A006327 18.6955 {a(n+3)-2*a(n+2)+a(n),a(0)=0,a(1)=2,a(2)=5} ogf A006331 20.2741 -(2*x+2*x^2)/(-1+4*x-x^4-6*x^2+4*x^3) ogf A006331 37.5071 -(5+3*x)/(x-1)/(x+1) lgdogf A006331 50.0094 2*(x+1)/(x-1)^4 ogf A006331 6.75803 3586*x+3586*x^2+(-1793+9316*x-1793*x^4+7172*x^3-8614*x^2)*f(x)+(-1072*x^4-1072+4288*x+4288*x^3-6432*x^2)*f(x)^2 ogf A006331 12.7143 {(n+2)*a(n+3)-5*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=2,a(2)=10} ogf A006332 9.36495 -(-2*x-14*x^3-14*x^2-2*x^4)/(1-7*x+7*x^6+21*x^2-35*x^3+35*x^4-21*x^5-x^7) ogf A006332 14.2425 -2*(7+28*x+2*x^3+19*x^2)/(x-1)/(x+1)/(x^2+6*x+1) lgdogf A006332 24.4158 -2*(x+1)*(1+6*x+x^2)/(x-1)^7 ogf A006332 7.35098 {(-28-15*n-2*n^2)*a(n+1)+(62+24*n+4*n^2)*a(n+2)+(-10-9*n-2*n^2)*a(n+3),a(0)=0,a(1)=2,a(2)=28} ogf A006333 5.34661 -(-2*x-40*x^5-2*x^6-150*x^3-40*x^2-150*x^4)/(1-10*x-10*x^9+45*x^2+x^10-120*x^3+45*x^8+210*x^4-252*x^5+210*x^6-120*x^7) ogf A006333 8.19351 -5*(6+66*x+25*x^4+x^5+121*x^3+165*x^2)/(x-1)/(x+1)/(x^4+19*x^3+56*x^2+19*x+1) lgdogf A006333 14.6721 2*(x+1)*(x^4+19*x^3+56*x^2+19*x+1)/(x-1)^10 ogf A006333 4.81603 {(45+19*n+2*n^2)*a(n+1)+(-414-126*n-12*n^2)*a(n+2)+(174+66*n+12*n^2)*a(n+3)+(-21-13*n-2*n^2)*a(n+4),a(0)=0,a(1)=2,a(2)=60,a(3)=660} ogf A006334 6.27682 -(55+1232*x+10829*x^4+301*x^6+3164*x^5+14014*x^3+7007*x^2+6*x^7)/(x-1)/(x+1)/(x^6+41*x^5+323*x^4+678*x^3+323*x^2+41*x+1) lgdogf A006334 12.3478 -2*(x+1)*(x^6+41*x^5+323*x^4+678*x^3+323*x^2+41*x+1)/(x-1)^13 ogf A006334 9.91076 {(-330-181*n-33*n^2-2*n^3)*a(n+1)+(13*n+6+9*n^2+2*n^3)*a(n+2),a(0)=0,a(1)=2} ogf A006335 15.616 1-54*x+(-1+72*x)*f(x)-16*x*f(x)^2-64*x^2*f(x)^3 ogf A006335 19.8366 1/108+2/3*x-1/108*(-(24*x-1)^3)^(1/2) revogf A006335 11.2916 {(54*n^2+162*n+120)*a(n+1)+(-2*n^2-11*n-15)*a(n+2),a(0)=1,a(1)=2} ogf A006342 11.9898 -(1+2*x+12*x^3-11*x^2)/(x-1)/(3*x-1)/(2*x-1)/(x+1) lgdogf A006342 23.0573 -(1-2*x)/(x^2-1+3*x-3*x^3) ogf A006342 20.6721 -(2*x-1)/(x-1)/(-1+3*x)/(x+1) ogf A006342 9.22293 -3+6*x+(22-47*x+9*x^3-3*x^2)*f(x)+(-19-57*x^3+57*x+19*x^2)*f(x)^2 ogf A006342 11.3111 {-a(n+3)+3*a(n+2)+a(n+1)-3*a(n),a(0)=1,a(1)=1,a(2)=4} ogf A006343 17.1731 -1+(2-x)*f(x)+(-1+x)*f(x)^2-x^3*f(x)^3 ogf A006343 15.1762 1/2/(1+x+x^3)*(2+x+(-x^2*(-1+4*x))^(1/2))*x revogf A006347 15.5612 (-2-3*x-x^3+3*exp(x))/exp(x)/(x-1)^4 egf A006347 9.8281 {(-n-4)*a(n+1)+(-n-4)*a(n+2)+a(n+3),a(0)=0,a(1)=1,a(2)=3} ogf A006348 9.51149 (-9-8*x-6*x^2-x^4+8*exp(x))/exp(x)/(x-1)^5 egf A006348 7.00847 {(-n-5)*a(n+1)+(-n-5)*a(n+2)+a(n+3),a(0)=0,a(1)=1,a(2)=4} ogf A006351 58.916 -x+2*ln(1+x) revegf A006353 17.3742 -(-5-3*x+x^3-x^2-4*x^4)/(1+x+x^3+x^5+x^2+x^4) ogf_with_Euler_Transform A006353 17.3742 -(-5-3*x-4*x^4+x^3-x^2)/(x^2+1+x+x^4+x^3+x^5) ogf_with_Euler_Transform A006353 17.3742 -(-5-3*x-x^2+x^3-4*x^4)/(1+x+x^2+x^3+x^4+x^5) ogf_with_Euler_Transform A006355 35.7633 -(-x+1+x^2)/(x^2-1+x) ogf A006355 37.5515 -(x^2-x+1)/(x^2+x-1) ogf A006355 34.1377 1-x+x^2+(x^2-1+x)*f(x) ogf A006355 25.0343 2*x*(-2+x)/(x^2-x+1)/(x^2+x-1) lgdogf A006355 17.0689 {-a(n+3)+a(n+2)+a(n+1),a(0)=1,a(1)=0,a(2)=2} ogf A006356 24.2943 -(-1-x+x^2)/(-x^2+1-2*x+x^3) ogf A006356 17.006 -(3+x^4-2*x^3)/(x^2-x-1)/(x^3-x^2-2*x+1) lgdogf A006356 26.1631 -(x^2-x-1)/(1-2*x+x^3-x^2) ogf A006356 9.06987 11+11*x-11*x^2+(14+47*x-11*x^3-14*x^2)*f(x)+(-25+50*x+25*x^2-25*x^3)*f(x)^2 ogf A006356 13.6048 {a(n+3)-2*a(n+2)-a(n+1)+a(n),a(0)=1,a(1)=3,a(2)=6} ogf A006357 20.7548 -(-1-2*x+x^3+x^2)/(x+1)/(x^3-3*x+1) ogf A006357 19.1163 -(1+2*x-x^3-x^2)/(3*x^2-1+2*x-x^4-x^3) ogf A006357 10.3774 -(4+4*x-2*x^4+x^6+2*x^5-4*x^3+2*x^2)/(x+1)/(x^3-3*x+1)/(x^3+x^2-2*x-1) lgdogf A006357 7.56687 -11-22*x+11*x^3+11*x^2+(28+12*x+11*x^4-6*x^3-50*x^2)*f(x)+(-17+34*x+51*x^2-17*x^3-17*x^4)*f(x)^2 ogf A006358 12.013 -(1+2*x-x^3-3*x^2+x^4)/(3*x^2-1+3*x-x^4-4*x^3+x^5) ogf A006358 7.06649 -(5+5*x^4-4*x^6+8*x^5-10*x^3-2*x^7+x^8)/(x-1)/(x^3-3*x-1)/(x^5-x^4-4*x^3+3*x^2+3*x-1) lgdogf A006358 13.0576 -(x-1)*(x^3-3*x-1)/(3*x^2-1+3*x-x^4-4*x^3+x^5) ogf A006359 11.6295 -(1+3*x+x^5-4*x^3-3*x^2+x^4)/(6*x^2-1+3*x-5*x^4-4*x^3+x^6+x^5) ogf A006360 4.70749 -2*(25+537*x+4716*x^4+133*x^6+1371*x^5+6111*x^3+3042*x^2+3*x^7)/(x-1)/(x+1)/(x^6+36*x^5+279*x^4+594*x^3+279*x^2+36*x+1) lgdogf A006367 38.5798 (x-1)^2/(x^2+x-1)^2 ogf A006367 20.3616 -(-1+2*x-x^2)/(-x^2+1-2*x+x^4+2*x^3) ogf A006367 8.62373 -11+22*x-11*x^2+(6-12*x+11*x^4+22*x^3-16*x^2)*f(x)+(5*x^4-5*x^2+5-10*x+10*x^3)*f(x)^2 ogf A006367 27.1488 -2*x*(-2+x)/(x-1)/(x^2+x-1) lgdogf A006367 9.16271 {(n+4)*a(n+4)+(-2*n-6)*a(n+3)-4*a(n+2)+(n+3)*a(n+1),a(0)=1,a(1)=0,a(2)=2,a(3)=2} ogf A006368 19.6727 (1+3*x+3*x^3+x^2+x^4)/(x^2+1)/(x-1)^2/(x+1)^2 ogf A006368 21.592 -(-x-x^5-x^3-3*x^2-3*x^4)/(1-x^4-x^2+x^6) ogf A006368 9.94686 -(3+4*x+21*x^4+9*x^6+6*x^5+12*x^3+15*x^2+2*x^7)/(x-1)/(x+1)/(1+x^2)/(x^4+3*x^3+x^2+3*x+1) lgdogf A006369 22.4799 (x^2+1)*(x^2+3*x+1)/(x-1)^2/(x^2+x+1)^2 ogf A006369 21.3834 -(-x-x^5-2*x^3-3*x^2-3*x^4)/(1-2*x^3+x^6) ogf A006369 11.5358 -(3+4*x+8*x^4+2*x^6+9*x^5+19*x^3+15*x^2)/(x-1)/(x^2+x+1)/(x^2+3*x+1)/(1+x^2) lgdogf A006370 31.6551 (2*x^2+x+4)/(x-1)^2/(x+1)^2 ogf A006370 18.9931 -(1+20*x+4*x^3+3*x^2)/(x-1)/(x+1)/(2*x^2+x+4) lgdogf A006370 31.6551 -(4+x+2*x^2)/(-1+2*x^2-x^4) ogf A006370 8.3793 209348+52337*x+104674*x^2+(6743+14770*x-52337*x^4+134214*x^2)*f(x)+(-14770-14770*x^4+29540*x^2)*f(x)^2 ogf A006380 13.0327 (1-x+x^2+x^4+x^6+x^8-x^7)/(x^2+1)/(x^2+x+1)^2/(x+1)^2/(x-1)^8 ogf A006398 0.918902 1+(-2+4*x)*f(x)+(4*x^2+1-4*x)*f(x)^2 ogf A006399 0.918902 1+(-2+4*x)*f(x)+(4*x^2+1-4*x)*f(x)^2 ogf A006408 2.52034 -(x+13)*(5*x+3)/(x-1)/(x^2+11*x+4) lgdogf A006408 4.08055 -(x^2+11*x+4)/(x-1)^7 ogf A006411 39.6807 (3+2*x)/(x-1)^6 ogf A006411 12.4002 -(3+2*x)/(-15*x^2-1+6*x+6*x^5-x^6+20*x^3-15*x^4) ogf A006411 25.8787 -10*(x+2)/(2*x+3)/(x-1) lgdogf A006411 8.503 {(-3*n-9)*a(n+3)+(22+n)*a(n+2)+(12+2*n)*a(n+1),a(0)=3,a(1)=20,a(2)=75} ogf A006414 41.682 (x^2+3*x+1)/(x-1)^6 ogf A006414 23.9987 -(9+17*x+4*x^2)/(x-1)/(x^2+3*x+1) lgdogf A006414 7.26567 -110259-208267*x-49004*x^2+(76718+146273*x-12251*x^3+4150*x^2)*f(x)+(-7163-14326*x+14326*x^2+7163*x^3)*f(x)^2 lgdogf A006414 8.60824 {(n+4)*a(n+4)+(-3+2*n)*a(n+3)+(-21-2*n)*a(n+2)+(-5-n)*a(n+1),a(0)=1,a(1)=9,a(2)=40,a(3)=125} ogf A006416 26.579 (1+4*x+2*x^3-6*x^2)/(x-1)^4 ogf A006416 15.9474 -(1+4*x+2*x^3-6*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A006416 17.0865 -2*(x+1)*(x-2)^2/(x-1)/(2*x^3-6*x^2+4*x+1) lgdogf A006416 7.17633 -65-260*x-130*x^3+390*x^2+(58-288*x+65*x^4-274*x^3+432*x^2)*f(x)+(42*x^2+7-28*x+7*x^4-28*x^3)*f(x)^2 ogf A006416 7.17633 {(78+69*n+15*n^2)*a(n+1)+(-396-262*n-44*n^2)*a(n+2)+(151*n+192+29*n^2)*a(n+3),a(0)=1,a(1)=8,a(2)=20} ogf A006419 10.7871 x+(-1+7*x-12*x^2)*f(x)+(-8*x^3+16*x^4+x^2)*f(x)^2 ogf A006419 5.80844 {(120+88*n+16*n^2)*a(n+1)+(-70-50*n-8*n^2)*a(n+2)+(10+7*n+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=7} ogf A006431 7.32731 (-1-2*x+5*x^5+17*x^9+32*x^11-x^3-3*x^2+2*x^4+12*x^6+28*x^12+36*x^13+14*x^8+21*x^10+13*x^7)/(-1+4*x^3) ogf A006431 7.04818 -(-5*x^6+x-36*x^14-28*x^13-32*x^12-21*x^11-17*x^10-14*x^9-13*x^8-12*x^7-2*x^5+3*x^3+2*x^2+x^4)/(-1+4*x^3) ogf A006438 35.2577 -(x-4)/(x^2+1-8*x) lgdegf A006438 30.2209 -1+(1-8*x+x^2)*f(x)^2 egf A006438 25.3856 -5/2*exp(-x)-3/2*exp(x)+4 revegf A006438 33.4021 1/(1-8*x+x^2)^(1/2) egf A006438 9.61574 {(-4*n-n^2-4)*a(n+1)+(20+8*n)*a(n+2)-a(n+3),a(0)=1,a(1)=4,a(2)=47} ogf A006442 31.4552 -(-5+x)/(x^2+1-10*x) lgdogf A006442 28.5956 -1+(1-10*x+x^2)*f(x)^2 ogf A006442 31.4552 1/(x^2-10*x+1)^(1/2) ogf A006442 9.25152 {(-n-3)*a(n+3)+(25+10*n)*a(n+2)+(-2-n)*a(n+1),a(0)=1,a(1)=5,a(2)=37} ogf A006446 24.8359 (x^3-x^2-x-1)/(x^2+x+1)^2/(x-1)^3 ogf A006446 19.9899 -(-1-x+x^3-x^2)/(x^6+1-x+2*x^4-2*x^3-x^7) ogf A006446 14.1308 -2*(2*x^2+1)*(x^3-x^2-2*x-1)/(x-1)/(x^2+x+1)/(x^3-x^2-x-1) lgdogf A006451 13.4019 (-2-3*x+x^3+2*x^2)/(x-1)/(-1+2*x+x^2)/(-2*x-1+x^2) ogf A006451 6.76861 -(-5-20*x-19*x^4+5*x^6-16*x^5+42*x^3+19*x^2+2*x^7)/(x-1)/(-1+x^2+2*x)/(x^2-2*x-1)/(x^3+2*x^2-3*x-2) lgdogf A006451 13.6754 -(2*x-2*x^3+3*x^2-x^4)/(-1+x+6*x^2-6*x^3-x^4+x^5) ogf A006452 14.8897 -(-1-x+2*x^3+4*x^2)/(-1+2*x+x^2)/(-2*x-1+x^2) ogf A006452 8.93382 -(1+4*x+9*x^4+2*x^6+8*x^5-4*x^3)/(-1+x^2+2*x)/(x^2-2*x-1)/(2*x^3+4*x^2-x-1) lgdogf A006452 20.3041 -(1+x-2*x^3-4*x^2)/(-1-x^4+6*x^2) ogf A006452 7.283 31+31*x-62*x^3-124*x^2+(-143-112*x-31*x^4+224*x^3+634*x^2)*f(x)+(112+112*x^4-672*x^2)*f(x)^2 ogf A006453 21.5083 -(-6+x)/(x^2+1-12*x) lgdegf A006453 17.2067 -7/2*exp(-x)-5/2*exp(x)+6 revegf A006453 19.553 1+(-1+12*x-x^2)*f(x)^2 egf A006453 21.5083 1/(1-12*x+x^2)^(1/2) egf A006453 6.32598 {(-4*n-n^2-4)*a(n+1)+(30+12*n)*a(n+2)-a(n+3),a(0)=1,a(1)=6,a(2)=107} ogf A006454 11.7975 -(3*x+3*x^3+12*x^2)/(-1+x+34*x^2+x^5-34*x^3-x^4) ogf A006454 6.58466 -(5+70*x-41*x^4+3*x^6+14*x^5-276*x^3+33*x^2)/(x-1)/(x^2+6*x+1)/(1-6*x+x^2)/(x^2+4*x+1) lgdogf A006454 12.87 -3*(x^2+4*x+1)/(x-1)/(1+6*x+x^2)/(1-6*x+x^2) ogf A006457 13.3105 (1+x+2*x^3)/(2*x-1)/(2*x^2-1)/(x-1)^2 ogf A006457 10.7063 -(-1-x-2*x^3)/(3*x^2+1-4*x-10*x^4+4*x^5+6*x^3) ogf A006457 6.56652 -(5-x+12*x^4+16*x^6-4*x^5-4*x^3-16*x^2)/(x-1)/(2*x-1)/(2*x^2-1)/(2*x^3+x+1) lgdogf A006458 13.3599 (1+2*x+6*x^5+x^2+2*x^4)/(-1+3*x)/(2*x^3+2*x^2-1)/(x-1)^2 ogf A006458 11.8755 -(-1-2*x-6*x^5-x^2-2*x^4)/(5*x^2+1-5*x-4*x^4-8*x^5+5*x^3+6*x^6) ogf A006468 3.02511 -(37+4*x+4*x^3-17*x^2)/(x-1)/(x^3-4*x^2+2*x+5) lgdogf A006468 4.96982 -1/(x-1)^7*(x^3-4*x^2+2*x+5) ogf A006469 2.83396 -(-79-48*x+15*x^2)/(x-1)/(3*x^2-9*x-10) lgdogf A006469 4.60518 1/(x-1)^7*(3*x^2-9*x-10) ogf A006469 1.08357 {(-10*n-40)*a(n+4)+(82+n)*a(n+3)+(72+12*n)*a(n+2)+(-18-3*n)*a(n+1),a(0)=10,a(1)=79,a(2)=340,a(3)=1071} ogf A006470 69.7076 (3*x+2)/(x-1)^6 ogf A006470 21.7836 -(2+3*x)/(-15*x^2-1+6*x+6*x^5-x^6+20*x^3-15*x^4) ogf A006470 45.4615 -15*(x+1)/(3*x+2)/(x-1) lgdogf A006470 14.9373 {(-2*n-6)*a(n+3)+(13-n)*a(n+2)+(18+3*n)*a(n+1),a(0)=2,a(1)=15,a(2)=60} ogf A006471 2.80509 -4*(21+94*x+7*x^3+73*x^2)/(x-1)/(4*x^3+35*x^2+34*x+5) lgdogf A006471 4.64593 1/(x-1)^10*(4*x^3+35*x^2+34*x+5) ogf A006472 13.8469 {(n^2+5*n+6)*a(n+1)-2*a(n+2),a(0)=1,a(1)=1} ogf A006478 26.7264 -(-3-x+5*x^2)/(x-1)/(x^2+x-1) lgdogf A006478 26.7264 -1/(-1+3*x-x^2-3*x^3+x^4+x^5) ogf A006478 38.7533 -1/(x-1)/(x^2+x-1)^2 ogf A006478 9.68833 {(-n-4)*a(n+4)+(9+2*n)*a(n+3)+a(n+2)+(-6-n)*a(n+1),a(0)=1,a(1)=3,a(2)=8,a(3)=18} ogf A006479 17.8219 (x^2+x+1)/(x-1)/(x^2+x-1)^3 ogf A006479 9.07911 -(-5-6*x+5*x^4+4*x^3+5*x^2)/(x-1)/(x^2+x+1)/(x^2+x-1) lgdogf A006479 8.44198 -(x^5+x^3+x^4)/(-1+4*x-3*x^2-5*x^3+5*x^4-x^7+3*x^5-2*x^6) ogf A006480 19.1486 hypergeom([1/3,2/3],[1],27*x) ogf A006480 9.41202 {(-60-81*n-27*n^2)*a(n+1)+(n^2+4*n+4)*a(n+2),a(0)=1,a(1)=6} ogf A006483 24.0778 -(-1+6*x^2)/(1-3*x-2*x^2+4*x^3) ogf A006483 24.0778 -(-1+6*x^2)/(x-1)/(4*x^2+2*x-1) ogf A006483 14.0833 -(3-8*x+24*x^4+6*x^2)/(x-1)/(-1+2*x+4*x^2)/(-1+6*x^2) lgdogf A006483 9.33016 111-666*x^2+(-196+333*x-444*x^3+732*x^2)*f(x)+(-170*x^2+340*x^3+85-255*x)*f(x)^2 ogf A006483 13.8225 {a(n+3)-3*a(n+2)-2*a(n+1)+4*a(n),a(0)=1,a(1)=3,a(2)=5} ogf A006484 35.8827 -(1-2*x+5*x^2)/(x-1)^5 ogf A006484 22.5549 -(3+2*x+15*x^2)/(x-1)/(5*x^2-2*x+1) lgdogf A006484 16.1106 -(x+5*x^3-2*x^2)/(-1+5*x-10*x^2+x^5+10*x^3-5*x^4) ogf A006484 8.67495 {(n+3)*a(n+4)+(-3*n-9)*a(n+3)+(5+7*n)*a(n+2)+(-15-5*n)*a(n+1),a(0)=0,a(1)=1,a(2)=3,a(3)=10} ogf A006490 28.3006 (1-2*x+2*x^2)/(x^2+x-1)^2 ogf A006490 18.6188 -(-1+2*x-2*x^2)/(-x^2+1-2*x+x^4+2*x^3) ogf A006490 16.8456 -2*x*(3+2*x^2-3*x)/(2*x^2-2*x+1)/(x^2+x-1) lgdogf A006490 6.80303 467-934*x+934*x^2+(-192+384*x-467*x^4-934*x^3+1017*x^2)*f(x)+(-275+550*x-275*x^4+275*x^2-550*x^3)*f(x)^2 ogf A006490 8.62823 {(-12-7*n-n^2)*a(n+1)+(-6*n-8-n^2)*a(n+2)+(5*n+6+n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=3} ogf A006490 8.62823 {(-7*n-12-n^2)*a(n+1)+(-6*n-8-n^2)*a(n+2)+(6+5*n+n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=3} ogf A006491 23.092 (x-1)*(1-2*x+2*x^2)/(x^2+x-1)^3 ogf A006491 16.2693 -(1-3*x-2*x^3+4*x^2)/(x^6-1+3*x+3*x^5-5*x^3) ogf A006491 13.0155 -x*(-8+6*x^3-16*x^2+17*x)/(x-1)/(2*x^2-2*x+1)/(x^2+x-1) lgdogf A006491 6.75331 {(8+2*n)*a(n+1)+(30+13*n+n^2)*a(n+2)+(7*n+12+n^2)*a(n+3)+(-7*n-12-n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=4,a(3)=5} ogf A006492 14.4817 (1-2*x+2*x^2)*(x-1)^2/(x^2+x-1)^4 ogf A006492 6.37196 -(1-4*x-6*x^3+7*x^2+2*x^4)/(-x^8-1+4*x-2*x^6-2*x^2-8*x^3+5*x^4+8*x^5-4*x^7) ogf A006492 8.38415 -2*x*(-5+4*x^3-11*x^2+11*x)/(x-1)/(2*x^2-2*x+1)/(x^2+x-1) lgdogf A006492 3.08321 {(-388*n-165*n^2-17*n^3)*a(n)+(1740+1417*n+222*n^2+5*n^3)*a(n+1)+(816*n+612+333*n^2+39*n^3)*a(n+2)+(-584*n-510-204*n^2-22*n^3)*a(n+3),a(0)=1,a(1)=0,a(2)=5} ogf A006493 24.1502 (1-2*x+2*x^2)*(x-1)^3/(x^2+x-1)^5 ogf A006493 13.9817 -x*(-12+10*x^3-28*x^2+27*x)/(x-1)/(2*x^2-2*x+1)/(x^2+x-1) lgdogf A006493 5.42148 {(-336-146*n-21*n^2-n^3)*a(n+1)+(448+120*n+8*n^2)*a(n+2)+(180*n+288+34*n^2+2*n^3)*a(n+3)+(-94*n-168-17*n^2-n^3)*a(n+4),a(0)=1,a(1)=0,a(2)=6,a(3)=7} ogf A006495 30.466 -(-1+x)/(5*x^2+1-2*x) ogf A006495 18.2796 -(1-10*x+5*x^2)/(x-1)/(5*x^2-2*x+1) lgdogf A006495 31.9894 -(x-1)/(1-2*x+5*x^2) ogf A006495 13.0569 3-3*x+(-7+10*x-15*x^2)*f(x)+(20*x^2+4-8*x)*f(x)^2 ogf A006495 16.8365 {a(n+2)-2*a(n+1)+5*a(n),a(0)=1,a(1)=1} ogf A006496 31.7462 -2*(-1+5*x)/(5*x^2-2*x+1) lgdogf A006496 34.5067 2*x+(-1+2*x-5*x^2)*f(x) ogf A006496 52.9103 2/(1-2*x+5*x^2) ogf A006496 20.8856 {a(n+2)-2*a(n+1)+5*a(n),a(0)=0,a(1)=2} ogf A006497 31.0622 (3*x-2)/(-1+3*x+x^2) ogf A006497 17.7498 -(-3-4*x+3*x^2)/(3*x-2)/(x^2+3*x-1) lgdogf A006497 31.0622 -(2-3*x)/(x^2-1+3*x) ogf A006497 11.5045 34-51*x+(-43+90*x+17*x^2)*f(x)+(13-39*x-13*x^2)*f(x)^2 ogf A006497 16.7904 {-a(n+2)+3*a(n+1)+a(n),a(0)=2,a(1)=3} ogf A006498 20.6584 -(x+1)*(4*x^2-x+1)/(1+x^2)/(x^2+x-1) lgdogf A006498 17.7072 -1+(2-x-x^4-x^3)*f(x)+(x^3+x^4-1+x)*f(x)^2 ogf A006498 37.1851 -1/(x^2+1)/(x^2+x-1) ogf A006498 49.5802 1/(1-x-x^3-x^4) ogf A006498 13.5219 {a(n+4)-a(n+3)-a(n+1)-a(n),a(0)=1,a(1)=1,a(2)=1,a(3)=2} ogf A006499 20.4773 -(1+2*x+2*x^3+6*x^2)/(-1+x+x^3+x^4) ogf A006499 18.8606 -(1+2*x+2*x^3+6*x^2)/(x^2+1)/(x^2+x-1) ogf A006499 9.0722 -(3+12*x+12*x^4+2*x^6+12*x^5+4*x^3+3*x^2)/(1+x^2)/(x^2+x-1)/(2*x^3+6*x^2+2*x+1) lgdogf A006499 7.79026 -52-104*x-104*x^3-312*x^2+(77-2*x-52*x^4-2*x^3+150*x^2)*f(x)+(-25+25*x^3+25*x+25*x^4)*f(x)^2 ogf A006499 12.5738 {-a(n+4)+a(n+3)+a(n+1)+a(n),a(0)=1,a(1)=3,a(2)=9,a(3)=12} ogf A006500 10.4201 -(-1+2*x^6-x+x^7+x^5-3*x^3-x^2-x^4)/(-x^2+1-x+x^8-x^4+x^3-x^6-x^5+x^7) ogf A006500 12.7966 -(-1-x+x^5-3*x^3-x^2-x^4+2*x^6+x^7)/(x^2+x-1)/(x^6-x^3-1) ogf A006501 29.9922 (x^2+1)/(x^2+x+1)^2/(x-1)^4 ogf A006501 15.279 -(1+x^2)/(-x^6-1+2*x-x^2+2*x^3-4*x^4+2*x^5+2*x^7-x^8) ogf A006501 16.1958 -2*(1+2*x+3*x^4+x^3+5*x^2)/(x-1)/(1+x^2)/(x^2+x+1) lgdogf A006501 62.2914 2+x+2*x^2-x^3 ogf_with_Euler_Transform A006501 5.91086 {(-252-120*n-19*n^2-n^3)*a(n+1)+(-80-25*n-2*n^2)*a(n+2)+(-47-19*n-2*n^2)*a(n+3)+(65*n+100+14*n^2+n^3)*a(n+4),a(0)=1,a(1)=2,a(2)=4,a(3)=8} ogf A006501 21.8862 {a(n+4),a(0)=2,a(1)=1,a(2)=2,a(3)=-1} ogf_with_Euler_Transform A006503 17.6468 -(-3*x+2*x^2)/(1-4*x+x^4+6*x^2-4*x^3) ogf A006503 38.4078 -(-3+2*x)/(x-1)^4 ogf A006503 26.1173 -2*(-5+3*x)/(x-1)/(2*x-3) lgdogf A006503 6.33914 -3687*x+2458*x^2+(1229-5138*x+1229*x^4-4916*x^3+7522*x^2)*f(x)+(74*x^4+74-296*x-296*x^3+444*x^2)*f(x)^2 ogf A006503 9.19622 {(-6-3*n)*a(n+3)+(15+5*n)*a(n+2)+(-6-2*n)*a(n+1),a(0)=0,a(1)=3,a(2)=10} ogf A006504 17.5427 -(-5+5*x-x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A006504 23.2182 -(20-18*x+3*x^2)/(x-1)/(x^2-5*x+5) lgdogf A006504 39.471 -(5-5*x+x^2)/(x-1)^5 ogf A006504 8.13835 {(-5*n-20)*a(n+4)+(50+10*n)*a(n+3)+(-30-6*n)*a(n+2)+(n+4)*a(n+1),a(0)=5,a(1)=20,a(2)=51,a(3)=105} ogf A006505 59.2382 -x-1+exp(x) lgdegf A006505 14.4804 {-a(n+1)+(n+2)*a(n+2),a(0)=0,a(1)=0,a(2)=1/2} lgdegf A006516 16.6633 -1/16*(-1-6*x+(1+12*x+4*x^2)^(1/2))/x revogf A006516 22.8349 -2*(-3+8*x)/(4*x-1)/(2*x-1) lgdogf A006516 36.2672 1/(4*x-1)/(2*x-1) ogf A006516 29.3591 x+(-1+6*x-8*x^2)*f(x) ogf A006516 41.1028 x/(1-6*x+8*x^2) ogf A006516 16.2248 {a(n+2)-6*a(n+1)+8*a(n),a(0)=0,a(1)=1} ogf A006522 19.9089 -(-5*x+10*x^2-9*x^3+1+4*x^4)/(x-1)^5 ogf A006522 12.1478 -(5*x-10*x^2+9*x^3-1-4*x^4)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A006522 14.0533 -x^2*(4*x^2-2*x+3)/(x-1)/(4*x^4-9*x^3+10*x^2-5*x+1) lgdogf A006522 7.02666 1-5*x+4*x^4-9*x^3+10*x^2+(-2+10*x+x^5-9*x^4+19*x^3-20*x^2)*f(x)+(1-5*x+10*x^2-10*x^3+5*x^4-x^5)*f(x)^2 ogf A006522 6.45693 {(4*n+4*n^2)*a(n)+(4*n+10-6*n^2)*a(n+1)+(21*n+22+5*n^2)*a(n+2)+(-9*n-3*n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=0,a(3)=1} ogf A006527 50.1493 (x^2+1)/(x-1)^4 ogf A006527 22.7952 -(-x-x^3)/(1-4*x+x^4+6*x^2-4*x^3) ogf A006527 28.9323 -2*(2+x+x^2)/(x-1)/(1+x^2) lgdogf A006527 21.4926 -x-x^3+(1-4*x+x^4+6*x^2-4*x^3)*f(x) ogf A006527 107.463 4+x-x^3 ogf_with_Euler_Transform A006527 8.95524 {(n+3)*a(n+4)+(-6-n)*a(n+3)+(n-1)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=4,a(3)=11} ogf A006528 14.7916 -(-x-4*x^3-x^2)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A006528 34.7601 -(1+4*x^2+x)/(x-1)^5 ogf A006528 20.4471 -6*(1+2*x+2*x^2)/(x-1)/(4*x^2+x+1) lgdogf A006528 8.17886 {(n+3)*a(n+4)-6*a(n+3)+(-9+3*n)*a(n+2)+(-12-4*n)*a(n+1),a(0)=0,a(1)=1,a(2)=6,a(3)=24} ogf A006529 21.5197 -(1+5*x+77*x^3+17*x^2)/(x-1)^5 ogf A006529 11.3261 -(x+17*x^3+5*x^2+77*x^4)/(-1+5*x-10*x^2+10*x^3-5*x^4+x^5) ogf A006529 11.9554 -2*(5+27*x+77*x^3+141*x^2)/(x-1)/(77*x^3+17*x^2+5*x+1) lgdogf A006529 5.92285 {(5928+3554*n+295*n^2)*a(n+1)+(4788-3912*n-630*n^2)*a(n+2)+(-944+198*n+335*n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=10} ogf A006542 13.1491 -(-1-3*x-x^2)/(21*x^2+1-7*x+35*x^4-21*x^5+7*x^6-35*x^3-x^7) ogf A006542 38.79 -(x^2+3*x+1)/(x-1)^7 ogf A006542 24.2437 -5*(2+4*x+x^2)/(x-1)/(x^2+3*x+1) lgdogf A006542 8.52527 {(-n-4)*a(n+4)+(4-2*n)*a(n+3)+(24+2*n)*a(n+2)+(6+n)*a(n+1),a(0)=1,a(1)=10,a(2)=50,a(3)=175} ogf A006548 4.95698 {(420+428*n+144*n^2+16*n^3)*a(n+1)+(14+4*n)*a(n+2)+(-2-n)*a(n+3),a(0)=0,a(1)=24,a(2)=240} egf A006550 16.6794 (-1-3*x+6*x^5-10*x^3-8*x^2-14*x^4)/(x-1)^7 ogf A006550 8.33969 -(-6*x^6+x+14*x^5+8*x^3+3*x^2+10*x^4)/(-1+7*x-21*x^2+35*x^3-35*x^4+21*x^5-7*x^6+x^7) ogf A006550 8.9812 -2*(-5-17*x-6*x^4+6*x^5-48*x^3-35*x^2)/(x-1)/(6*x^5-14*x^4-10*x^3-8*x^2-3*x-1) lgdogf A006564 35.3366 (6*x^2+8*x+1)/(x-1)^4 ogf A006564 19.0274 -(1+8*x+6*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A006564 21.202 -12*(1+3*x+x^2)/(x-1)/(6*x^2+8*x+1) lgdogf A006564 7.81125 {(n+4)*a(n+4)+(9+7*n)*a(n+3)+(-40-2*n)*a(n+2)+(-18-6*n)*a(n+1),a(0)=1,a(1)=12,a(2)=48,a(3)=124} ogf A006565 17.1113 -(1+7*x+49*x^3+53*x^2+10*x^4)/(x-1)^7 ogf A006565 8.1169 -(x+10*x^5+53*x^3+49*x^4+7*x^2)/(-1+7*x-21*x^2+x^7+35*x^3-35*x^4+21*x^5-7*x^6) ogf A006565 9.17562 -2*(7+74*x+15*x^4+118*x^3+206*x^2)/(x-1)/(10*x^4+49*x^3+53*x^2+7*x+1) lgdogf A006566 31.7133 (1+16*x+10*x^2)/(x-1)^4 ogf A006566 16.9629 -(-x-10*x^3-16*x^2)/(1-4*x+6*x^2-4*x^3+x^4) ogf A006566 18.7027 -4*(5+17*x+5*x^2)/(x-1)/(10*x^2+16*x+1) lgdogf A006566 5.44333 19553*x+195530*x^3+312848*x^2+(-19553+81371*x-19553*x^4+109802*x^3-66774*x^2)*f(x)+(-18954*x^2-3159+12636*x-3159*x^4+12636*x^3)*f(x)^2 ogf A006566 7.59798 {(n+3)*a(n+4)+(10+15*n)*a(n+3)+(-74-6*n)*a(n+2)+(-20-10*n)*a(n+1),a(0)=0,a(1)=1,a(2)=20,a(3)=84} ogf A006571 15.6825 -(-2-2*x-2*x^2-2*x^3-2*x^4-2*x^5-2*x^6-2*x^7-2*x^8-2*x^9-4*x^10)/(-1+x^11) ogf_with_Euler_Transform A006578 28.8873 -(-x-2*x^2)/(1-2*x+2*x^3-x^4) ogf A006578 38.0787 -(2*x+1)/(x+1)/(x-1)^3 ogf A006578 23.2703 -2*(2+4*x+3*x^2)/(x-1)/(2*x+1)/(x+1) lgdogf A006578 9.20584 -319*x-638*x^2+(319-503*x-319*x^4+638*x^3+270*x^2)*f(x)+(-135+270*x-270*x^3+135*x^4)*f(x)^2 ogf A006578 10.2162 {(-3-n)*a(n+4)-2*n*a(n+3)+(9+n)*a(n+2)+(6+2*n)*a(n+1),a(0)=0,a(1)=1,a(2)=4,a(3)=8} ogf A006584 27.8518 -2*(1+3*x)/(x-1)/(x+1) lgdogf A006584 15.7113 -2*x^3/(-1+2*x+x^2-4*x^3+x^4+2*x^5-x^6) ogf A006584 36.0435 2/(x+1)^2/(x-1)^4 ogf A006584 10.0449 {-a(n+3)*n+2*a(n+2)+(n+4)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=2} ogf A006587 18.913 -27-27*f(x)+(4-108*x)*f(x)^3 ogf A006587 16.0474 3*hypergeom([1/3,2/3],[1/2],27*x) ogf A006587 8.27445 {(120+162*n+54*n^2)*a(n+1)+(-7*n-6-2*n^2)*a(n+2),a(0)=3,a(1)=36} ogf A006588 19.728 -1-3*f(x)+(4-108*x)*f(x)^3 ogf A006588 16.5461 hypergeom([1/3,2/3],[1/2],27*x) ogf A006588 8.01452 {(120+162*n+54*n^2)*a(n+1)+(-7*n-6-2*n^2)*a(n+2),a(0)=1,a(1)=12} ogf A006589 24.074 (3*x-2)/(x-1)/(2*x-1)^2 ogf A006589 16.7788 -(-2*x+3*x^2)/(1-5*x+8*x^2-4*x^3) ogf A006589 14.5711 -(7-18*x+12*x^2)/(x-1)/(2*x-1)/(3*x-2) lgdogf A006589 15.82 2*x-3*x^2+(-1+5*x-8*x^2+4*x^3)*f(x) ogf A006589 10.0673 {-a(n+3)+5*a(n+2)-8*a(n+1)+4*a(n),a(0)=0,a(1)=2,a(2)=7} ogf A006592 18.6434 -(-4*x-16*x^3-40*x^2)/(1-4*x+6*x^2-4*x^3+x^4) ogf A006592 22.0778 -2*(7+19*x+4*x^2)/(x-1)/(4*x^2+10*x+1) lgdogf A006592 34.9565 4*(4*x^2+10*x+1)/(x-1)^4 ogf A006592 9.02102 {(n+3)*a(n+4)+(4+9*n)*a(n+3)+(-44-6*n)*a(n+2)+(-8-4*n)*a(n+1),a(0)=0,a(1)=4,a(2)=56,a(3)=216} ogf A006595 15.5252 -(-2+2*x-x^2)/(6*x^2+2-6*x-2*x^3) egf A006595 17.0778 -(4-2*x+x^2)/(x-1)/(x^2-2*x+2) lgdegf A006595 21.3472 -1/2*(2-2*x+x^2)/(x-1)^3 egf A006595 6.8311 14-14*x+7*x^2+(62-34*x+14*x^3-4*x^2)*f(x)+(-228*x^2-76+228*x+76*x^3)*f(x)^2 egf A006595 4.87936 {(-4-4*n-n^2)*a(n+1)+(14+8*n+n^2)*a(n+2)+(-26-11*n-n^2)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=2,a(2)=7,a(3)=33} ogf A006597 35.7151 (4*x^2+10*x+1)/(x-1)^4 ogf A006597 18.7079 -(-x-4*x^3-10*x^2)/(1-4*x+6*x^2-4*x^3+x^4) ogf A006597 20.6771 -2*(7+19*x+4*x^2)/(x-1)/(4*x^2+10*x+1) lgdogf A006597 8.54056 {(n+3)*a(n+4)+(4+9*n)*a(n+3)+(-44-6*n)*a(n+2)+(-8-4*n)*a(n+1),a(0)=0,a(1)=1,a(2)=14,a(3)=54} ogf A006603 17.6272 -1+(1-x-2*x^2)*f(x)+(x^2-x^4-x-x^3)*f(x)^2 ogf A006604 16.2407 -1+(1+x-2*x^2)*f(x)+(x^2-x^4-2*x+x^3)*f(x)^2 ogf A006605 19.9392 1/2*(-x+1+(-(1+x)*(-1+3*x))^(1/2))*x revogf A006629 14.3639 1+(-1+4*x)*f(x)+2*x^2*f(x)^2-x^4*f(x)^3 ogf A006629 23.3413 16*x/(1+(1+4*x)^(1/2))^4 revogf A006629 6.83161 {(504+573*n+216*n^2+27*n^3)*a(n+1)+(-116*n-112-38*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=4} ogf A006630 8.99304 216+(-36+324*x)*f(x)+(-24*x+162*x^2)*f(x)^2+(27*x^3-4*x^2)*f(x)^3 lgdogf A006630 7.12863 {(990+897*n+270*n^2+27*n^3)*a(n+1)+(-166*n-180-46*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=6} ogf A006631 11.336 512+(-64+576*x)*f(x)+(-32*x+216*x^2)*f(x)^2+(27*x^3-4*x^2)*f(x)^3 lgdogf A006631 8.77191 {(1716+1293*n+324*n^2+27*n^3)*a(n+1)+(-224*n-264-54*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=8} ogf A006632 69.2393 -x*(x-1)^3 revogf A006632 7.8681 {(3568*n+256*n^3+1664*n^2+2520)*a(n+1)+(-27*n^3-216*n^2-573*n-504)*a(n+2),a(0)=1,a(1)=3} ogf A006633 3.64999 {(-17160-24104*n-12656*n^2-2944*n^3-256*n^4)*a(n+1)+(3492*n+2640+1680*n^2+351*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=6} ogf A006634 6.79472 {(-43680-48488*n-20144*n^2-3712*n^3-256*n^4)*a(n+1)+(6252*n+5460+2517*n^2+432*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=9} ogf A006635 3.41053 {(-93024-85400*n-29360*n^2-4480*n^3-256*n^4)*a(n+1)+(10092*n+9792+3516*n^2+513*n^3+27*n^4)*a(n+2),a(0)=1,a(1)=12} ogf A006645 34.3465 -4*(x+1)/(x^2-1+2*x) lgdogf A006645 20.816 -x^2+(1-4*x+2*x^2+4*x^3+x^4)*f(x) ogf A006645 42.9331 1/(-1+2*x+x^2)^2 ogf A006645 25.4418 x^2/(1-4*x+2*x^2+4*x^3+x^4) ogf A006645 10.7333 {(-1-n)*a(n+3)+(2*n+4)*a(n+2)+(n+3)*a(n+1),a(0)=0,a(1)=0,a(2)=1} ogf A006645 10.7333 {(-n-1)*a(n+3)+(2*n+4)*a(n+2)+(n+3)*a(n+1),a(0)=0,a(1)=0,a(2)=1} ogf A006646 13.2915 -2*(-3+4*x+12*x^2)/(2*x-1)/(4*x^2+4*x-1) lgdogf A006646 17.1503 -2*x^2+(1-6*x+4*x^2+8*x^3)*f(x) ogf A006646 19.6911 -2*x^2/(-1+6*x-4*x^2-8*x^3) ogf A006646 23.1156 2/(2*x-1)/(4*x^2+4*x-1) ogf A006646 9.66653 {-a(n+3)+6*a(n+2)-4*a(n+1)-8*a(n),a(0)=0,a(1)=0,a(2)=2} ogf A006659 14.8045 32/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^4 ogf A006659 15.6269 32/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^4 ogf A006659 9.37615 {(-56-30*n-4*n^2)*a(n+1)+(8*n+12+n^2)*a(n+2),a(0)=2,a(1)=12} ogf A006668 14.2665 -2*(-3+4*x+12*x^2)/(2*x-1)/(4*x^2+4*x-1) lgdogf A006668 19.6779 -x^2+(1-6*x+4*x^2+8*x^3)*f(x) ogf A006668 22.8264 -x^2/(-1+6*x-4*x^2-8*x^3) ogf A006668 24.8113 1/(2*x-1)/(4*x^2+4*x-1) ogf A006668 10.3756 {-a(n+3)+6*a(n+2)-4*a(n+1)-8*a(n),a(0)=0,a(1)=0,a(2)=1} ogf A006670 2.01331 -(-1-x^10-2*x^8+x^5-2*x^6)/(-x^3+1-x+x^2+x^6+x^4-x^5+x^10+x^7) ogf_with_Euler_Transform A006673 9.62211 1/2*2^(1/2)*(arctanh(1/2*(-1+x)*2^(1/2))+arctanh(1/2*2^(1/2))) revegf A006673 11.6975 {-a(n)*n+(2*n+2)*a(n+1)+(n+2)*a(n+2),a(0)=0,a(1)=1} revegf A006674 1.34552 1+(-2+2*x)*f(x)+(x^2+1-2*x)*f(x)^2 egf A006675 4.62305 {(-24-44*n-30*n^2-9*n^3-n^4)*a(n+1)+(15+26*n+13*n^2+2*n^3)*a(n+2)+(-2-3*n-n^2)*a(n+3),a(0)=0,a(1)=0,a(2)=2} ogf A006675 6.03251 {(n^2+4*n+4)*a(n+1)+(-5-7*n-2*n^2)*a(n+2)+(2+3*n+n^2)*a(n+3),a(0)=0,a(1)=0,a(2)=1} egf A006678 10.7006 -(-1+2*x+2*x^2+(-(2*x^2+2*x-1)*(x+2)^2)^(1/2))/(2*x^2+2*x-1)/(x+1)^2 egf A006678 29.1056 -2*x+2*f(x)+(-1-x)*f(x)^2 egf A006678 45.4775 -x*(x-2)/(2+x^2) revegf A006678 10.1061 {-2*a(n)*n+(-4*n-3)*a(n+1)-a(n+2)*n+(n+3)*a(n+3),a(0)=0,a(1)=1,a(2)=1/2} egf A006679 15.7113 -ln(2+x^2)+ln(1+x)+ln(2) revegf A006684 19.8169 -(-3+4*x^3+9*x^2)/(x^2+x-1)/(x^2+2*x-1) lgdogf A006684 28.6244 -x^2+(1-3*x+3*x^3+x^4)*f(x) ogf A006684 33.6026 -x^2/(-1+3*x-3*x^3-x^4) ogf A006684 32.2025 1/(x^2+x-1)/(-1+2*x+x^2) ogf A006684 12.881 {-a(n+4)+3*a(n+3)-3*a(n+1)-a(n),a(0)=0,a(1)=0,a(2)=1,a(3)=3} ogf A006707 20.5542 -(-7-3*x+3*x^2+7*x^3)/(1+x+x^2+x^3+x^4+x^5) ogf_with_Euler_Transform A006707 20.5542 -(-7-3*x+7*x^3+3*x^2)/(1+x+x^3+x^5+x^2+x^4) ogf_with_Euler_Transform A006707 20.5542 -(-7-3*x+7*x^3+3*x^2)/(x^2+1+x+x^4+x^5+x^3) ogf_with_Euler_Transform A006708 27.7357 -(1+8*x+6*x^2+8*x^3+x^4)/(1-x^6) ogf_with_Euler_Transform A006709 21.1373 -(-2-4*x-12*x^2-4*x^3-2*x^4)/(-1+x^6) ogf_with_Euler_Transform A006710 18.188 -(4*x+4*x^3+8*x^4+4*x^5+4*x^7)/(-1+x^10) ogf_with_Euler_Transform A006821 2.61658 -1-x^3+(2*x^3+3)*f(x)+(-x^3-3)*f(x)^2+f(x)^3 ogf A006822 10.2367 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A006847 13.2797 (-1)^(1/4)/(x-1)^(1/4)*(x+1)^(1/4)*exp(1/2*(x+1)*x) egf A006847 16.9316 (2+2*x-2*x^3-x^2)*f(x)+(-2+2*x^2)*f(x)^2 lgdegf A006847 19.9196 1/2*(-2-2*x+2*x^3+x^2)/(x-1)/(x+1) lgdegf A006847 6.91088 {(-2*n-10)*a(n+5)+2*a(n+4)+(8+2*n)*a(n+3)-a(n+2)-2*a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=5/6,a(4)=7/12} egf A006848 5.6245 (-1)^(1/4)/(x-1)^(1/4)*(x+1)^(1/4)*exp(1/2*x*(-x+x^3-3+2*x^2)/(x-1)/(x+1)) egf A006848 10.1515 (2+x+x^4+x^5-2*x^3-2*x^2)/(x-1)^2/(x+1)^2 lgdegf A006857 9.16665 -(-1-6*x-x^3-6*x^2)/(-x^9+1-9*x-36*x^7+36*x^2-126*x^5-84*x^3+126*x^4+84*x^6+9*x^8) ogf A006857 28.9102 -(x+1)*(x^2+5*x+1)/(x-1)^9 ogf A006857 15.6597 -3*(5+20*x+2*x^3+15*x^2)/(x-1)/(x+1)/(x^2+5*x+1) lgdogf A006857 13.1871 {(-42-13*n-n^2)*a(n+1)+(5*n+6+n^2)*a(n+2),a(0)=1,a(1)=15} ogf A006858 10.3532 -(-x-7*x^3-x^4-7*x^2)/(1-7*x+7*x^6+21*x^2-35*x^3+35*x^4-21*x^5-x^7) ogf A006858 26.6795 -(x+1)*(1+6*x+x^2)/(x-1)^7 ogf A006858 14.4514 -2*(7+28*x+2*x^3+19*x^2)/(x-1)/(x+1)/(x^2+6*x+1) lgdogf A006858 7.45877 {(-28-15*n-2*n^2)*a(n+1)+(62+24*n+4*n^2)*a(n+2)+(-10-9*n-2*n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=14} ogf A006859 18.9366 (x+1)*(x^4+19*x^3+56*x^2+19*x+1)/(x-1)^10 ogf A006859 10.0832 -5*(6+66*x+25*x^4+x^5+121*x^3+165*x^2)/(x-1)/(x+1)/(x^4+19*x^3+56*x^2+19*x+1) lgdogf A006859 5.79405 {(66+23*n+2*n^2)*a(n+1)+(-552-150*n-12*n^2)*a(n+2)+(252+90*n+12*n^2)*a(n+3)+(-17*n-36-2*n^2)*a(n+4),a(0)=1,a(1)=30,a(2)=330,a(3)=2145} ogf A006864 22.5849 -1/(-1+2*x+2*x^2-2*x^3+x^4) ogf A006864 13.2564 -2*(1+2*x+2*x^3-3*x^2)/(2*x^2-1+2*x+x^4-2*x^3) lgdogf A006864 9.52801 -x+(1-4*x-x^4+2*x^3-2*x^2)*f(x)+(2-4*x-4*x^2+4*x^3-2*x^4)*f(x)^2 ogf A006864 24.3917 x/(1-2*x-2*x^2+2*x^3-x^4) ogf A006865 27.4409 -(-1-3*x)/(-2*x^3+1-11*x) ogf A006865 29.8271 -(3*x+1)/(2*x^3-1+11*x) ogf A006865 16.7322 -2*(7+6*x^3+3*x^2)/(3*x+1)/(2*x^3+11*x-1) lgdogf A006865 10.7191 65+195*x+(458+2284*x+130*x^3)*f(x)+(-523+5753*x+1046*x^3)*f(x)^2 ogf A006865 14.0005 {a(n+3)-11*a(n+2)-2*a(n),a(0)=1,a(1)=14,a(2)=154} ogf A006882 6.69468 {(-6-5*n-n^2)*a(n+1)+(-16-8*n-n^2)*a(n+2)+(n+2)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=1,a(2)=2,a(3)=3} ogf A006904 11.587 -(1+7*x+2*x^3+2*x^2)/(2*x-1)/(x+1)/(x^2+x+1) lgdogf A006904 19.6087 -(x^2+x+1)/(2*x-1)/(x+1)^2 ogf A006904 6.62112 69+69*x+69*x^2+(214+283*x+138*x^3+490*x^2)*f(x)+(-283+566*x^3+849*x^2)*f(x)^2 ogf A006904 11.0832 {-a(n+3)+3*a(n+1)+2*a(n),a(0)=1,a(1)=1,a(2)=4} ogf A006918 40.7964 -2*(1+3*x)/(x-1)/(x+1) lgdogf A006918 52.7953 1/(x+1)^2/(x-1)^4 ogf A006918 179.504 2+2*x ogf_with_Euler_Transform A006918 15.4745 {(-2-n)*a(n+3)+2*a(n+2)+(6+n)*a(n+1),a(0)=0,a(1)=1,a(2)=2} ogf A006922 64.4096 24/(1-x) ogf_with_Euler_Transform A006922 24.537 {a(n+1)-a(n),a(0)=24} ogf_with_Euler_Transform A006950 38.1949 -(-1-x^2-x^3)/(1-x^4) ogf_with_Euler_Transform A006963 14.0181 {(2*n+4*n^2)*a(n)+(-1-n)*a(n+1),a(0)=1,a(1)=1} ogf A006974 45.179 (x-1)/(2*x-1)^5 ogf A006974 15.4019 -(-1+x)/(40*x^2+1-10*x-32*x^5-80*x^3+80*x^4) ogf A006974 29.4646 -(-9+8*x)/(2*x-1)/(x-1) lgdogf A006974 9.82152 {(n+3)*a(n+3)+(-15-3*n)*a(n+2)+(10+2*n)*a(n+1),a(0)=1,a(1)=9,a(2)=50} ogf A006975 24.7888 -(-11+10*x)/(2*x-1)/(x-1) lgdogf A006975 11.4763 -(1-x)/(-60*x^2-1+12*x+192*x^5-64*x^6+160*x^3-240*x^4) ogf A006975 38.7325 -(x-1)/(2*x-1)^6 ogf A006975 8.85314 {(n+3)*a(n+3)+(-17-3*n)*a(n+2)+(12+2*n)*a(n+1),a(0)=1,a(1)=11,a(2)=72} ogf A006976 40.1343 (x-1)/(2*x-1)^7 ogf A006976 9.55578 -(-1+x)/(84*x^2+1-14*x-672*x^5+448*x^6-280*x^3+560*x^4-128*x^7) ogf A006976 24.0806 -(-13+12*x)/(2*x-1)/(x-1) lgdogf A006976 8.6002 {(n+3)*a(n+3)+(-19-3*n)*a(n+2)+(14+2*n)*a(n+1),a(0)=1,a(1)=13,a(2)=98} ogf A006977 6.80797 -(-1-3*x+4*x^5-3*x^3-x^2-2*x^4)/(x-1)/(2*x+1)/(2*x-1)/(x+1)/(x^2+1) ogf A006979 8.0295 -(-2-2*x+15*x^4+21*x^6+24*x^5+4*x^3+16*x^7+9*x^8)/(x^4+x^3+x^2+x-1)/(x^5+x^4+x^3+x^2+x-1) lgdogf A006979 17.4299 1/(x^4+x^3+x^2+x-1)/(x^5+x^4+x^3+x^2+x-1) ogf A006980 5.77903 -(-2-2*x+10*x^4+35*x^6+24*x^5+4*x^3+11*x^10+32*x^7+20*x^9+27*x^8)/(x^5+x^4+x^3+x^2+x-1)/(x^6+x^5+x^4+x^3+x^2+x-1) lgdogf A006980 10.7054 -1/(-1+2*x+x^2-x^4-2*x^5-4*x^6-5*x^7-4*x^8-3*x^9-2*x^10-x^11) ogf A006980 13.3272 1/(x^5+x^4+x^3+x^2+x-1)/(x^6+x^5+x^4+x^3+x^2+x-1) ogf A006981 6.16952 3+x+2*x^2+(-7-6*x^2)*f(x)+(4+6*x^2)*f(x)^2+(-2*x-x^2)*f(x)^3 ogf A007004 23.3525 hypergeom([1/3,2/3],[2],27*x) ogf A007004 11.4783 {(-60-81*n-27*n^2)*a(n+1)+(5*n+6+n^2)*a(n+2),a(0)=1,a(1)=3} ogf A007009 14.9061 -(-1-x-x^2)/(x^2+1-3*x-5*x^4-x^5+3*x^6+5*x^3-x^7) ogf A007009 28.0922 -(1+x^2+x)/(x+1)^2/(x-1)^5 ogf A007009 16.986 -(4+12*x+5*x^3+9*x^2)/(x-1)/(x+1)/(x^2+x+1) lgdogf A007009 81.1554 4+2*x-x^2 ogf_with_Euler_Transform A007009 5.03723 {(-2202-865*n-83*n^2)*a(n+1)+(-6970-2035*n-131*n^2)*a(n+2)+(-1432+57*n+83*n^2)*a(n+3)+(1131*n+2428+131*n^2)*a(n+4),a(0)=1,a(1)=4,a(2)=12,a(3)=27} ogf A007009 24.3466 {a(n+3),a(0)=4,a(1)=2,a(2)=-1} ogf_with_Euler_Transform A007010 7.10388 -1/(x-1)^9/(x+1)^3*(1+6*x+21*x^2+28*x^3+21*x^4+6*x^5+x^6) ogf A007010 4.04921 -6*(2+15*x+68*x^4+8*x^6+35*x^5+77*x^3+46*x^2+x^7)/(x-1)/(x+1)/(x^6+6*x^5+21*x^4+28*x^3+21*x^2+6*x+1) lgdogf A007019 9.77652 {(2*n^2+9*n+10)*a(n+1)-a(n+2),a(0)=1,a(1)=3} ogf A007021 2.17532 1+(-3+3*x)*f(x)+(3-6*x+3*x^2)*f(x)^2+(3*x-3*x^2+x^3-1)*f(x)^3 ogf A007026 2.15923 -1-x^4+(2*x^4+3)*f(x)+(-x^4-3)*f(x)^2+f(x)^3 ogf A007039 10.4201 -(1-2*x-x^4+2*x^6-4*x^3+7*x^2)/(x+1)/(x^2-x+1)/(x^2+x-1)/(2*x^2-2*x+1) lgdogf A007039 23.5292 -(2-2*x+4*x^3)/(-x^2-1+2*x+x^4) ogf A007039 17.3668 -2*(x+1)*(2*x^2-2*x+1)/(1-x+x^2)/(x^2+x-1) ogf A007039 8.2887 -224+224*x-448*x^3+(82-194*x-112*x^4-60*x^3+112*x^2)*f(x)+(15+15*x^2-15*x^4-30*x)*f(x)^2 ogf A007040 9.99186 (1+6*x+7*x^4+2*x^6+6*x^5+4*x^3+7*x^2)/(x^2+x+1)/(x^4-2*x^2-x-1)/(x^2+x-1) lgdogf A007040 18.7027 -(-2-2*x+2*x^4-4*x^2)/(1-x^4-x^2-2*x^3) ogf A007040 19.1949 2*(-1-x-2*x^2+x^4)/(1+x^2+x)/(x^2+x-1) ogf A007040 7.15104 328+328*x-328*x^4+656*x^2+(-314-150*x+314*x^4+328*x^3-136*x^2)*f(x)+(-75*x^4-75*x^2+75-150*x^3)*f(x)^2 ogf A007043 4.53138 -1/2*(5*x-2)*(2*x+x*(1/(x-1)/(5*x-1))^(1/2)-(1/(x-1)/(5*x-1))^(1/2)+1)/x/(x-1)/(5*x+4) lgdogf A007051 33.5266 -(-1+2*x)/(3*x^2+1-4*x) ogf A007051 35.0505 -(2*x-1)/(3*x-1)/(x-1) ogf A007051 20.2924 -2*(1-3*x+3*x^2)/(x-1)/(3*x-1)/(2*x-1) lgdogf A007051 17.5253 1-2*x+(2*x-3*x^2)*f(x)+(-1+4*x-3*x^2)*f(x)^2 ogf A007051 20.2924 {a(n+2)-4*a(n+1)+3*a(n),a(0)=1,a(1)=2} ogf A007052 18.0752 (-1+x)*f(x)+(2*x^2+1-4*x)*f(x)^2 ogf A007052 27.5431 -(-1+x)/(2*x^2+1-4*x) ogf A007052 17.0119 -(3-4*x+2*x^2)/(x-1)/(2*x^2-4*x+1) lgdogf A007052 28.9203 -(x-1)/(2*x^2+1-4*x) ogf A007052 14.1074 -1/2*(-1-4*x+(1+4*x+8*x^2)^(1/2))/(2*x+1) revogf A007052 15.2212 {a(n+2)-4*a(n+1)+2*a(n),a(0)=1,a(1)=3} ogf A007054 8.3038 (1-4*x-(-4*x+1)^(1/2)+8*(-4*x+1)^(1/2)*x)/(1+(-4*x+1)^(1/2))/x/(-4*x+1)^(1/2) ogf A007054 8.75881 (1-4*x-(1-4*x)^(1/2)+8*(1-4*x)^(1/2)*x)/(1+(1-4*x)^(1/2))/x/(1-4*x)^(1/2) ogf A007054 20.6256 -3+16*x+(1-6*x)*f(x)+x^2*f(x)^2 ogf A007054 13.6041 3/32+3/16*x-1/32*x^2-1/32*((x-9)*(x-1)^3)^(1/2) revogf A007054 14.5317 {(-4*n-6)*a(n+1)+(n+4)*a(n+2),a(0)=3,a(1)=2} ogf A007055 25.5407 1+(-2+4*x)*f(x)+(4*x^2+1-4*x)*f(x)^2 ogf A007068 21.9942 -(-1-3*x+2*x^3)/(1-4*x^2+2*x^4) ogf A007068 9.88144 -(3+8*x-10*x^4+4*x^6-8*x^3+6*x^2)/(x+1)/(2*x^2-2*x-1)/(2*x^4-4*x^2+1) lgdogf A007068 18.9394 -(x+1)*(2*x^2-2*x-1)/(1-4*x^2+2*x^4) ogf A007068 8.31487 45+135*x-90*x^3+(-11+102*x-90*x^4-68*x^3+180*x^2)*f(x)+(-34+136*x^2-68*x^4)*f(x)^2 ogf A007070 31.5393 -1/(-1+4*x-2*x^2) ogf A007070 15.3191 -1/4*(-1-4*x+(1+8*x+8*x^2)^(1/2))/x revogf A007070 10.5131 -23+(-18-92*x+46*x^2)*f(x)+(82*x^2+41-164*x)*f(x)^2 ogf A007070 24.3713 -4*(x-1)/(2*x^2+1-4*x) lgdogf A007070 35.7446 1/(2*x^2+1-4*x) ogf A007070 13.7479 {-a(n+2)+4*a(n+1)-2*a(n),a(0)=1,a(1)=4} ogf A007086 8.55917 -(-1-x-7*x^11-2*x^3-x^2-2*x^4+2*x^6-2*x^12+x^15-15*x^8+2*x^7-21*x^16+22*x^17)/(1+x^2+x)/(x-1)^2 ogf A007090 6.99525 (1+x+x^5+x^9+7*x^11+7*x^3+x^2+x^4+x^6+x^12+x^13+x^14+67*x^15+x^8+x^10+7*x^7)/(x+1)/(1+x^2)/(x^4+1)/(x^8+1)/(x-1)^2 ogf A007090 8.22122 -(-x-7*x^12-x^13-x^3-7*x^4-x^10-67*x^16-x^15-x^14-x^5-x^6-x^7-7*x^8-x^11-x^2-x^9)/(1-x+x^17-x^16) ogf A007095 12.5936 (1+x+x^5+x^3+x^2+x^4+x^6+2*x^8+x^7)/(1+x^2+x)/(1+x^3+x^6)/(x-1)^2 ogf A007095 15.159 -(-x-x^3-x^4-x^5-x^6-x^7-x^8-x^2-2*x^9)/(1-x-x^9+x^10) ogf A007096 32.2638 -(-4+2*x-4*x^2)/(1-x^4) ogf_with_Euler_Transform A007102 6.00386 1-420*x+35*x^4+(-3+1260*x-70*x^4)*f(x)+(3-1260*x+35*x^4)*f(x)^2+(420*x-1)*f(x)^3 ogf A007109 6.02505 4-95*x+96*x^5+(-12+285*x-192*x^5)*f(x)+(12-285*x+96*x^5)*f(x)^2+(95*x-4)*f(x)^3 ogf A007113 24.8428 (ln(x+1)*x+ln(x+1)+x)/(x+1) lgdegf A007113 9.7211 {-n^2*a(n)+(-3*n^2-6*n-3)*a(n+1)+(-6*n-4-2*n^2)*a(n+2),a(0)=0,a(1)=2} lgdegf A007114 8.29983 {n^2*a(n)+(-3*n^2-6*n-3)*a(n+1)+(6*n+4+2*n^2)*a(n+2),a(0)=0,a(1)=-2} lgdegf A007115 4.06088 {(2*n^2+n^3)*a(n)+(-16*n^2-26*n-12-2*n^3)*a(n+1)+(-20*n^2-32*n-16-4*n^3)*a(n+2)+(33*n+18+18*n^2+3*n^3)*a(n+3),a(0)=0,a(1)=-2,a(2)=-9/2} lgdegf A007120 8.6002 {-n^2*a(n)+(9*n+5+4*n^2)*a(n+1)+(-9*n-6-3*n^2)*a(n+2),a(0)=-1,a(1)=-3} lgdegf A007123 198.744 x+1 lgdegf A007123 3.87164 {(144+216*n+104*n^2+16*n^3)*a(n+1)+(-12-40*n-4*n^3-24*n^2)*a(n+2)+(-80-100*n-4*n^3-36*n^2)*a(n+3)+(29*n+20+10*n^2+n^3)*a(n+4),a(0)=1,a(1)=1,a(2)=2,a(3)=4} ogf A007151 15.1892 (exp(-x)+2*exp(-x)*x-1)*exp(x)/(1+x) revegf A007160 3.84535 {(-216-84*n-8*n^2)*a(n+1)+(-1644-470*n-34*n^2)*a(n+2)+(-388-33*n+n^2)*a(n+3)+(28*n+80+2*n^2)*a(n+4),a(0)=1,a(1)=20,a(2)=225,a(3)=1925} ogf A007165 21.9455 -x*(-1-2*x+x^2)/(1+x)/(2*x+1) revogf A007165 13.8352 1+(-1+3*x)*f(x)+(-2*x+2*x^2)*f(x)^2+x^2*f(x)^3 ogf A007179 12.6978 -(1+4*x+8*x^3-14*x^2)/(x-1)/(2*x-1)/(2*x^2-1) lgdogf A007179 22.8561 -(x-1)/(2*x-1)/(-1+2*x^2) ogf A007179 19.7035 -(x-x^2)/(-1+2*x+2*x^2-4*x^3) ogf A007179 10.2036 x-x^2+(-1+3*x-4*x^3+x^2)*f(x)+(2*x^2-1+2*x-4*x^3)*f(x)^2 ogf A007179 10.3891 {-a(n+3)+2*a(n+2)+2*a(n+1)-4*a(n),a(0)=0,a(1)=1,a(2)=1} ogf A007183 7.27251 (1+x^4+x^8-2*x^9+2*x^10-x^13+x^14-x^15+x^16-x^17+x^18-x^19+x^20)/(x-1)^2 ogf A007191 54.5147 24/(-1+x^2) ogf_with_Euler_Transform A007191 59.9662 24/(x^2-1) ogf_with_Euler_Transform A007191 19.9887 {-a(n+2)+a(n),a(0)=-24,a(1)=0} ogf_with_Euler_Transform A007202 17.4697 (1+10*x+10*x^3+20*x^2+x^4)/(x+1)/(x-1)^4 ogf A007202 12.048 -(1+10*x+10*x^3+20*x^2+x^4)/(-2*x^2-1+3*x+3*x^4-2*x^3-x^5) ogf A007202 9.31715 -(13+75*x+23*x^4+x^5+94*x^3+130*x^2)/(x-1)/(x+1)/(x^4+10*x^3+20*x^2+10*x+1) lgdogf A007202 7.20398 {(-n-n^2)*a(n)+(36+7*n+n^2)*a(n+1)+(24+n+n^2)*a(n+2)+(-7*n-12-n^2)*a(n+3),a(0)=1,a(1)=13,a(2)=57} ogf A007204 13.0475 -(-1-20*x-20*x^3-54*x^2-x^4)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A007204 22.3672 -(1+20*x+20*x^3+54*x^2+x^4)/(x-1)^5 ogf A007204 12.4262 -(25+188*x+x^4+44*x^3+222*x^2)/(x-1)/(x^4+20*x^3+54*x^2+20*x+1) lgdogf A007226 30.2147 (-1+(1-x)^(1/2))*(x-1) revogf A007226 17.0442 2-x+(-1-2*x)*f(x)+2*x*f(x)^2-x^2*f(x)^3 ogf A007226 10.5512 {(27*n^2+81*n+60)*a(n+1)+(-4*n^2-18*n-18)*a(n+2),a(0)=2,a(1)=3} ogf A007228 33.7071 (x-1)*((1-x)^(1/3)-1) revogf A007228 8.13619 {(1152*n^2+1712*n+256*n^3+840)*a(n+1)+(-27*n^3-162*n^2-303*n-180)*a(n+2),a(0)=3,a(1)=6} ogf A007249 54.4991 12/(-1+x^2) ogf_with_Euler_Transform A007249 59.949 12/(x^2-1) ogf_with_Euler_Transform A007249 19.983 {-a(n+2)+a(n),a(0)=-12,a(1)=0} ogf_with_Euler_Transform A007259 80.0484 8/(-1+x^2) ogf_with_Euler_Transform A007259 88.9426 8/(x^2-1) ogf_with_Euler_Transform A007259 27.6029 {-a(n+2)+a(n),a(0)=-8,a(1)=0} ogf_with_Euler_Transform A007262 6.69737 -(-6-6*x)/(-1+x^3) ogf_with_Euler_Transform A007272 5.72278 (-28*x^2+32*(-4*x+1)^(1/2)*x^2+11*x-9*(-4*x+1)^(1/2)*x-1+(-4*x+1)^(1/2))/(1+(-4*x+1)^(1/2))/x^2/(-4*x+1)^(1/2) ogf A007272 5.99529 (-28*x^2+32*(1-4*x)^(1/2)*x^2+11*x-9*(1-4*x)^(1/2)*x-1+(1-4*x)^(1/2))/(1+(1-4*x)^(1/2))/x^2/(1-4*x)^(1/2) ogf A007272 13.1147 -10+95*x-256*x^2+(1-10*x+30*x^2)*f(x)-x^3*f(x)^2 ogf A007272 13.989 {(-4*n-6)*a(n+1)+(n+5)*a(n+2),a(0)=10,a(1)=5} ogf A007275 3.87402 1+(-3+18*x)*f(x)+(3-36*x+108*x^2)*f(x)^2+(18*x-108*x^2+216*x^3-1)*f(x)^3 ogf A007283 32.4884 -1/2*ln(3)+1/2*ln(2*x+3) revegf A007283 77.9722 -2/(2*x-1) lgdogf A007283 51.9814 -3+(1-2*x)*f(x) ogf A007283 77.9722 -3/(2*x-1) ogf A007283 86.6357 3/(1-2*x) ogf A007283 86.6357 x/(3+2*x) revogf A007283 35.4419 {a(n+1)-2*a(n),a(0)=3} ogf A007290 91.6792 -4/(x-1) lgdogf A007290 20.9553 2*x^3+(-1+4*x-6*x^2+4*x^3-x^4)*f(x) ogf A007290 25.2908 2*x^3/(1-4*x+6*x^2-4*x^3+x^4) ogf A007290 81.4927 2/(x-1)^4 ogf A007290 12.8673 {(-1+n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=2} ogf A007290 13.097 {(n-1)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=2} ogf A007291 12.3468 -(-7-28*x-9*x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A007291 15.196 -(63+130*x+27*x^2)/(x-1)/(9*x^2+28*x+7) lgdogf A007291 25.7672 -(7+28*x+9*x^2)/(x-1)^5 ogf A007291 6.0474 {(7*n+28)*a(n+4)+21*a(n+3)*n+(-168-19*n)*a(n+2)+(-36-9*n)*a(n+1),a(0)=7,a(1)=63,a(2)=254,a(3)=710} ogf A007291 6.0474 {(7*n+28)*a(n+4)+21*n*a(n+3)+(-168-19*n)*a(n+2)+(-36-9*n)*a(n+1),a(0)=7,a(1)=63,a(2)=254,a(3)=710} ogf A007293 1.45937 (1+2*x^5-3*x^2+x^4+2*x^6)/(-x^3+1-4*x^2+3*x^5+2*x^4+4*x^6) ogf A007297 36.5105 -x*(x-1)/(1+x)^3 revogf A007297 13.5853 1+(-1+3*x)*f(x)+(x+3*x^2)*f(x)^2+x^3*f(x)^3 ogf A007297 8.00229 {(-108*n^2-648*n-924)*a(n+1)+(n^2+7*n+12)*a(n+3),a(0)=4,a(1)=30,a(2)=256} lgdogf A007299 1.74485 1+(-2+2*x)*f(x)+(1+x^2-2*x)*f(x)^2 ogf A007307 30.6269 -(2*x+1)/(-1+x^2+x^3) ogf A007307 16.0791 -(2+2*x+4*x^3+5*x^2)/(2*x+1)/(x^3+x^2-1) lgdogf A007307 27.9637 -(x+2*x^2)/(-1+x^2+x^3) ogf A007307 10.7194 -6*x-12*x^2+(6-5*x-6*x^3-16*x^2)*f(x)+(5-5*x^3-5*x^2)*f(x)^2 ogf A007307 15.3135 {-a(n+3)+a(n+1)+a(n),a(0)=0,a(1)=1,a(2)=2} ogf A007309 29.3549 -(1+4*x)/(-1+x^2+x^3) ogf A007309 15.4113 -(4+2*x+8*x^3+7*x^2)/(4*x+1)/(x^3+x^2-1) lgdogf A007309 26.8023 -(x+4*x^2)/(-1+x^2+x^3) ogf A007309 7.8032 465*x+1860*x^2+(-465+172*x+465*x^3+1153*x^2)*f(x)+(-172+172*x^3+172*x^2)*f(x)^2 ogf A007309 14.6774 {-a(n+3)+a(n+1)+a(n),a(0)=0,a(1)=1,a(2)=4} ogf A007310 25.5064 (1+4*x+x^2)/(x+1)/(x-1)^2 ogf A007310 22.7735 -(-1-4*x-x^2)/(-x^2+1-x+x^3) ogf A007310 15.1824 -(5+9*x+x^3+9*x^2)/(x-1)/(x+1)/(x^2+4*x+1) lgdogf A007310 8.98112 -19-76*x-19*x^2+(11-51*x+19*x^3-27*x^2)*f(x)+(8-8*x-8*x^2+8*x^3)*f(x)^2 ogf A007310 13.2846 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=1,a(1)=5,a(2)=7} ogf A007312 6.79876 -x*(-1-x-x^2+3*x^4+2*x^5-3*x^8+3*x^6-3*x^7-3*x^9+2*x^11+x^12)/(x-1)/(x^4+x^3-1)/(x^8+3*x^7-x^5-2*x^4-x^3+1) revogf A007317 25.0537 -1+(1-x)*f(x)+(-x+x^2)*f(x)^2 ogf A007317 15.4586 -1/2*(-(x-1)^(1/2)+(5*x-1)^(1/2))/(x-1)^(1/2)/x ogf A007317 7.72932 -1/2*(x-1+2*x*(x-1)^(1/2)*(5*x-1)^(1/2)-(x-1)^(1/2)*(5*x-1)^(1/2))/x/(x-1)^(3/2)/(5*x-1)^(1/2) lgdogf A007317 42.7386 x*(x-1)/(x^2-x-1) revogf A007317 10.5298 {(-5*n-10)*a(n+1)+(6*n+16)*a(n+2)+(-n-4)*a(n+3),a(0)=1,a(1)=2,a(2)=5} ogf A007325 29.7764 -(-1+x^2)/(-1-x-x^2-x^3-x^4) ogf_with_Euler_Transform A007325 30.8793 -(x^2-1)/(-1-x-x^2-x^3-x^4) ogf_with_Euler_Transform A007331 83.2047 -8/(-1-x) ogf_with_Euler_Transform A007332 31.8792 -(-6-6*x-12*x^2)/(-1+x^3) ogf_with_Euler_Transform A007339 10.3296 -(1+x^4*exp(x)+2*x^3*exp(x)-2*x^2*exp(x)-x*exp(x))/(x-1) egf A007375 1.52903 -1+(3-3*x)*f(x)+(-3+6*x-3*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 ogf A007380 13.5259 -(-1-2*x-x^3-x^5-x^6)/(1-x^2-x^7) ogf A007380 13.5259 -(1+2*x+x^3+x^5+x^6)/(-1+x^2+x^7) ogf A007380 5.07221 -(2+2*x+4*x^4+4*x^6+6*x^5+5*x^2+2*x^11+x^12+8*x^7+4*x^9)/(x^6+x^5+x^3+2*x+1)/(x^7+x^2-1) lgdogf A007382 10.8235 (-x+x^3-3+2*x^2)/(x^2+x-1)/(x-1)^2/(x+1)^2 ogf A007382 5.82802 -(4+14*x+x^4+3*x^6+10*x^5-24*x^3-12*x^2)/(x-1)/(x+1)/(x^2+x-1)/(x^3+2*x^2-x-3) lgdogf A007382 8.26519 -(x^3-x^5+3*x^2-2*x^4)/(-1+x+3*x^2-2*x^3-3*x^4+x^5+x^6) ogf A007383 16.4239 -1/(-1+x^2+x^3)/(x-1)^2/(x+1)^2 ogf A007383 10.8328 -x*(-6+7*x^3+6*x^2-3*x)/(x-1)/(x+1)/(x^3+x^2-1) lgdogf A007383 13.7605 x^2/(1-3*x^2-x^6-x^3+3*x^4+2*x^5-x^7) ogf A007384 17.2062 -1/(x^5+x^2-1)/(x-1)^2/(x+1)^2 ogf A007384 10.5344 -x*(-6-5*x^3+9*x^5+6*x^2)/(x-1)/(x+1)/(x^5+x^2-1) lgdogf A007384 13.951 x^4/(1-3*x^2+3*x^4-x^9-x^5-x^6+2*x^7) ogf A007385 17.0899 -1/(-1+x^2+x^7)/(x-1)^2/(x+1)^2 ogf A007385 10.5957 -x*(-6+6*x^2-7*x^5+11*x^7)/(x-1)/(x+1)/(x^7+x^2-1) lgdogf A007385 13.9418 x^6/(1-3*x^2+3*x^4-x^6-x^7+2*x^9-x^11) ogf A007386 17.2289 -1/(x^9+x^2-1)/(x-1)^2/(x+1)^2 ogf A007386 10.3373 -x*(-6+6*x^2-9*x^7+13*x^9)/(x-1)/(x+1)/(x^9+x^2-1) lgdogf A007386 12.6065 -x^8/(-1+3*x^2-3*x^4+x^6+x^9-2*x^11+x^13) ogf A007387 25.3126 (-2-3*x-2*x^3+3*x^6)/(x^5+x^2-1) ogf A007387 11.4085 (3+4*x+8*x^4-6*x^5+3*x^10+9*x^2+16*x^7)/(x^5+x^2-1)/(3*x^6-2*x^3-3*x-2) lgdogf A007387 21.892 -(2*x-3*x^7+3*x^2+2*x^4)/(-1+x^5+x^2) ogf A007389 14.5731 (-2-3*x-2*x^3-2*x^5-2*x^7+3*x^10+5*x^12+7*x^14)/(x^9+x^2-1) ogf A007389 13.4346 -(2*x+2*x^6+2*x^8+3*x^2+2*x^4-3*x^11-7*x^15-5*x^13)/(-1+x^2+x^9) ogf A007391 13.6629 (-3+x^2)/(-1+x^2+x^3)/(x-1)^2/(x+1)^2 ogf A007391 10.5319 -(-x^7+3*x^5)/(-1+3*x^2+x^3-3*x^4-2*x^5+x^6+x^7) ogf A007391 7.3265 -x*(16-22*x^3+5*x^5+4*x^4-20*x^2+9*x)/(x-1)/(x+1)/(x^3+x^2-1)/(x^2-3) lgdogf A007392 13.9671 (-5+3*x^2)/(x^5+x^2-1)/(x-1)^2/(x+1)^2 ogf A007392 6.98354 -x*(24+25*x^3-54*x^5+12*x^4-36*x^2+21*x^7)/(x-1)/(x+1)/(3*x^2-5)/(x^5+x^2-1) lgdogf A007393 13.6649 (-7+5*x^2)/(-1+x^2+x^7)/(x-1)^2/(x+1)^2 ogf A007393 10.2487 -(7*x^13-5*x^15)/(-1+3*x^2-3*x^4+x^6+x^7-2*x^9+x^11) ogf A007393 6.9212 -x*(32+49*x^5+20*x^4-52*x^2+45*x^9-102*x^7)/(x-1)/(x+1)/(5*x^2-7)/(x^7+x^2-1) lgdogf A007394 14.2623 (-9+7*x^2)/(x^9+x^2-1)/(x-1)^2/(x+1)^2 ogf A007394 10.2258 -(9*x^17-7*x^19)/(-1+3*x^2-3*x^4+x^6+x^9-2*x^11+x^13) ogf A007394 6.94831 -x*(40-68*x^2+28*x^4+81*x^7-166*x^9+77*x^11)/(x-1)/(x+1)/(7*x^2-9)/(x^9+x^2-1) lgdogf A007395 117.359 -1/(x-1) lgdogf A007395 72.2207 -2+(1-x)*f(x) ogf A007395 117.359 -2/(x-1) ogf A007395 67.0621 -ln(2)+ln(x+2) revegf A007395 134.124 2/(1-x) ogf A007395 134.124 x/(2+x) revogf A007395 58.6793 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A007395 46.9434 {a(n+1)-a(n),a(0)=2} ogf A007403 13.0103 -(4*x-1+3*(-x^2*(-1+8*x))^(1/2))/(-1+8*x)^2 ogf A007403 6.08091 -1+8*x-72*x^3-7*x^2+(2-40*x-512*x^3+256*x^2)*f(x)+(-384*x^2-1+32*x-4096*x^4+2048*x^3)*f(x)^2 ogf A007405 20.9033 {2*a(n)+(-n-1)*a(n+1),a(0)=2,a(1)=2} lgdegf A007412 7.87568 (3-x-11*x^6+6*x^5-47*x^24+5*x^7+23*x^25+24*x^23)/(x-1)/(x^25-x^24+x^7-x^6+x-2) lgdogf A007412 18.6152 -(-2+x-x^6+x^7+x^25-x^24)/(x-1)^2 ogf A007415 22.4818 -(-4*x-2*x^2-2*x^3)/(4-x^4) egf A007415 22.4818 -(4*x-2*x^2+2*x^3)/(-4-x^4) egf A007415 10.1168 -(4-8*x-3*x^4+2*x^5+8*x^3)/(x^2+2*x+2)/(x^2-2*x+2)/(x^2-x+2) lgdegf A007415 9.79044 -2*(x^2-2)*(x^4-2*x^3+8*x^2-4*x+4)/(2-2*x+x^2)^2/(2+2*x+x^2)^2 egf A007415 20.9313 4*x-2*x^2+2*x^3+(-4-x^4)*f(x) egf A007417 25.166 2+x-x^2-x^5+x^6+x^19-x^20 ogf_with_Euler_Transform A007420 28.9065 -1/(-1+2*x-4*x^2+4*x^3) ogf A007420 17.9689 -2*(1-4*x+6*x^2)/(-4*x^2-1+2*x+4*x^3) lgdogf A007420 22.9259 x^2+(-1+2*x-4*x^2+4*x^3)*f(x) ogf A007420 28.9065 x^2/(1-2*x+4*x^2-4*x^3) ogf A007420 12.312 {a(n+3)-2*a(n+2)+4*a(n+1)-4*a(n),a(0)=0,a(1)=0,a(2)=1} ogf A007440 18.1513 -((1+2*x+5*x^2)^(1/2)-1)/(1+2*x+5*x^2)^(1/2)/x lgdogf A007440 64.2277 -x/(-1+x+x^2) revogf A007440 34.79 1+(-1-x)*f(x)-x^2*f(x)^2 ogf A007440 24.5577 1/2*(-1-x+(2*x+1+5*x^2)^(1/2))/x^2 ogf A007440 12.4621 {(5*n+10)*a(n+1)+(2*n+7)*a(n+2)+(n+5)*a(n+3),a(0)=1,a(1)=-1,a(2)=0} ogf A007450 12.8638 -(-5*x-2*x^6+3*x^7-7*x^8+6*x^4-3*x^2-x^5)/(1-x-x^9+x^8) ogf A007450 14.1501 -(5+3*x+2*x^5-6*x^3+x^4-3*x^6+7*x^7)/(x-1)/(x^8+1) ogf A007452 25.0099 -(-4-4*x-2*x^3)/(4-x^4) egf A007452 25.0099 -(4-4*x+2*x^3)/(-4-x^4) egf A007452 9.13059 -(8-6*x^4+x^6+8*x^3-12*x^2)/(x^2+2*x+2)/(x^2-2*x+2)/(x^3-2*x+2) lgdegf A007452 15.5467 2*(2-2*x+x^3)/(2-2*x+x^2)/(2+2*x+x^2) egf A007452 9.91771 8-8*x+4*x^3+(12-20*x-2*x^4+10*x^3)*f(x)+(-5*x^4-20)*f(x)^2 egf A007452 12.2389 {-4*a(n+4)-a(n),a(0)=1,a(1)=-1,a(2)=0,a(3)=1/2} egf A007455 24.5629 -(-1-x-2*x^3)/(1-3*x^2-2*x^4) ogf A007455 24.5629 -(1+x+2*x^3)/(-1+3*x^2+2*x^4) ogf A007455 10.7928 -(x+1)*(4*x^5-4*x^4+4*x^3+4*x^2+5*x+1)/(1+2*x^3+x)/(2*x^4+3*x^2-1) lgdogf A007455 11.3067 -1-x-2*x^3+(2+x-2*x^4+2*x^3-3*x^2)*f(x)+(-1+3*x^2+2*x^4)*f(x)^2 ogf A007455 13.6986 {a(n+4)-3*a(n+2)-2*a(n),a(0)=1,a(1)=1,a(2)=3,a(3)=5} ogf A007465 8.66741 -(-1+4*x+12*x^3-6*x^4-10*x^2)/(40*x^2+1-10*x+80*x^4-80*x^3-32*x^5) ogf A007465 15.0539 -(1-4*x-12*x^3+10*x^2+6*x^4)/(2*x-1)^5 ogf A007465 8.93827 -6*(1-2*x+2*x^4-4*x^3+4*x^2)/(2*x-1)/(6*x^4-12*x^3+10*x^2-4*x+1) lgdogf A007465 6.42752 {(28+18*n+2*n^2)*a(n+1)+(-44-25*n-3*n^2)*a(n+2)+(n^2+6*n+9)*a(n+3),a(0)=1,a(1)=6,a(2)=30} ogf A007466 17.2116 -(-1+2*x-2*x^2)/(12*x^2+1-6*x-8*x^3) ogf A007466 25.8174 -(2*x^2-2*x+1)/(2*x-1)^3 ogf A007466 18.2241 -4*(1-x+x^2)/(2*x-1)/(2*x^2-2*x+1) lgdogf A007466 8.15287 7-14*x+14*x^2+(31-34*x+56*x^3-8*x^2)*f(x)+(-38+228*x-456*x^2+304*x^3)*f(x)^2 ogf A007466 11.0646 {a(n+3)-6*a(n+2)+12*a(n+1)-8*a(n),a(0)=1,a(1)=4,a(2)=14} ogf A007473 2.06311 -(-x^3-x+1+2*x^5)/(-x^2-1+2*x-2*x^4-x^5+2*x^3) ogf_with_Euler_Transform A007477 29.704 -1-x+f(x)-x^2*f(x)^2 ogf A007477 12.9148 -1/2-1/2*x^2+1/2*((1+x)*(x^3-x^2+3*x+1))^(1/2) revogf A007477 7.92107 {(-4*n-6)*a(n+1)+(-4*n-12)*a(n+2)+(n+6)*a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=2} ogf A007478 1.45186 (1-2*x^3-x+x^4+x^5+2*x^6)/(x^2+1-2*x+2*x^4-2*x^3+x^5) ogf A007481 25.0493 -(-1-2*x-x^3)/(1-3*x^2-2*x^4) ogf A007481 25.0493 -(1+2*x+x^3)/(-1+3*x^2+2*x^4) ogf A007481 12.1072 -(2+6*x+9*x^4+2*x^6+8*x^3+9*x^2)/(x^3+2*x+1)/(2*x^4+3*x^2-1) lgdogf A007481 9.68574 7+14*x+7*x^3+(19+52*x+14*x^4+26*x^3+21*x^2)*f(x)+(-26+78*x^2+52*x^4)*f(x)^2 ogf A007482 27.0134 -(3+4*x)/(2*x^2-1+3*x) lgdogf A007482 34.9585 -1/(-1+3*x+2*x^2) ogf A007482 16.9799 1/4/x*(-3*x-1+(17*x^2+6*x+1)^(1/2)) revogf A007482 12.6446 4+(-17+12*x+8*x^2)*f(x)+(13-39*x-26*x^2)*f(x)^2 ogf A007482 15.2383 {-a(n+2)+3*a(n+1)+2*a(n),a(0)=1,a(1)=3} ogf A007483 25.1596 -(-1-2*x)/(-2*x^2+1-3*x) ogf A007483 26.2535 -(2*x+1)/(-1+3*x+2*x^2) ogf A007483 16.773 -(5+4*x+4*x^2)/(2*x+1)/(2*x^2-1+3*x) lgdogf A007483 15.0957 1/4*(-3*x-1+(17*x^2+14*x+1)^(1/2))/(1+x) revogf A007483 11.393 6+12*x+(13+56*x+12*x^2)*f(x)+(-19+57*x+38*x^2)*f(x)^2 ogf A007483 15.8902 {a(n+2)-3*a(n+1)-2*a(n),a(0)=1,a(1)=5} ogf A007484 34.9082 -(2+x)/(-1+3*x+2*x^2) ogf A007484 21.561 -(7+8*x+2*x^2)/(x+2)/(2*x^2-1+3*x) lgdogf A007484 34.9082 -(x+2)/(-1+3*x+2*x^2) ogf A007484 17.4541 1/2/(2*x+1)*(-2-3*x+(4+16*x+17*x^2)^(1/2)) revogf A007484 14.0975 18+9*x+(-67-2*x+18*x^2)*f(x)+(29-87*x-58*x^2)*f(x)^2 ogf A007484 18.7967 {-a(n+2)+3*a(n+1)+2*a(n),a(0)=2,a(1)=7} ogf A007486 34.4223 -(1+2*x)/(x^2-1+x+x^3) ogf A007486 34.4223 -(2*x+1)/(x^2-1+x+x^3) ogf A007486 18.0307 -(3+2*x+4*x^3+5*x^2)/(2*x+1)/(x^3+x^2+x-1) lgdogf A007486 10.0972 -151-302*x+(126-201*x-151*x^3-151*x^2)*f(x)+(-25*x^2+25-25*x-25*x^3)*f(x)^2 ogf A007486 15.4549 {-a(n+3)+a(n+2)+a(n+1)+a(n),a(0)=1,a(1)=3,a(2)=4} ogf A007487 4.48767 -(x+x^9+14608*x^7+502*x^8+14608*x^3+88234*x^4+502*x^2+156190*x^5+88234*x^6)/(-1+11*x-165*x^8-55*x^2+55*x^9+165*x^3-11*x^10-330*x^4+x^11+462*x^5-462*x^6+330*x^7) ogf A007487 8.54794 -1/(x-1)^11*(1+502*x+14608*x^2+88234*x^3+156190*x^4+88234*x^5+14608*x^6+502*x^7+x^8) ogf A007489 11.481 {(-n-3)*a(n+1)+(n+4)*a(n+2)-a(n+3),a(0)=0,a(1)=1,a(2)=3} ogf A007492 31.3149 (x^2-2)/(x+1)/(x^2+x-1) ogf A007492 32.7383 -(2-x^2)/(x^3-1+2*x^2) ogf A007492 10.2892 -998+499*x^2+(755-499*x^3-1126*x^2)*f(x)+(-128+256*x^2+128*x^3)*f(x)^2 ogf A007492 18.4678 -x*(-6+x^3-6*x)/(x+1)/(x^2-2)/(x^2+x-1) lgdogf A007492 16.7498 {a(n+3)-2*a(n+1)-a(n),a(0)=2,a(1)=0,a(2)=3} ogf A007494 25.3036 (2*x+x^2)*f(x)+(-1+x+x^2-x^3)*f(x)^2 ogf A007494 47.9437 (x+2)/(x+1)/(x-1)^2 ogf A007494 28.4666 -(x+3)*(2*x+1)/(x-1)/(x+2)/(x+1) lgdogf A007494 18.5904 {-a(n+3)+a(n+2)+a(n+1)-a(n),a(0)=0,a(1)=2,a(2)=3} ogf A007496 3.67678 exp(1/5760*x^6) lgdegf A007502 26.6711 (1+x^3-x^2)/(x^2+x-1)^2 ogf A007502 17.5267 -(1+x^3-x^2)/(-1+2*x+x^2-2*x^3-x^4) ogf A007502 13.3356 -(2+2*x+x^4-3*x^3+3*x^2)/(x^2+x-1)/(x^3-x^2+1) lgdogf A007502 5.57669 -567-567*x^3+567*x^2+(1217-1134*x+567*x^4+1784*x^3-1217*x^2)*f(x)+(650*x^2-650*x^4-650+1300*x-1300*x^3)*f(x)^2 ogf A007502 9.15576 {-a(n+4)+2*a(n+3)+a(n+2)-2*a(n+1)-a(n),a(0)=1,a(1)=2,a(2)=4,a(3)=9} ogf A007518 32.2393 -(3+5*x)/(x-1)/(x+1) lgdogf A007518 19.539 3*x/(1-3*x+x^5+2*x^2+2*x^3-3*x^4) ogf A007518 42.9858 3/(x+1)/(x-1)^4 ogf A007518 11.117 {(-2-n)*a(n+3)+3*a(n+2)+(5+n)*a(n+1),a(0)=0,a(1)=3,a(2)=9} ogf A007518 11.117 {(-2-n)*a(n+3)+3*a(n+2)+(n+5)*a(n+1),a(0)=0,a(1)=3,a(2)=9} ogf A007526 47.9317 (x-2)/(x-1) lgdegf A007526 21.0899 -exp(x)*(x^2-x-1)/(x-1)^2 egf A007526 7.02998 {(-6-5*n-n^2)*a(n+1)+(9+6*n+n^2)*a(n+2)+(-2-n)*a(n+3),a(0)=0,a(1)=1,a(2)=4} ogf A007526 7.02998 {(-6-5*n-n^2)*a(n+1)+(n^2+6*n+9)*a(n+2)+(-2-n)*a(n+3),a(0)=0,a(1)=1,a(2)=4} ogf A007531 99.6718 -4/(x-1) lgdogf A007531 22.7821 6*x^3+(-1+4*x-6*x^2+4*x^3-x^4)*f(x) ogf A007531 27.4957 6*x^3/(1-4*x+6*x^2-4*x^3+x^4) ogf A007531 88.5972 6/(x-1)^4 ogf A007531 13.989 {(-1+n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=6} ogf A007533 18.1831 -(-2-35*x-13*x^2)/(3*x^2+1-3*x-x^3) ogf A007533 26.517 -(2+35*x+13*x^2)/(x-1)^3 ogf A007533 16.3181 -(41+96*x+13*x^2)/(x-1)/(13*x^2+35*x+2) lgdogf A007533 11.571 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=2,a(1)=41,a(2)=130} ogf A007559 54.339 -1/(3*x-1) lgdegf A007559 12.9378 -1/3*(1-2*x)^(1/2)+2/3*(1-2*x)^(1/2)*x+1/3 revegf A007559 31.9641 1+(-1+3*x)*f(x)^3 egf A007559 36.226 1/(1-3*x)^(1/3) egf A007559 14.2997 {(-3*n-4)*a(n+1)+a(n+2),a(0)=1,a(1)=1} ogf A007564 25.5663 -1+(1+2*x)*f(x)-3*x*f(x)^2 ogf A007564 12.3097 -1/2*(2*x-1+(1-8*x+4*x^2)^(1/2))/x/(1-8*x+4*x^2)^(1/2) lgdogf A007564 18.9921 -1/6*(-1-2*x+(1-8*x+4*x^2)^(1/2))/x ogf A007564 34.9855 x*(-1+3*x)/(-1+2*x) revogf A007564 6.09838 {(8*n+8*n^2)*a(n)+(-56*n-36-20*n^2)*a(n+1)+(66+52*n+10*n^2)*a(n+2)+(-7*n-12-n^2)*a(n+3),a(0)=1,a(1)=1,a(2)=4} ogf A007566 20.1998 (2*x+1)*(4*x^2-3)/(2*x-1)/(4*x^2+1) lgdegf A007566 8.62186 -51-102*x+136*x^3+68*x^2+(8-52*x-112*x^3+80*x^2)*f(x)+(12*x^2+3-6*x-24*x^3)*f(x)^2 lgdegf A007566 28.2797 -exp(x)*(4*x^2+1)/(2*x-1) egf A007572 25.6292 (-5+13*x)/(x+1)/(4*x-1) ogf A007572 25.6292 -(5-13*x)/(4*x^2-1+3*x) ogf A007572 14.0351 -2*(-1-20*x+26*x^2)/(4*x-1)/(13*x-5)/(x+1) lgdogf A007572 8.07496 -21605+56173*x+(8646-24208*x-17284*x^2)*f(x)+(3460*x^2-865+2595*x)*f(x)^2 ogf A007572 13.0994 1/2/(-13+4*x)*(-5-3*x+(25-22*x+25*x^2)^(1/2)) revogf A007572 15.1147 {-a(n+2)+3*a(n+1)+4*a(n),a(0)=5,a(1)=2} ogf A007574 16.9077 -(-1+x+2*x^5-x^3+x^2-x^4)/(x-1)^2/(x^2+x-1)^2 ogf A007574 13.8335 -(-1+x-x^3-x^4+x^2+2*x^5)/(4*x^2+1-4*x+x^6-4*x^4+2*x^3) ogf A007574 8.95112 -(3-4*x-10*x^4-2*x^6+9*x^5+7*x^3-3*x^2+2*x^7)/(x-1)/(x^2+x-1)/(2*x^5-x^4-x^3+x^2+x-1) lgdogf A007581 16.4199 -(1-5*x+5*x^2)/(-14*x^2-1+7*x+8*x^3) ogf A007581 16.4199 -(1-5*x+5*x^2)/(x-1)/(2*x-1)/(4*x-1) ogf A007581 8.95632 -(2-18*x+40*x^4-80*x^3+59*x^2)/(x-1)/(4*x-1)/(2*x-1)/(5*x^2-5*x+1) lgdogf A007581 15.5557 -1+5*x-5*x^2+(1-7*x+14*x^2-8*x^3)*f(x) ogf A007581 10.5557 {-a(n+3)+7*a(n+2)-14*a(n+1)+8*a(n),a(0)=1,a(1)=2,a(2)=5} ogf A007582 26.9443 -(-1+3*x)/(8*x^2+1-6*x) ogf A007582 25.8217 -(3*x-1)/(4*x-1)/(2*x-1) ogf A007582 15.493 -(3-16*x+24*x^2)/(3*x-1)/(2*x-1)/(4*x-1) lgdogf A007582 9.53415 1/4*ln(8*x+3)+1/4*ln(2*(1+2*x)^(1/2)-1)-1/4*ln(2*(1+2*x)^(1/2)+1) revegf A007582 11.9177 7-21*x+(-5+36*x-56*x^2)*f(x)+(-2+12*x-16*x^2)*f(x)^2 ogf A007582 16.3084 {a(n+2)-6*a(n+1)+8*a(n),a(0)=1,a(1)=3} ogf A007583 18.6009 (-1+2*x)*f(x)+(4*x^2+1-5*x)*f(x)^2 ogf A007583 27.497 -(-1+2*x)/(4*x^2+1-5*x) ogf A007583 28.7469 -(2*x-1)/(4*x-1)/(x-1) ogf A007583 17.5676 -(3-8*x+8*x^2)/(x-1)/(4*x-1)/(2*x-1) lgdogf A007583 15.4252 -1/4*(-1-5*x+(1+2*x+9*x^2)^(1/2))/(2*x+1) revogf A007583 16.6429 {a(n+2)-5*a(n+1)+4*a(n),a(0)=1,a(1)=3} ogf A007584 53.0749 (1+6*x)/(x-1)^4 ogf A007584 22.7464 -(-x-6*x^2)/(1-4*x+x^4+6*x^2-4*x^3) ogf A007584 33.1718 -2*(5+9*x)/(6*x+1)/(x-1) lgdogf A007584 11.7077 {(-2-n)*a(n+3)+(5-5*n)*a(n+2)+(18+6*n)*a(n+1),a(0)=0,a(1)=1,a(2)=10} ogf A007585 42.7633 (1+7*x)/(x-1)^4 ogf A007585 18.3271 -(-x-7*x^2)/(1-4*x+x^4+6*x^2-4*x^3) ogf A007585 26.7271 -(11+21*x)/(7*x+1)/(x-1) lgdogf A007585 9.43309 {(-2-n)*a(n+3)+(5-6*n)*a(n+2)+(21+7*n)*a(n+1),a(0)=0,a(1)=1,a(2)=11} ogf A007586 54.3208 (1+8*x)/(x-1)^4 ogf A007586 23.2803 -(-x-8*x^2)/(1-4*x+x^4+6*x^2-4*x^3) ogf A007586 32.5925 -12*(2*x+1)/(8*x+1)/(x-1) lgdogf A007586 11.9825 {(-2-n)*a(n+3)+(5-7*n)*a(n+2)+(24+8*n)*a(n+1),a(0)=0,a(1)=1,a(2)=12} ogf A007587 54.57 (1+9*x)/(x-1)^4 ogf A007587 23.3871 -(-x-9*x^2)/(1-4*x+x^4+6*x^2-4*x^3) ogf A007587 34.1062 -(13+27*x)/(9*x+1)/(x-1) lgdogf A007587 12.0375 {(-2-n)*a(n+3)+(5-8*n)*a(n+2)+(27+9*n)*a(n+1),a(0)=0,a(1)=1,a(2)=13} ogf A007587 12.0375 {(-2-n)*a(n+3)+(5-8*n)*a(n+2)+(9*n+27)*a(n+1),a(0)=0,a(1)=1,a(2)=13} ogf A007588 40.2922 (1+10*x+x^2)/(x-1)^4 ogf A007588 20.1461 -(x+x^3+10*x^2)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A007588 23.7013 -2*(7+16*x+x^2)/(x-1)/(x^2+10*x+1) lgdogf A007588 6.7718 2207*x+2207*x^3+22070*x^2+(-2207+9380*x-2207*x^4+9380*x^3-7722*x^2)*f(x)+(-3312*x^2-552+2208*x-552*x^4+2208*x^3)*f(x)^2 ogf A007588 8.95383 {(n+3)*a(n+4)+(4+9*n)*a(n+3)+(-41-9*n)*a(n+2)+(-2-n)*a(n+1),a(0)=0,a(1)=1,a(2)=14,a(3)=51} ogf A007589 13.1142 -(-x+7*x^3-x^4-17*x^2-24*x^5)/(1-3*x+3*x^2-x^3) ogf A007589 16.6585 -(x+1)*(24*x^3-23*x^2+16*x+1)/(x-1)^3 ogf A007589 9.94138 4*(-5-5*x+6*x^4-24*x^3+x^2)/(x-1)/(x+1)/(24*x^3-23*x^2+16*x+1) lgdogf A007590 36.9887 -2*(2*x+1)/(x-1)/(x+1) lgdogf A007590 28.0604 -2*x^2+(1-2*x+2*x^3-x^4)*f(x) ogf A007590 50.8595 -2/(x+1)/(x-1)^3 ogf A007590 35.3805 2*x^2/(1-2*x+2*x^3-x^4) ogf A007590 13.7924 {a(n+4)-2*a(n+3)+2*a(n+1)-a(n),a(0)=0,a(1)=0,a(2)=2,a(3)=4} ogf A007598 22.3381 -(-x+x^2)/(1-2*x-2*x^2+x^3) ogf A007598 13.7075 -(1+4*x+2*x^3-5*x^2)/(x-1)/(x+1)/(x^2-3*x+1) lgdogf A007598 25.1303 -(x-1)/(x+1)/(x^2-3*x+1) ogf A007598 11.3798 -x+x^2+(1-3*x+x^3-x^2)*f(x)+(-2*x^2+1-2*x+x^3)*f(x)^2 ogf A007598 11.5986 {a(n+3)-2*a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=1,a(2)=1} ogf A007601 7.95249 (-2-2*x+5*x^4-12*x^6+2*x^5+10*x^3-2*x^2-6*x^7+3*x^8)/(x-1)/(3*x^3-1)/(x^5+2*x^4+2*x^3-x^2-x-1) lgdogf A007601 16.6119 -(-1-x+2*x^3+2*x^4-x^2+x^5)/(1-x+3*x^4-3*x^3) ogf A007601 17.3845 -(-1-x+x^5+2*x^3-x^2+2*x^4)/(x-1)/(3*x^3-1) ogf A007611 19.079 (-1+exp(2*x)*x-exp(2*x))/(x-1) egf A007611 4.27142 {(-2*n-4*n^2-2*n^3)*a(n)+(67*n+34+40*n^2+7*n^3)*a(n+1)+(-17-51*n-25*n^2-3*n^3)*a(n+2)+(9*n+3*n^2)*a(n+3),a(0)=2,a(1)=3,a(2)=6,a(3)=14} ogf A007612 19.2635 (1+3*x^3+x^2+4*x^4)/(x+1)/(1-x+x^2)/(x-1)^2 ogf A007612 13.8055 (1+4*x^4+3*x^3+x^2)*f(x)^2+(-1+2*x-x^2-x^3+2*x^4-x^5)*f(x)^3 ogf A007612 17.624 -(1+3*x^3+4*x^4+x^2)/(-1+2*x-x^2-x^3+2*x^4-x^5) ogf A007612 9.41284 -(2+2*x-9*x^4+10*x^6+3*x^5+18*x^3+6*x^2+4*x^7)/(x-1)/(x+1)/(4*x^4+3*x^3+x^2+1)/(x^2-x+1) lgdogf A007613 26.1446 (5*x-1)/(x+1)/(-1+8*x) ogf A007613 26.1446 -(1-5*x)/(8*x^2-1+7*x) ogf A007613 8.84893 -125+625*x+(254-1520*x-1000*x^2)*f(x)+(1032*x^2-129+903*x)*f(x)^2 ogf A007613 14.0288 -2*(10*x+1)*(2*x-1)/(8*x-1)/(5*x-1)/(x+1) lgdogf A007613 13.6948 1/2/(-5+8*x)*(-1-7*x+(1-6*x+81*x^2)^(1/2)) revogf A007613 14.7482 {-a(n+2)+7*a(n+1)+8*a(n),a(0)=1,a(1)=2} ogf A007654 14.5953 -(-3*x^2-3*x)/(1-15*x+15*x^2-x^3) ogf A007654 10.4706 -2*(8-15*x+x^3-6*x^2)/(x-1)/(x+1)/(x^2-14*x+1) lgdogf A007654 17.8387 -3*(x+1)/(x-1)/(x^2-14*x+1) ogf A007654 6.88065 9*x+9*x^2+(-3+93*x+3*x^3+3*x^2)*f(x)+(-240*x^2-16+240*x+16*x^3)*f(x)^2 ogf A007654 8.75719 {a(n+3)-15*a(n+2)+15*a(n+1)-a(n),a(0)=0,a(1)=3,a(2)=48} ogf A007655 10.101 -1/2*(-14*x-1+(16*x+1)^(1/2)*(1+12*x)^(1/2))/x revogf A007655 21.1203 -2*(-7+x)/(x^2-14*x+1) lgdogf A007655 33.189 1/(x^2-14*x+1) ogf A007655 23.2323 x+(-1+14*x-x^2)*f(x) ogf A007655 33.189 x/(1-14*x+x^2) ogf A007655 12.558 {a(n+2)-14*a(n+1)+a(n),a(0)=0,a(1)=1} ogf A007661 12.5164 {(-n-4)*a(n+1)+a(n+4),a(0)=1,a(1)=1,a(2)=2,a(3)=3} ogf A007661 10.79 {a(n+1)+(-n^2-5*n-6)*a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=1/2} egf A007667 10.4098 -(5+5*x^2-130*x)/(-99*x^2-1+99*x+x^3) ogf A007667 2.85304 -267230+6947980*x-267230*x^2+(11461821-301908904*x-53446*x^3+16699529*x^2)*f(x)+(-225885825*x^2-2281675+225885825*x+2281675*x^3)*f(x)^2 ogf A007667 11.3283 -5*(1-26*x+x^2)/(x-1)/(x^2-98*x+1) ogf A007667 6.31412 {-a(n+3)+99*a(n+2)-99*a(n+1)+a(n),a(0)=5,a(1)=365,a(2)=35645} ogf A007679 19.31 -(-1-3*x^2+x)/(x^2+1-2*x-2*x^3) ogf A007679 21.379 -(1-x+3*x^2)/(2*x-1)/(1+x^2) ogf A007679 11.0854 -(3*x+1)*(2*x^3-2*x^2+x+1)/(2*x-1)/(x^2+1)/(3*x^2-x+1) lgdogf A007679 6.88059 -239+239*x-717*x^2+(464-703*x-478*x^3+914*x^2)*f(x)+(-225+450*x-225*x^2+450*x^3)*f(x)^2 ogf A007679 11.5118 {a(n+3)-2*a(n+2)+a(n+1)-2*a(n),a(0)=1,a(1)=1,a(2)=4} ogf A007680 49.4149 (x+1)/(x-1)^2 egf A007680 33.8102 -(1+x)/(-x^2-1+2*x) egf A007680 35.6885 -(x+3)/(x-1)/(x+1) lgdegf A007680 30.5902 1+x+(-x^2-1+2*x)*f(x) egf A007680 7.83407 {(-4-4*n-n^2)*a(n+1)+(-24-13*n-2*n^2)*a(n+2)+(2*n+6)*a(n+3),a(0)=1,a(1)=3,a(2)=10} ogf A007681 16.2234 -(-1-x^2-6*x)/(3*x^2+1-3*x-x^3) egf A007681 25.1462 -(1+6*x+x^2)/(x-1)^3 egf A007681 16.2234 -(9+14*x+x^2)/(x-1)/(x^2+6*x+1) lgdegf A007681 5.91676 -154-924*x-154*x^2+(193-228*x-154*x^3+501*x^2)*f(x)+(-117*x^2-39+117*x+39*x^3)*f(x)^2 egf A007681 4.22626 {(-4-4*n-n^2)*a(n+1)+(-198-111*n-16*n^2)*a(n+2)+(-72-4*n^2-24*n)*a(n+3)+(4*n+16)*a(n+4),a(0)=1,a(1)=9,a(2)=50,a(3)=294} ogf A007689 25.2829 -(-2+5*x)/(3*x-1)/(2*x-1) ogf A007689 27.4814 -(-2+5*x)/(6*x^2+1-5*x) ogf A007689 15.8018 -(5-24*x+30*x^2)/(3*x-1)/(2*x-1)/(5*x-2) lgdogf A007689 11.4922 46-115*x+(-21+110*x-138*x^2)*f(x)+(-1+5*x-6*x^2)*f(x)^2 ogf A007689 16.6335 {a(n+2)-5*a(n+1)+6*a(n),a(0)=2,a(1)=5} ogf A007690 32.3792 -(x+x^2+x^3+x^5)/(-1+x^6) ogf_with_Euler_Transform A007696 44.9518 -1+(1-4*x)*f(x) lgdegf A007696 67.4277 -1/(4*x-1) lgdegf A007696 16.0542 -1/4*(1-3*x)^(1/3)+3/4*(1-3*x)^(1/3)*x+1/4 revegf A007696 42.1423 1/(-4*x+1)^(1/4) egf A007696 44.9518 1/(1-4*x)^(1/4) egf A007696 17.7441 {(-4*n-5)*a(n+1)+a(n+2),a(0)=1,a(1)=1} ogf A007698 9.89267 -(-10+5*x^3-8*x^2+x)/(3*x^2+1-22*x+11*x^4-18*x^3) ogf A007698 9.89267 -(x-2)*(5*x^2+2*x+5)/(3*x^2+1-22*x+11*x^4-18*x^3) ogf A007698 4.32804 -580+58*x+290*x^3-464*x^2+(-692-1201*x+638*x^4-669*x^3-426*x^2)*f(x)+(75-1650*x+225*x^2-1350*x^3+825*x^4)*f(x)^2 ogf A007699 13.0675 -(-10+5*x^3-8*x^2+x)/(3*x^2+1-22*x+11*x^4-18*x^3) ogf A007699 13.0675 -(x-2)*(5*x^2+2*x+5)/(3*x^2+1-22*x+11*x^4-18*x^3) ogf A007699 5.71701 -580+58*x+290*x^3-464*x^2+(-692-1201*x+638*x^4-669*x^3-426*x^2)*f(x)+(75-1650*x+225*x^2-1350*x^3+825*x^4)*f(x)^2 ogf A007715 15.7498 -(-1-2*x^2-2*x)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A007715 33.6472 -(2*x^2+2*x+1)/(x-1)^5 ogf A007715 21.1497 -(7+12*x+6*x^2)/(x-1)/(2*x^2+2*x+1) lgdogf A007715 8.91854 {(-n-4)*a(n+4)+(4-n)*a(n+3)+12*a(n+2)+(8+2*n)*a(n+1),a(0)=1,a(1)=7,a(2)=27,a(3)=75} ogf A007742 25.4419 -(3*x^2+5*x)/(-1+3*x-3*x^2+x^3) ogf A007742 49.2937 -(5+3*x)/(x-1)^3 ogf A007742 7.80891 -58695*x-35217*x^2+(11739-15697*x-11739*x^3+46929*x^2)*f(x)+(-3904+11712*x-11712*x^2+3904*x^3)*f(x)^2 ogf A007742 35.85 -6*(x+3)/(3*x+5)/(x-1) lgdogf A007742 14.8811 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=5,a(2)=18} ogf A007744 23.0202 (1+6*x)/(-4*x+1)^(7/2) ogf A007744 24.1164 (1+6*x)/(1-4*x)^(7/2) ogf A007744 18.7572 -20*(1+3*x)/(6*x+1)/(4*x-1) lgdogf A007744 6.93758 -50700-152100*x+(5075+12690*x-60840*x^2)*f(x)+(3048*x^2-127-254*x)*f(x)^2 lgdogf A007744 7.03394 {(-n-3)*a(n+3)+(16-2*n)*a(n+2)+(84+24*n)*a(n+1),a(0)=1,a(1)=20,a(2)=210} ogf A007750 18.5868 -(1+6*x+x^2)/(x-1)/(x^4-16*x^2+1) ogf A007750 7.96576 -(7+34*x-29*x^4+3*x^6+22*x^5-196*x^3+47*x^2)/(x-1)/(x^2+6*x+1)/(x^4-16*x^2+1) lgdogf A007750 14.2643 -(x^3+6*x^2+x)/(-1+x+16*x^2+x^5-16*x^3-x^4) ogf A007751 20.7391 -(x+7)/(x-1)/(x^2-16*x+1) ogf A007751 16.7251 -(x^2+7*x)/(-1+17*x-17*x^2+x^3) ogf A007751 3.92786 -10933769*x-1561967*x^2+(1561967+70332959*x-1561967*x^3+40394353*x^2)*f(x)+(-13840914+235295538*x-235295538*x^2+13840914*x^3)*f(x)^2 ogf A007751 10.8016 -2*(60-119*x+x^3+2*x^2)/(x-1)/(x+7)/(x^2-16*x+1) lgdogf A007751 9.25853 {a(n+3)-17*a(n+2)+17*a(n+1)-a(n),a(0)=0,a(1)=7,a(2)=120} ogf A007752 16.3487 -(-1-7*x)/(17*x^2+1-17*x-x^3) ogf A007752 17.5597 -(1+7*x)/(x-1)/(x^2-16*x+1) ogf A007752 9.11756 -2*(12-17*x+7*x^3-58*x^2)/(x-1)/(7*x+1)/(x^2-16*x+1) lgdogf A007752 8.31777 {a(n+3)-17*a(n+2)+17*a(n+1)-a(n),a(0)=1,a(1)=24,a(2)=391} ogf A007756 1.30356 4*(-1/2+x^2)^2-4*(x^2+x-1)*(-1/2+x^2)*f(x)+(x^2+x-1)^2*f(x)^2 ogf A007758 22.0855 -(-4*x^2-2*x)/(1-6*x+12*x^2-8*x^3) ogf A007758 37.5454 -2*(2*x+1)/(2*x-1)^3 ogf A007758 31.2878 -8*(x+1)/(2*x-1)/(2*x+1) lgdogf A007758 11.2076 2*x+4*x^2+(-1+14*x+8*x^3+4*x^2)*f(x)+(-48*x^2-4+24*x+32*x^3)*f(x)^2 ogf A007758 13.4091 {a(n+3)-6*a(n+2)+12*a(n+1)-8*a(n),a(0)=0,a(1)=2,a(2)=16} ogf A007773 5.90129 (1-x+23*x^4-70*x^6+9*x^5+12*x^3-44*x^10+4*x^2+20*x^11-14*x^7-22*x^9+98*x^8)/(x-1)/(x+1)/(4*x^10-8*x^9-2*x^8+10*x^7-3*x^5-4*x^3+2*x-1) lgdogf A007773 12.8667 -(-1+2*x-3*x^5-8*x^9-4*x^3-2*x^8+4*x^10+10*x^7)/(x+1)/(x-1)^4 ogf A007773 10.1931 -(-1-4*x^3+2*x-3*x^5+4*x^10-8*x^9-2*x^8+10*x^7)/(2*x^2+1-3*x-3*x^4+x^5+2*x^3) ogf A007775 10.1941 (1+6*x+2*x^5+2*x^3+4*x^2+4*x^4+4*x^6+x^8+6*x^7)/(x+1)/(1+x^2)/(x^4+1)/(x-1)^2 ogf A007778 3.66651 {(792*n+1782*n^2+891*n^3)*a(n)+(1098*n+498+786*n^2+186*n^3)*a(n+1)+(143+187*n+60*n^2+8*n^3)*a(n+2)+(4+2*n)*a(n+3),a(0)=0,a(1)=1,a(2)=-4} revegf A007798 19.2356 -(9-46*x+45*x^2)/(x-1)/(3*x-1)/(5*x-1) lgdogf A007798 27.0723 -2*x/(-1+9*x-23*x^2+15*x^3) ogf A007798 30.4563 -2/(x-1)/(3*x-1)/(5*x-1) ogf A007798 11.2454 4*x+(-2+36*x+30*x^3-46*x^2)*f(x)+(-207*x^2-9+81*x+135*x^3)*f(x)^2 ogf A007798 12.8237 {a(n+3)-9*a(n+2)+23*a(n+1)-15*a(n),a(0)=0,a(1)=2,a(2)=18} ogf A007800 9.63872 (-1+x-x^4)*f(x)+(2-4*x+2*x^4-x^5+2*x^2)*f(x)^2+(x^5-2*x^2-1+3*x-x^4)*f(x)^3 ogf A007800 13.1437 -(-2+2*x+x^4+x^6+x^5+x^7)/(x-1)/(x^4-x+1)/(x^3+x^2+x-1) lgdogf A007800 21.9062 -(1+x^4-x)/(-2*x^2-1+3*x+x^5-x^4) ogf A007800 22.5907 -(1-x+x^4)/(x^2-1+x+x^3)/(x-1)^2 ogf A007805 24.1215 -(-1+x)/(x^2+1-18*x) ogf A007805 15.076 -(17-2*x+x^2)/(x-1)/(x^2-18*x+1) lgdogf A007805 25.3911 -(x-1)/(x^2+1-18*x) ogf A007805 11.2193 -1/2*(-1-18*x+(1+32*x+320*x^2)^(1/2))/(1+x) revogf A007805 7.9087 -15+15*x+(319-574*x+15*x^2)*f(x)+(-304+5472*x-304*x^2)*f(x)^2 ogf A007805 12.6955 {a(n+2)-18*a(n+1)+a(n),a(0)=1,a(1)=17} ogf A007808 12.9815 exp(x)*(x-3+2*exp(-x)*x+2*exp(-x))/(x-1)^3 egf A007808 5.00204 {(-6-5*n-n^2)*a(n+1)+(28+16*n+2*n^2)*a(n+2)+(-30-12*n-n^2)*a(n+3)+(n+4)*a(n+4),a(0)=1,a(1)=3,a(2)=13,a(3)=69} ogf A007813 9.59314 (-1-x-16*x^5+9*x^9+6*x^11-4*x^3-2*x^2-8*x^4-27*x^6+8*x^12+5*x^13+4*x^14+x^15+10*x^8+6*x^10-16*x^7)/(x-1) ogf A007813 9.50178 -(1+8*x^4+4*x^3+27*x^6+x-6*x^10-9*x^9-10*x^8+16*x^7-x^15-5*x^13-8*x^12+2*x^2-6*x^11+16*x^5-4*x^14)/(-1+x) ogf A007829 7.30949 -(4*x^6+6*x^7-6*x^5)/(1-2*x-3*x^2+6*x^3+4*x^4-5*x^5-5*x^6+2*x^7+2*x^8) ogf A007829 4.2997 -(4+12*x+117*x^4-137*x^6+74*x^5-24*x^3-54*x^2-84*x^7+36*x^9+58*x^8)/(x-1)/(2*x^2-1)/(x^2+x-1)/(x^3+x^2-1)/(3*x^2+2*x-3) lgdogf A007829 8.97657 -2*(-3+2*x+3*x^2)/(x-1)/(-1+2*x^2)/(x^2+x-1)/(-1+x^2+x^3) ogf A007830 15.6124 1/2*2^(1/2)*(ln(2)+ln(x+1/2))/(2+4*x)^(1/2) revegf A007852 23.1174 1/2*(1-3*x+(1-2*x+5*x^2)^(1/2))*x revogf A007854 27.5068 -1-f(x)+(2-9*x)*f(x)^2 ogf A007854 17.7985 -1/2*(1+3*(-4*x+1)^(1/2))/(-2+9*x) ogf A007854 16.8097 1/2*(-1-9*x+3*(1+2*x+9*x^2)^(1/2))*x revogf A007854 14.4083 3/2*(3-12*x+(1-4*x)^(1/2))/(9*x-2)/(4*x-1) lgdogf A007854 8.1777 {(-36*n-54)*a(n+1)+(17*n+39)*a(n+2)+(-2*n-6)*a(n+3),a(0)=1,a(1)=3,a(2)=12} ogf A007863 21.4986 -1+(-x+1)*f(x)-x*f(x)^2-x^2*f(x)^3 ogf A007863 22.15 -1+(1-x)*f(x)-x*f(x)^2-x^2*f(x)^3 ogf A007863 38.4711 -x*(-1+x+x^2)/(1+x) revogf A007868 14.2351 1/2*(-1+exp(1/2*x*(x+2))*x-exp(1/2*x*(x+2)))/(x-1) egf A007868 7.9084 {(n+2)*a(n+1)+a(n+2)+(-7-n^2-6*n)*a(n+3)+(5*n+4+n^2)*a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=5/6} egf A007873 5.47611 -(1-5*x^4+5*x^3-3*x^6+x+5*x^7+2*x^8-6*x^10+3*x^2+5*x^5+6*x^14+8*x^12+4*x^9)/(-1+x^8+16*x^4-16*x^12) ogf A007877 49.7656 -(x+1)/(x-1)/(1+x^2) ogf A007877 14.637 -15*x-15*x^2+(15-17*x-15*x^3+13*x^2)*f(x)+(2-2*x+2*x^2-2*x^3)*f(x)^2 ogf A007877 27.6476 -2*(1-x+x^2+x^3)/(x-1)/(x+1)/(x^2+1) lgdogf A007877 110.59 2-2*x+x^3 ogf_with_Euler_Transform A007877 20.7357 {a(n+3)-a(n+2)+a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=2} ogf A007890 4.67976 -(-1-20*x^4-1190*x^3-1010*x^6-10*x-99990*x^7+98010*x^8-100010*x^10-10*x^2-129990*x^5+9899010*x^12-9900990*x^11-13997020*x^9)/(1-x) ogf A007891 15.4639 -(-1+x^4-x^3-3*x+3*x^2-x^5)/(1-x+2*x^4-2*x^3+x^6-x^7) ogf A007891 17.8171 -(1+3*x+x^5+x^3-3*x^2-x^4)/(1+x^2+x)^2/(x-1)^3 ogf A007891 9.99495 -2*(2-x-5*x^4-x^6+2*x^5+6*x^3+5*x^2+x^7)/(x-1)/(x^2+x+1)/(x^5-x^4+x^3-3*x^2+3*x+1) lgdogf A007892 11.8615 -(-1-x^4+8*x^3+3*x^6-3*x-4*x^7-5*x^2+x^5)/(-x^9+1-x+2*x^5-2*x^4+x^8) ogf A007892 12.221 -(1+3*x-x^5-8*x^3+5*x^2+x^4-3*x^6+4*x^7)/(x+1)^2/(1+x^2)^2/(x-1)^3 ogf A007892 6.30145 -(4+14*x+17*x^4-23*x^6+9*x^5+13*x^3+8*x^10-15*x^2+5*x^7-5*x^9-3*x^8)/(x-1)/(x+1)/(x^2+1)/(4*x^7-3*x^6-x^5+x^4-8*x^3+5*x^2+3*x+1) lgdogf A007893 10.0158 -(-1+15*x^4-7*x^3+x^6-3*x+3*x^7+5*x^8-5*x^2-x^5-9*x^9)/(1-x-2*x^5+2*x^6+x^10-x^11) ogf A007893 10.1395 -(1+3*x+x^5+9*x^9+7*x^3+5*x^2-15*x^4-x^6-5*x^8-3*x^7)/(x^4+x^3+x^2+x+1)^2/(x-1)^3 ogf A007899 15.4125 -(1+10*x+10*x^3+20*x^2+x^4)/(x+1)/(x-1)^3 ogf A007899 13.7372 -(1+x^4+10*x^3+10*x+20*x^2)/(-1+2*x+x^4-2*x^3) ogf A007899 9.0273 -4*(3+16*x+3*x^4+16*x^3+25*x^2)/(x-1)/(x+1)/(x^4+10*x^3+20*x^2+10*x+1) lgdogf A007899 6.25654 31+310*x+31*x^4+310*x^3+620*x^2+(6+432*x+68*x^4+308*x^3+740*x^2)*f(x)+(-37+74*x+37*x^4-74*x^3)*f(x)^2 ogf A007899 6.58241 {(n-n^2)*a(n)+(30+7*n+n^2)*a(n+1)+(18-n+n^2)*a(n+2)+(-7*n-12-n^2)*a(n+3),a(0)=1,a(1)=12,a(2)=44} ogf A007900 16.5394 (1+20*x+20*x^3+54*x^2+x^4)/(x-1)^4 ogf A007900 10.8142 -(1+x^4+20*x^3+20*x+54*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A007900 10.4137 -24*(x+1)*(x^2+6*x+1)/(x-1)/(x^4+20*x^3+54*x^2+20*x+1) lgdogf A007900 4.46301 718+14360*x+718*x^4+14360*x^3+38772*x^2+(-683+3572*x-683*x^4+3572*x^3-2418*x^2)*f(x)+(-35+140*x-210*x^2+140*x^3-35*x^4)*f(x)^2 ogf A007900 4.64743 {(29*n-5*n^2)*a(n)+(1614+1035*n+237*n^2)*a(n+1)+(-402-367*n-227*n^2)*a(n+2)+(-n+42-5*n^2)*a(n+3),a(0)=1,a(1)=24,a(2)=144} ogf A007904 16.8522 (1+2*x+2*x^3+4*x^2+x^4)/(x+1)/(x-1)^4 ogf A007904 11.337 -(1+x^4+2*x^3+2*x+4*x^2)/(-2*x^2-1+3*x+3*x^4-2*x^3-x^5) ogf A007904 9.0367 -(5+19*x+7*x^4+x^5+22*x^3+26*x^2)/(x-1)/(x+1)/(x^4+2*x^3+4*x^2+2*x+1) lgdogf A007907 10.1875 -(11+400*x^3-330*x^2)/(x-1)/(10*x-1)/(10*x^2-1) lgdogf A007907 17.1004 -1/(x-1)/(10*x-1)/(10*x^2-1) ogf A007907 4.31363 -46400+(1168611-510400*x-4640000*x^4+5104000*x^3)*f(x)+(-123443210*x^3+112221100*x^4-1122211+12344321*x)*f(x)^2 ogf A007907 18.4159 1/(1-11*x+110*x^3-100*x^4) ogf A007907 6.65017 {a(n+4)-11*a(n+3)+110*a(n+1)-100*a(n),a(0)=1,a(1)=11,a(2)=121,a(3)=1221} ogf A007908 6.45342 144-720*x+900*x^2+(-24+324*x+600*x^3-900*x^2)*f(x)+(100*x^4+141*x^2+1-22*x-220*x^3)*f(x)^2 lgdogf A007909 37.0772 (x-1)/(2*x-1)/(1+x^2) ogf A007909 18.1075 -(-1+2*x+4*x^3-7*x^2)/(x-1)/(2*x-1)/(1+x^2) lgdogf A007909 29.947 -(-x+1)/(-x^2-1+2*x+2*x^3) ogf A007909 12.977 -4+4*x+(7-11*x-8*x^3+4*x^2)*f(x)+(-3*x^2-3+6*x+6*x^3)*f(x)^2 ogf A007909 14.691 {-a(n+3)+2*a(n+2)-a(n+1)+2*a(n),a(0)=1,a(1)=1,a(2)=1} ogf A007910 42.5122 -1/(2*x-1)/(1+x^2) ogf A007910 25.5073 -2*(1-x+3*x^2)/(2*x-1)/(1+x^2) lgdogf A007910 12.3423 -20+(7-40*x-40*x^3+20*x^2)*f(x)+(13-26*x+13*x^2-26*x^3)*f(x)^2 ogf A007910 40.2747 1/(1-2*x+x^2-2*x^3) ogf A007910 14.7158 {a(n+3)-2*a(n+2)+a(n+1)-2*a(n),a(0)=1,a(1)=2,a(2)=3} ogf A007911 9.50336 {(16+8*n+n^2)*a(n+1)+a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=1,a(2)=5} ogf A007928 6.71695 (4+8*x^5-5*x^24+20*x^10+3*x^25-10*x^9+10*x^20-20*x^14+24*x^15-10*x^19)/(x-1)/(x^15-x^10-2*x^5-2)/(x^2+x+1)/(x^8-x^7+x^5-x^4+x^3-x+1) lgdogf A007928 13.6406 -(-2-2*x^5+x^15-x^10)/(1+x^2+x)/(x^8-x^7+x^5-x^4+x^3-x+1)/(x-1)^2 ogf A007929 10.4011 -(-21-2*x+9*x^5-2*x^3-2*x^2-2*x^4)/(x^4+x^3+x^2+x+1)/(x-1)^2 ogf A007929 13.0014 -(-21-2*x^4-2*x^3-2*x-2*x^2+9*x^5)/(1-x-x^5+x^6) ogf A007929 5.33392 -(-23-27*x-89*x^4-3*x^6-7*x^5-35*x^3-31*x^2+x^7+9*x^9+5*x^8)/(x-1)/(x^4+x^3+x^2+x+1)/(9*x^5-2*x^4-2*x^3-2*x^2-2*x-21) lgdogf A007945 30.9872 (-2+x+2*x^2)/(x-1)/(1-x+x^2) ogf A007945 27.9884 -(-2+x+2*x^2)/(2*x^2+1-2*x-x^3) ogf A007945 24.7898 -(-2-3*x-4*x^3-5*x^4-2*x^5)/(1-x^6) ogf A007945 15.2218 -(-3+12*x+2*x^4+2*x^3-12*x^2)/(x-1)/(x^2-x+1)/(2*x^2+x-2) lgdogf A007945 11.7249 32-16*x-32*x^2+(30+9*x+16*x^3-78*x^2)*f(x)+(-46*x^2-23+46*x+23*x^3)*f(x)^2 ogf A007945 16.6854 {a(3+n)-2*a(n+2)+2*a(n+1)-a(n),a(0)=2,a(1)=3,a(2)=0} ogf A007946 9.35748 -2*(-1+(-4*x+1)^(1/2)-2*x)/(-4*x+1)^(1/2)/(1+(-4*x+1)^(1/2))^2/x ogf A007946 9.81768 -2*(-1+(1-4*x)^(1/2)-2*x)/(1-4*x)^(1/2)/(1+(1-4*x)^(1/2))^2/x ogf A007946 16.6355 x+2+(-1+4*x)*f(x)+(4*x^4-x^3)*f(x)^2 ogf A007946 10.1505 {(-40-26*n-4*n^2)*a(n+1)+(7*n+10+n^2)*a(n+2),a(0)=2,a(1)=9} ogf A007953 10.2831 -(-1-x-x^5+8*x^9-x^3-x^2-x^4-x^6-x^8-x^7)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x-1)^2 ogf A007953 11.14 -(x^4+x^3+x-8*x^10+x^6+x^2+x^8+x^33+x^7+x^5+x^9+9*x^40-9*x^39-x^43)/(-1+x+x^10-x^11) ogf A007958 9.32454 -2*(-5+4*x-5*x^5+5*x^11+5*x^6-5*x^15-5*x^10+5*x^21+5*x^16-5*x^20)/(x-1)^2 ogf A007971 23.5655 -1/3+1/3*(1+6*x-3*x^2)^(1/2) revogf A007971 27.493 -2*x-3*x^2+2*f(x)-f(x)^2 ogf A007971 6.87326 {(9*n-9*n^2)*a(n)+(-9*n-9*n^2)*a(n+1)+(-n-6+n^2)*a(n+2)+(5*n+6+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=2} ogf A007979 14.4571 (1+x^2)*(x^4+1)/(x+1)/(1+x^2+x)/(x-1)^4 ogf A007979 13.1122 -(1+x^4+x^2+x^6)/(-x^3-1+2*x+2*x^6-x^4-x^7) ogf A007979 5.81264 -(2+8*x+13*x^4+13*x^6+17*x^5+17*x^3+13*x^2+9*x^7+x^9+3*x^8)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1)/(x^4+1) lgdogf A007979 43.3713 2+2*x+x^2-x^7 ogf_with_Euler_Transform A007980 31.7383 -(1+x^2)/(1+x^2+x)/(x-1)^3 ogf A007980 23.577 -(x^2+1)/(-1+2*x-x^2+x^3-2*x^4+x^5) ogf A007980 17.9391 -(x^2+2)*(3*x^2+2*x+1)/(x-1)/(x^2+1)/(x^2+x+1) lgdogf A007980 75.0179 2+x+x^2-x^3 ogf_with_Euler_Transform A007980 8.25197 {(n^2+9*n+21)*a(n+1)+(2*n+8)*a(n+2)+(2*n+8)*a(n+3)+(-n^2-7*n-13)*a(n+4),a(0)=1,a(1)=2,a(2)=4,a(3)=7} ogf A007980 22.3026 {a(n+4),a(0)=2,a(1)=1,a(2)=1,a(3)=-1} ogf_with_Euler_Transform A007981 3.22381 -(-2-8*x-x^4+5*x^6+6*x^5-12*x^3-12*x^2)/(x-1)/(x+1)/(x^2+x+1)/(x^3-x-1) lgdogf A007981 6.35808 -(x^3-x-1)/(1+x^2+x)/(x+1)^2/(x-1)^4 ogf A007983 2.29496 -1/(x+1)*(x-1)*x^8+(2*x^2+3*x+2)/(x+1) ogf_with_Euler_Transform A007986 2.41665 -2*(1-5*x+66*x^2)/(11*x-1)/(11*x^2+1) ogf A007988 18.4151 (2-x^3-x^2+x^4)/(1+x^2+x)/(x+1)^2/(x-1)^4 ogf A007988 13.246 -(2+x^4-x^3-x^2)/(-x^8-1+x+2*x^2-x^3+2*x^6-2*x^4-x^5+x^7) ogf A007988 9.67974 -2*(1+5*x-4*x^4-3*x^5+5*x^3+6*x^2+2*x^7)/(x-1)/(x+1)/(x^2+x+1)/(x^4-x^3-x^2+2) lgdogf A007993 9.33872 -(-12+4*x-9*x^4+3*x^5+6*x^3+2*x^2)/(x-1)/(3*x^5-12*x^4+18*x^3-13*x^2+6*x-3) lgdogf A007993 15.9183 -(-3+6*x+3*x^5+18*x^3-13*x^2-12*x^4)/(x-1)^6 ogf A007993 9.33872 -(3+12*x^4-18*x^3-6*x+13*x^2-3*x^5)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A007993 4.51874 {(11874+7483*n+773*n^2)*a(n+1)+(-10278-10221*n-1461*n^2)*a(n+2)+(9822+4999*n+799*n^2)*a(n+3)+(-1281*n-3348-111*n^2)*a(n+4),a(0)=3,a(1)=12,a(2)=40,a(3)=102} ogf A007994 8.50588 (4-18*x+60*x^5+8*x^9-137*x^3+70*x^2+102*x^4-178*x^6-54*x^8+144*x^7)/(x-1)^10 ogf A007997 16.9847 -(1+2*x+3*x^4-2*x^3+5*x^2)/(x-1)/(1+x^2+x)/(x^2-x+1) lgdogf A007997 31.5431 -(1-x+x^2)/(1+x^2+x)/(x-1)^3 ogf A007997 21.5416 -(x^4-x^3+x^2)/(-1+2*x-x^2+x^3-2*x^4+x^5) ogf A007997 67.9389 1+x+2*x^2-x^5 ogf_with_Euler_Transform A007997 13.1822 x^4-x^3+x^2+(-1+2*x-x^4+x^5)*f(x)+(-1+x^3+2*x-x^2-2*x^4+x^5)*f(x)^2 ogf A007997 8.83206 {(-n^2-5*n-8)*a(n+1)+(-2*n-4)*a(n+2)+(-2*n-4)*a(n+3)+(n^2+3*n+4)*a(n+4),a(0)=0,a(1)=0,a(2)=1,a(3)=1} ogf A008000 11.503 -(-1-9*x^4-9*x^3-3*x-6*x^2-3*x^6-x^7-6*x^5)/(-x^7+1-x+2*x^4-2*x^3+x^6) ogf A008000 12.9873 -(x+1)*(x^6+2*x^5+4*x^4+5*x^3+4*x^2+2*x+1)/(1+x^2+x)^2/(x-1)^3 ogf A008000 7.38724 -(x^2+1)*(4*x^6+16*x^5+39*x^4+53*x^3+39*x^2+16*x+4)/(x-1)/(x+1)/(1+x^2+x)/(x^6+2*x^5+4*x^4+5*x^3+4*x^2+2*x+1) lgdogf A008013 7.81757 -(-1-14*x^4-10*x^3-3*x-6*x^2-18*x^6-14*x^7-18*x^5-10*x^8-6*x^9-x^11-3*x^10)/(1-x-x^11+2*x^6+x^10-2*x^5) ogf A008013 12.9873 -(x^8+3*x^6+5*x^4+3*x^2+1)*(x+1)^3/(x^4+x^3+x^2+x+1)^2/(x-1)^3 ogf A008014 7.7424 -(1+4*x^4+3*x^3+2*x+4*x^2+6*x^6+4*x^7+x^12+4*x^5+4*x^8+3*x^9+2*x^11+4*x^10)/(x^10-1+2*x-2*x^11-x^2+x^12) ogf A008014 7.45564 -(1+x^2+x)*(1-x+x^2)*(x^8+2*x^7+3*x^6+x^5+x^3+3*x^2+2*x+1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x-1)^3 ogf A008036 8.72084 -(x+1)*(x^10+x^9+4*x^8+6*x^7+6*x^6+9*x^5+6*x^4+6*x^3+4*x^2+x+1)/(1+x^2+x)/(x-1)^3/(1+x^2)^3 ogf A008039 6.43119 -(-1-28*x^4-19*x^3-4*x-10*x^2-45*x^6-45*x^7-4*x^12-37*x^5-37*x^8-28*x^9-x^13-10*x^11-19*x^10)/(-x^3+1+x^10-2*x^5-x^13+2*x^8) ogf A008039 7.7424 -(x^10+x^9+4*x^8+3*x^7+6*x^6+6*x^5+6*x^4+3*x^3+4*x^2+x+1)*(x+1)^3/(1+x^2+x)/(x^4+x^3+x^2+x+1)^2/(x-1)^3 ogf A008066 7.70951 -(-1-6*x^4-5*x^3-2*x-3*x^2-5*x^6-3*x^7-6*x^5-2*x^8-x^9)/(2*x^2+1-2*x+2*x^8+x^4-x^9-2*x^3+2*x^6-x^5-2*x^7) ogf A008066 9.63689 -(x+1)*(x^8+x^7+2*x^6+3*x^5+3*x^4+3*x^3+2*x^2+x+1)/(x^4+x^3+x^2+x+1)/(1+x^2)/(x-1)^3 ogf A008084 9.38197 -(-1-6*x^4-6*x^3-2*x-3*x^2-2*x^6-x^7-3*x^5)/(2*x^2+1-2*x+3*x^4-3*x^3+2*x^6-2*x^5-x^7) ogf A008084 7.7424 -(4+2*x+38*x^4+25*x^6+4*x^5+4*x^3+25*x^2+2*x^7+4*x^8)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1)/(x^4-x^3+3*x^2-x+1) lgdogf A008084 14.7679 -(x^4-x^3+3*x^2-x+1)*(x+1)^3/(1+x^2)/(1+x^2+x)/(x-1)^3 ogf A008085 7.97467 -(-1-3*x^4-7*x^3-2*x-2*x^2+2*x^6-5*x^7-10*x^5+8*x^8-4*x^9)/(2*x^2+1-2*x+3*x^4-3*x^3+2*x^6-2*x^5-x^7) ogf A008085 9.60804 -(1+2*x+10*x^5+4*x^9+7*x^3+2*x^2+3*x^4-2*x^6-8*x^8+5*x^7)/(1+x^2)/(1+x^2+x)/(x-1)^3 ogf A008105 7.06038 -(-1-2*x^4-2*x^3-x-x^2-3*x^6-2*x^7-3*x^5-2*x^8-x^9-x^11-x^10)/(4*x^2+1-3*x-4*x^9+x^4+3*x^10-3*x^3-x^11-x^7+3*x^8) ogf A008105 10.2285 -(x+1)*(1+x^2)*(x^8+x^5+x^4+x^3+1)/(1-x+x^2)/(1+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^3 ogf A008123 9.99381 -(-1-4*x^4-3*x^3-2*x-2*x^2-3*x^6-2*x^7-4*x^5-2*x^8-x^9)/(x^2+1-2*x+2*x^8-x^7-x^9) ogf A008123 12.6484 -(1+x^2+x)*(1-x+x^2)^2*(x+1)^3/(1+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^3 ogf A008123 6.32421 -(4+6*x+19*x^4+19*x^6+12*x^5+15*x^3+4*x^10+13*x^2+15*x^7+6*x^9+13*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008123 47.6176 4-x+x^2-2*x^5+x^6 ogf_with_Euler_Transform A008130 25.3791 -(x+1)/(1+x^2+x)^2/(x-1)^3 ogf A008130 17.834 -(x^4+x^3)/(-1+x+2*x^3+x^7-2*x^4-x^6) ogf A008130 15.7109 -2*(1+x+3*x^3+4*x^2)/(x-1)/(x+1)/(x^2+x+1) lgdogf A008130 73.3175 2-x+2*x^2 ogf_with_Euler_Transform A008130 6.94586 {(n^2+7*n+12)*a(n+1)+(n+1)*a(n+2)+(n+4)*a(n+3)+(-n^2-3*n-2)*a(n+4),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A008133 20.6413 -(1+3*x+5*x^4+x^3+8*x^2)/(x-1)/(1+x^2)/(x^2+x+1) lgdogf A008133 35.3851 -(1+x^2)/(1+x^2+x)^2/(x-1)^3 ogf A008133 26.7779 -(x^3+x^5)/(-1+x+2*x^3+x^7-2*x^4-x^6) ogf A008133 76.214 1+x+2*x^2-x^3 ogf_with_Euler_Transform A008137 11.7319 -(-1-3*x^4-3*x^3-2*x-2*x^2-2*x^6-x^7-2*x^5)/(x^2+1-2*x-x^5+2*x^6-x^7) ogf A008137 15.5673 -(1+x^2)*(1-x+x^2)*(x+1)^3/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008137 8.01484 -(4+2*x+18*x^4+11*x^6+4*x^5+4*x^3+11*x^2+2*x^7+4*x^8)/(x-1)/(x+1)/(x^2-x+1)/(x^4+x^3+x^2+x+1)/(1+x^2) lgdogf A008137 42.6052 4-x+x^2-x^3+x^4-x^5 ogf_with_Euler_Transform A008160 9.34931 -(-1-11*x^4-8*x^3-3*x-5*x^2-8*x^6-5*x^7-11*x^5-3*x^8-x^9)/(1-x-x^9-x^3+x^8+x^4-x^5+x^6) ogf A008160 11.9616 -(x^6+2*x^4+x^3+2*x^2+1)*(x+1)^3/(x^4+x^3+x^2+x+1)/(1+x^2+x)/(x-1)^3 ogf A008217 17.1067 -(1-5*x^4+6*x^5+6*x^3+4*x^2)/(x-1)/(x+1)/(x^2+1)/(x^2-x+1) lgdogf A008217 29.182 -(1-x+x^2)/(1+x^2)^2/(x+1)/(x-1)^3 ogf A008217 17.4068 -(x^4+x^6-x^5)/(-1+2*x-2*x^2+2*x^3-2*x^5+x^8+2*x^6-2*x^7) ogf A008217 66.1458 1+x^2+2*x^3-x^5 ogf_with_Euler_Transform A008218 20.0361 (1+2*x^3+x^2+x^4+x^6)/(x+1)^3/(1+x^2)^3/(x-1)^4 ogf A008218 9.41698 -(1+3*x+4*x^4+22*x^6+20*x^5+20*x^3+8*x^2+10*x^7+7*x^9+x^8)/(x-1)/(x+1)/(x^2+1)/(x^6+x^4+2*x^3+x^2+1) lgdogf A008218 14.2682 -(x^4+x^6+2*x^7+x^8+x^10)/(-1+x+3*x^4-3*x^8-3*x^5+3*x^9+x^12-x^13) ogf A008233 16.9456 -(1+2*x^3+x^2+x^4+x^6)/(x+1)^3/(1+x^2)^3/(x-1)^5 ogf A008233 8.8412 -(x^4+x^6+2*x^7+x^8+x^10)/(-1+2*x-x^2+3*x^4-3*x^10-6*x^5+3*x^6+6*x^9+x^14-3*x^8+x^12-2*x^13) ogf A008233 8.05337 -2*(1+2*x+4*x^4+13*x^6+12*x^5+12*x^3+5*x^2+6*x^7+4*x^9+x^8)/(x-1)/(x+1)/(x^2+1)/(x^6+x^4+2*x^3+x^2+1) lgdogf A008238 25.5853 -1/(1+x^2)^2/(x+1)/(x-1)^3 ogf A008238 18.4782 -2*(1+x^2+4*x^3)/(x-1)/(x+1)/(x^2+1) lgdogf A008238 14.1535 -x^4/(-1+2*x-2*x^2+2*x^3-2*x^5+2*x^6-2*x^7+x^8) ogf A008238 73.913 2-x+2*x^3 ogf_with_Euler_Transform A008239 7.89571 -(-1-3*x^4-4*x^3-2*x-2*x^2-4*x^6-2*x^7-3*x^5-2*x^8-x^9)/(x^2+1-2*x+2*x^8+3*x^4-x^9-x^3+x^6-3*x^5-x^7) ogf A008239 13.2911 -(x+1)*(x^4+x^3-x^2+x+1)*(1+x^2)^2/(1+x^2+x)/(x^4+1)/(x-1)^3 ogf A008249 8.09317 (-1-3*x-15*x^5+x^9+x^11-10*x^3-7*x^2-16*x^4-12*x^6-x^8+x^10-6*x^7)/(x+1)/(1+x^2)/(1+x^2+x)/(x-1)^3 ogf A008249 8.81257 -(-1-16*x^4-10*x^3-3*x-7*x^2-12*x^6-6*x^7-15*x^5-x^8+x^9+x^11+x^10)/(-x^8+1-x+x^7+x^5-x^3) ogf A008250 7.77579 (-1-3*x-13*x^5+3*x^9+x^11-12*x^3-7*x^2-14*x^4-12*x^6-3*x^8+x^10-8*x^7)/(x+1)/(1+x^2)/(1+x^2+x)/(x-1)^3 ogf A008250 8.43756 -(-1-14*x^4-12*x^3-3*x-7*x^2-12*x^6-8*x^7-13*x^5-3*x^8+3*x^9+x^11+x^10)/(-x^8+1-x+x^7+x^5-x^3) ogf A008253 21.3935 -(1+2*x+2*x^3+4*x^2+x^4)/(x+1)/(x-1)^3 ogf A008253 18.9059 -(1+x^4+2*x^3+2*x+4*x^2)/(-1+2*x+x^4-2*x^3) ogf A008253 13.5492 -4*(x^2+x+1)*(x^2+3*x+1)/(x-1)/(x+1)/(x^4+2*x^3+4*x^2+2*x+1) lgdogf A008253 9.56414 -5-10*x-5*x^4-10*x^3-20*x^2+(6-8*x-4*x^4+12*x^3+4*x^2)*f(x)+(-1-2*x^3+2*x+x^4)*f(x)^2 ogf A008254 9.70132 -(-1-12*x^4-8*x^3-3*x-6*x^2-3*x^6+x^7-8*x^5+2*x^8-2*x^9)/(-x^7+1-x+2*x^4-2*x^3+x^6) ogf A008254 11.503 -(x+1)*(2*x^8-4*x^7+3*x^6+8*x^4+4*x^3+4*x^2+2*x+1)/(1+x^2+x)^2/(x-1)^3 ogf A008255 11.1835 -(-1-10*x^4-10*x^3-3*x-6*x^2-3*x^6-x^7-6*x^5)/(-x^7+1-x+2*x^4-2*x^3+x^6) ogf A008255 19.1717 -(x^4+3*x^2+1)*(x+1)^3/(1+x^2+x)^2/(x-1)^3 ogf A008255 10.3232 -2*(2+4*x+13*x^4+2*x^6+4*x^5+7*x^3+13*x^2)/(x-1)/(x+1)/(x^2+x+1)/(x^4+3*x^2+1) lgdogf A008258 9.74796 -(-1-10*x^4-12*x^3-3*x-6*x^2+x^6-x^7-12*x^5+2*x^8-2*x^9)/(-x^7+1-x+2*x^4-2*x^3+x^6) ogf A008258 10.7877 -(1+3*x+12*x^5+2*x^9+12*x^3+6*x^2+10*x^4-x^6-2*x^8+x^7)/(1+x^2+x)^2/(x-1)^3 ogf A008259 11.2372 -(-1-11*x^4-11*x^3-3*x-7*x^2-3*x^6-x^7-7*x^5)/(-x^7+1-x+2*x^4-2*x^3+x^6) ogf A008259 13.0497 -(x+1)*(x^6+2*x^5+5*x^4+6*x^3+5*x^2+2*x+1)/(1+x^2+x)^2/(x-1)^3 ogf A008259 7.42276 -2*(x^2+1)*(2*x^6+9*x^5+23*x^4+31*x^3+23*x^2+9*x+2)/(x-1)/(x+1)/(x^2+x+1)/(x^6+2*x^5+5*x^4+6*x^3+5*x^2+2*x+1) lgdogf A008260 11.6697 -(-1-5*x^4-5*x^3-2*x-3*x^2-2*x^6-x^7-3*x^5)/(x^2+1-2*x-x^5+2*x^6-x^7) ogf A008260 12.5814 -(x+1)*(x^6+x^5+2*x^4+3*x^3+2*x^2+x+1)/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008260 6.34023 -(x^2+x+1)*(4*x^8+8*x^7+15*x^6+19*x^5+18*x^4+19*x^3+15*x^2+8*x+4)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^6+x^5+2*x^4+3*x^3+2*x^2+x+1) lgdogf A008261 11.1227 -(1+11*x^4+14*x^3+3*x+7*x^2-x^6-2*x^7+3*x^5+2*x^8)/(x^2-1+x-x^4-x^5+x^6) ogf A008261 10.822 -(1+3*x+3*x^5+14*x^3+7*x^2+11*x^4-x^6+2*x^8-2*x^7)/(x-1)^3/(x+1)/(1+x^2+x) ogf A008264 12.904 -(1+5*x^4+5*x^3+2*x+5*x^2+x^6+2*x^5)/(-x^2-1+2*x+x^4-2*x^5+x^6) ogf A008264 15.6337 -(1+x^2+x)*(x^4+x^3+3*x^2+x+1)/(x+1)/(1+x^2)/(x-1)^3 ogf A008264 7.59768 -(4+16*x+50*x^4+31*x^6+50*x^5+50*x^3+31*x^2+16*x^7+4*x^8)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1)/(x^4+x^3+3*x^2+x+1) lgdogf A008265 7.85515 -(-1-15*x^4-11*x^3-3*x-7*x^2-20*x^6-15*x^7-20*x^5-11*x^8-7*x^9-x^11-3*x^10)/(1-x-x^11+2*x^6+x^10-2*x^5) ogf A008265 8.42793 -(x+1)*(x^10+2*x^9+5*x^8+6*x^7+9*x^6+11*x^5+9*x^4+6*x^3+5*x^2+2*x+1)/(x^4+x^3+x^2+x+1)^2/(x-1)^3 ogf A008266 9.5693 -(-1-5*x^4-5*x^3-2*x-3*x^2-2*x^6-x^7-3*x^5)/(2*x^2+1-2*x+3*x^4-3*x^3+2*x^6-2*x^5-x^7) ogf A008266 12.7092 -(x+1)*(x^6+x^5+2*x^4+3*x^3+2*x^2+x+1)/(1+x^2)/(1+x^2+x)/(x-1)^3 ogf A008266 6.07008 -2*(2+5*x+33*x^4+33*x^6+38*x^5+25*x^3+2*x^10+15*x^2+25*x^7+5*x^9+15*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2+1)/(x^6+x^5+2*x^4+3*x^3+2*x^2+x+1) lgdogf A008269 4.38804 {(10*n+2*n^2+12)*a(n+1)+(-25*n-4*n^2-39)*a(n+2)+(2*n^2+29+15*n)*a(n+3)-a(n+4),a(0)=1,a(1)=2,a(2)=9,a(3)=112} ogf A008340 7.42102 (1+232*x+107224*x^5+55384*x^3+7228*x^2+133510*x^4+24508*x^6+x^8+232*x^7)/(x-1)^8 ogf A008340 4.67466 -(1+232*x+7228*x^2+232*x^7+55384*x^3+24508*x^6+133510*x^4+x^8+107224*x^5)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A008343 9.67264 -(-1-x-x^2-6*x^3-4*x^4-16*x^8-46*x^23-44*x^24-14*x^9)/(-x^2+1+x-x^3) ogf A008343 9.96575 -(1+x+14*x^9+6*x^3+x^2+4*x^4+16*x^8+46*x^23+44*x^24)/(x-1)/(x+1)^2 ogf A008346 32.567 -1/(-1+2*x^2+x^3) ogf A008346 30.7577 -1/(x+1)/(x^2+x-1) ogf A008346 21.2938 -x*(4+3*x)/(x+1)/(x^2+x-1) lgdogf A008346 10.8557 31+(2+31*x^3+62*x^2)*f(x)+(33*x^3-33+66*x^2)*f(x)^2 ogf A008346 12.5827 {-a(n+3)+2*a(n+1)+a(n),a(0)=1,a(1)=0,a(2)=2} ogf A008349 4.14116 -(-1-232*x-7228*x^2-133510*x^4-232*x^7-55384*x^3-24508*x^6-x^8-107224*x^5)/(36*x^2+1-9*x+9*x^8+126*x^4-x^9-84*x^3+84*x^6-126*x^5-36*x^7) ogf A008349 6.95305 -(1+232*x+107224*x^5+55384*x^3+7228*x^2+133510*x^4+24508*x^6+x^8+232*x^7)/(x-1)^9 ogf A008353 13.3301 -(-1+4*x-8*x^2)/(20*x^2+1-8*x-16*x^3) ogf A008353 15.4129 -(1-4*x+8*x^2)/(4*x-1)/(2*x-1)^2 ogf A008353 9.13356 -4*(-1+4*x+16*x^3-8*x^2)/(2*x-1)/(4*x-1)/(8*x^2-4*x+1) lgdogf A008353 6.24319 6-24*x+48*x^2+(-23+116*x+96*x^3-256*x^2)*f(x)+(340*x^2+17-136*x-272*x^3)*f(x)^2 ogf A008353 8.65285 {a(n+3)-8*a(n+2)+20*a(n+1)-16*a(n),a(0)=1,a(1)=4,a(2)=20} ogf A008354 21.8462 -(x+1)*(x^2+8*x+1)/(x-1)^5 ogf A008354 10.717 -(x+9*x^2+x^4+9*x^3)/(-1+5*x-10*x^2+10*x^3-5*x^4+x^5) ogf A008354 12.3478 -2*(7+27*x+x^3+15*x^2)/(x-1)/(x+1)/(x^2+8*x+1) lgdogf A008354 6.68236 {(-4-4*n-n^2)*a(n+1)+(20+2*n^2+8*n)*a(n+2)+(-4-4*n-n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=14} ogf A008355 8.07442 -(-1-35*x-180*x^2-35*x^4-180*x^3-x^5)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A008355 13.2651 -(x+1)*(x^4+34*x^3+146*x^2+34*x+1)/(x-1)^5 ogf A008355 7.95907 -20*(2*x+1)*(x+2)*(x^2+10*x+1)/(x-1)/(x+1)/(x^4+34*x^3+146*x^2+34*x+1) lgdogf A008355 4.28565 {(-34*n+41*n^2)*a(n)+(-4961-2552*n-591*n^2)*a(n+1)+(2624+994*n+591*n^2)*a(n+2)+(-280*n-471-41*n^2)*a(n+3),a(0)=1,a(1)=40,a(2)=370} ogf A008356 12.7897 (x+1)*(x^4+34*x^3+146*x^2+34*x+1)/(x-1)^6 ogf A008356 6.89971 -(1+35*x+180*x^2+35*x^4+180*x^3+x^5)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008356 6.6377 -(41+535*x+75*x^4+x^5+680*x^3+1260*x^2)/(x-1)/(x+1)/(x^4+34*x^3+146*x^2+34*x+1) lgdogf A008356 3.79984 {(-6-13*n-5*n^2)*a(n+1)+(2358+991*n+123*n^2)*a(n+2)+(-840-485*n-123*n^2)*a(n+3)+(47*n+108+5*n^2)*a(n+4),a(0)=1,a(1)=41,a(2)=411,a(3)=2051} ogf A008357 10.1442 (1+54*x+54*x^5+852*x^3+447*x^2+447*x^4+x^6)/(x-1)^6 ogf A008357 6.159 -(1+54*x+447*x^2+447*x^4+852*x^3+x^6+54*x^5)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008357 5.81299 -12*(x+1)*(5*x^4+92*x^3+270*x^2+92*x+5)/(x-1)/(x^6+54*x^5+447*x^4+852*x^3+447*x^2+54*x+1) lgdogf A008358 5.99533 -(-1-54*x-447*x^2-447*x^4-852*x^3-x^6-54*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008358 10.4918 -(1+54*x+54*x^5+852*x^3+447*x^2+447*x^4+x^6)/(x-1)^7 ogf A008358 5.40174 -(61+1218*x+1611*x^4+x^6+114*x^5+5196*x^3+4791*x^2)/(x-1)/(x^6+54*x^5+447*x^4+852*x^3+447*x^2+54*x+1) lgdogf A008359 4.94358 -(-1-77*x-931*x^2-2863*x^4-x^7-2863*x^3-77*x^6-931*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008359 8.46273 -(x+1)*(x^6+76*x^5+855*x^4+2008*x^3+855*x^2+76*x+1)/(x-1)^7 ogf A008359 4.71039 -28*(3+83*x+473*x^4+3*x^6+83*x^5+818*x^3+473*x^2)/(x-1)/(x+1)/(x^6+76*x^5+855*x^4+2008*x^3+855*x^2+76*x+1) lgdogf A008360 8.21243 (x+1)*(x^6+76*x^5+855*x^4+2008*x^3+855*x^2+76*x+1)/(x-1)^8 ogf A008360 4.41038 -(1+77*x+931*x^2+2863*x^4+x^7+2863*x^3+77*x^6+931*x^5)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A008360 3.96934 -(85+2401*x+16107*x^4+161*x^6+3255*x^5+25767*x^3+14175*x^2+x^7)/(x-1)/(x+1)/(x^6+76*x^5+855*x^4+2008*x^3+855*x^2+76*x+1) lgdogf A008361 6.71044 (1+104*x+7768*x^5+7768*x^3+1724*x^2+12550*x^4+1724*x^6+x^8+104*x^7)/(x-1)^8 ogf A008361 3.75584 -16*(x+1)*(7*x^6+254*x^5+1849*x^4+3716*x^3+1849*x^2+254*x+7)/(x-1)/(x^8+104*x^7+1724*x^6+7768*x^5+12550*x^4+7768*x^3+1724*x^2+104*x+1) lgdogf A008362 6.77981 -(1+104*x+7768*x^5+7768*x^3+1724*x^2+12550*x^4+1724*x^6+x^8+104*x^7)/(x-1)^9 ogf A008363 17.1788 -(-x^6-x^5)/(1-x-2*x^5-x^11+2*x^6+x^10) ogf A008363 19.7051 -(x+1)/(x^4+x^3+x^2+x+1)^2/(x-1)^3 ogf A008363 11.5513 -2*(1+x+6*x^4+5*x^5+x^3+x^2)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1) lgdogf A008363 74.4414 2-x+2*x^4 ogf_with_Euler_Transform A008368 6.31372 1+2*x+x^2-x^4 ogf_with_Euler_Transform A008376 9.31176 -(x+1)*(x^8+134*x^7+2800*x^6+15386*x^5+27742*x^4+15386*x^3+2800*x^2+134*x+1)/(x-1)^9 ogf A008383 23.2586 (1+16*x+16*x^3+36*x^2+x^4)/(x-1)^4 ogf A008383 15.2075 -(-1-16*x-36*x^2-x^4-16*x^3)/(6*x^2+1-4*x+x^4-4*x^3) ogf A008383 14.6443 -20*(x+1)*(1+x^2+5*x)/(x-1)/(x^4+16*x^3+36*x^2+16*x+1) lgdogf A008383 6.7589 187+2992*x+187*x^4+2992*x^3+6732*x^2+(-173+972*x-173*x^4+972*x^3-618*x^2)*f(x)+(-84*x^2-14+56*x-14*x^4+56*x^3)*f(x)^2 ogf A008383 11.6293 {-a(n)*n^2+(22+2*n^2+4*n)*a(n+1)+(-n^2-4*n-4)*a(n+2),a(0)=1,a(1)=20} ogf A008384 8.89877 -(-1-16*x-36*x^2-x^4-16*x^3)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A008384 15.255 -(1+16*x+16*x^3+36*x^2+x^4)/(x-1)^5 ogf A008384 8.47502 -(21+136*x+x^4+36*x^3+156*x^2)/(x-1)/(x^4+16*x^3+36*x^2+16*x+1) lgdogf A008384 6.06734 {(-n^2-4*n-4)*a(n+1)+(33+10*n+2*n^2)*a(n+2)+(-n^2-6*n-9)*a(n+3),a(0)=1,a(1)=21,a(2)=131} ogf A008385 7.88555 -(-1-25*x-100*x^2-25*x^4-100*x^3-x^5)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A008385 13.2708 -(x+1)*(x^4+24*x^3+76*x^2+24*x+1)/(x-1)^5 ogf A008385 7.88555 -30*(1+10*x+x^4+10*x^3+20*x^2)/(x-1)/(x+1)/(x^4+24*x^3+76*x^2+24*x+1) lgdogf A008385 8.00151 {-a(n)*n^2+(32+2*n^2+4*n)*a(n+1)+(-n^2-4*n-4)*a(n+2),a(0)=1,a(1)=30} ogf A008386 13.5193 (x+1)*(x^4+24*x^3+76*x^2+24*x+1)/(x-1)^6 ogf A008386 7.11542 -(1+25*x+100*x^2+25*x^4+100*x^3+x^5)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008386 7.02301 -(31+325*x+55*x^4+x^5+400*x^3+700*x^2)/(x-1)/(x+1)/(x^4+24*x^3+76*x^2+24*x+1) lgdogf A008386 6.14513 {(-n^2-4*n-4)*a(n+1)+(43+10*n+2*n^2)*a(n+2)+(-n^2-6*n-9)*a(n+3),a(0)=1,a(1)=31,a(2)=271} ogf A008387 9.83683 (1+36*x+36*x^5+400*x^3+225*x^2+225*x^4+x^6)/(x-1)^6 ogf A008387 5.97236 -(1+36*x+225*x^2+225*x^4+400*x^3+x^6+36*x^5)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008387 5.83347 -42*(x+1)*(x^4+14*x^3+36*x^2+14*x+1)/(x-1)/(x^6+36*x^5+225*x^4+400*x^3+225*x^2+36*x+1) lgdogf A008387 7.37762 {-a(n)*n^2+(44+2*n^2+4*n)*a(n+1)+(-n^2-4*n-4)*a(n+2),a(0)=1,a(1)=42} ogf A008388 5.7886 -(-1-36*x-225*x^2-225*x^4-400*x^3-x^6-36*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008388 10.13 -(1+36*x+36*x^5+400*x^3+225*x^2+225*x^4+x^6)/(x-1)^7 ogf A008388 5.37513 -(43+666*x+855*x^4+x^6+78*x^5+2500*x^3+2325*x^2)/(x-1)/(x^6+36*x^5+225*x^4+400*x^3+225*x^2+36*x+1) lgdogf A008388 6.05474 {(n^2+4*n+4)*a(n+1)+(-55-10*n-2*n^2)*a(n+2)+(n^2+6*n+9)*a(n+3),a(0)=1,a(1)=43,a(2)=505} ogf A008389 5.08032 -(-1-49*x-441*x^2-1225*x^4-x^7-1225*x^3-49*x^6-441*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008389 8.84677 -(x+1)*(x^6+48*x^5+393*x^4+832*x^3+393*x^2+48*x+1)/(x-1)^7 ogf A008389 4.98168 -56*(1+21*x+105*x^4+x^6+21*x^5+175*x^3+105*x^2)/(x-1)/(x+1)/(x^6+48*x^5+393*x^4+832*x^3+393*x^2+48*x+1) lgdogf A008389 7.54577 {-a(n)*n^2+(58+2*n^2+4*n)*a(n+1)+(-n^2-4*n-4)*a(n+2),a(0)=1,a(1)=56} ogf A008390 9.43581 (x+1)*(x^6+48*x^5+393*x^4+832*x^3+393*x^2+48*x+1)/(x-1)^8 ogf A008390 4.98001 -(1+49*x+441*x^2+1225*x^4+x^7+1225*x^3+49*x^6+441*x^5)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A008390 4.59693 -(57+1225*x+7105*x^4+105*x^6+1617*x^5+11025*x^3+6321*x^2+x^7)/(x-1)/(x+1)/(x^6+48*x^5+393*x^4+832*x^3+393*x^2+48*x+1) lgdogf A008390 6.18208 {(n^2+4*n+4)*a(n+1)+(-69-10*n-2*n^2)*a(n+2)+(n^2+6*n+9)*a(n+3),a(0)=1,a(1)=57,a(2)=869} ogf A008391 10.6121 (1+64*x+3136*x^5+3136*x^3+784*x^2+4900*x^4+784*x^6+x^8+64*x^7)/(x-1)^8 ogf A008391 6.08891 -72*(x+1)*(x^6+27*x^5+169*x^4+321*x^3+169*x^2+27*x+1)/(x-1)/(x^8+64*x^7+784*x^6+3136*x^5+4900*x^4+3136*x^3+784*x^2+64*x+1) lgdogf A008391 10.9242 {-a(n)*n^2+(74+2*n^2+4*n)*a(n+1)+(-n^2-4*n-4)*a(n+2),a(0)=1,a(1)=72} ogf A008392 6.96191 -(1+64*x+3136*x^5+3136*x^3+784*x^2+4900*x^4+784*x^6+x^8+64*x^7)/(x-1)^9 ogf A008392 5.61699 {(n^2+4*n+4)*a(n+1)+(-85-10*n-2*n^2)*a(n+2)+(n^2+6*n+9)*a(n+3),a(0)=1,a(1)=73,a(2)=1405} ogf A008393 6.44082 -(x+1)*(x^8+80*x^7+1216*x^6+5840*x^5+10036*x^4+5840*x^3+1216*x^2+80*x+1)/(x-1)^9 ogf A008393 7.57743 {-a(n)*n^2+(92+2*n^2+4*n)*a(n+1)+(-n^2-4*n-4)*a(n+2),a(0)=1,a(1)=90} ogf A008394 5.92414 {(n^2+4*n+4)*a(n+1)+(-103-10*n-2*n^2)*a(n+2)+(n^2+6*n+9)*a(n+3),a(0)=1,a(1)=91,a(2)=2161} ogf A008395 7.19285 {-a(n)*n^2+(112+2*n^2+4*n)*a(n+1)+(-n^2-4*n-4)*a(n+2),a(0)=1,a(1)=110} ogf A008396 5.7253 {(n^2+4*n+4)*a(n+1)+(-123-10*n-2*n^2)*a(n+2)+(n^2+6*n+9)*a(n+3),a(0)=1,a(1)=111,a(2)=3191} ogf A008397 4.62198 -(-1-119*x-2037*x^2-8787*x^4-x^7-8211*x^3-119*x^6-2037*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008397 4.04424 -6*(21+798*x+6091*x^4+21*x^6+798*x^5+11332*x^3+5803*x^2)/(x-1)/(x^7+119*x^6+2037*x^5+8787*x^4+8211*x^3+2037*x^2+119*x+1) lgdogf A008398 4.46685 -(1+119*x+2037*x^2+8787*x^4+x^7+8211*x^3+119*x^6+2037*x^5)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A008398 3.90849 -(127+4907*x+45333*x^4+245*x^6+6825*x^5+76203*x^3+36855*x^2+x^7)/(x-1)/(x^7+119*x^6+2037*x^5+8787*x^4+8211*x^3+2037*x^2+119*x+1) lgdogf A008399 6.23409 -(1+66*x+645*x^2+645*x^4+1384*x^3+x^6+66*x^5)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008399 6.09078 -36*(x+1)*(x^2+4*x+1)*(2*x^2+35*x+2)/(x-1)/(x^6+66*x^5+645*x^4+1384*x^3+645*x^2+66*x+1) lgdogf A008400 5.64451 -(-1-66*x-645*x^2-645*x^4-1384*x^3-x^6-66*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008400 5.09112 -(73+1686*x+2265*x^4+x^6+138*x^5+8116*x^3+7377*x^2)/(x-1)/(x^6+66*x^5+645*x^4+1384*x^3+645*x^2+66*x+1) lgdogf A008401 6.12343 -(1+48*x+519*x^2+519*x^4+1024*x^3+x^6+48*x^5)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008401 5.78324 -18*(x+1)*(3*x^4+68*x^3+218*x^2+68*x+3)/(x-1)/(x^6+48*x^5+519*x^4+1024*x^3+519*x^2+48*x+1) lgdogf A008402 5.54371 -(-1-48*x-519*x^2-519*x^4-1024*x^3-x^6-48*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008402 5.00021 -(55+1326*x+1797*x^4+x^6+102*x^5+6172*x^3+5667*x^2)/(x-1)/(x^6+48*x^5+519*x^4+1024*x^3+519*x^2+48*x+1) lgdogf A008405 33.6923 -(ln(x+1)-1)/(x+1)^2 lgdegf A008405 7.48719 {(-9-6*n-n^2)*a(n+1)+(-11*n-14-2*n^2)*a(n+2)+(-5*n-6-n^2)*a(n+3),a(0)=1,a(1)=-3,a(2)=11/2} lgdegf A008412 37.1989 (x+1)^4/(x-1)^4 ogf A008412 11.3874 -(1+4*x+6*x^2+x^4+4*x^3)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A008412 39.856 -8/(x-1)/(x+1) lgdogf A008412 7.9712 1+4*x+x^4+4*x^3+6*x^2+(8*x+8*x^3)*f(x)+(-1+4*x-x^4-6*x^2+4*x^3)*f(x)^2 ogf A008412 111.597 8-4*x ogf_with_Euler_Transform A008412 12.6815 {(n+2)*a(n+2)-8*a(n+1)-n*a(n),a(0)=1,a(1)=8} ogf A008412 24.2602 {a(n+2),a(0)=8,a(1)=-4} ogf_with_Euler_Transform A008413 8.59957 -(-1-5*x-10*x^2-5*x^4-10*x^3-x^5)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A008413 34.9357 -(x+1)^5/(x-1)^5 ogf A008413 37.2648 -10/(x-1)/(x+1) lgdogf A008413 6.07578 1+5*x+5*x^4+10*x^3+x^5+10*x^2+(-2-10*x^4-20*x^2)*f(x)+(1+10*x^2-10*x^3-5*x+5*x^4-x^5)*f(x)^2 ogf A008413 93.162 10-5*x ogf_with_Euler_Transform A008413 12.1516 {(n+2)*a(n+2)-10*a(n+1)-n*a(n),a(0)=1,a(1)=10} ogf A008413 23.2905 {a(n+2),a(0)=10,a(1)=-5} ogf_with_Euler_Transform A008414 37.1331 (x+1)^6/(x-1)^6 ogf A008414 7.05059 -(-1-6*x-15*x^2-15*x^4-20*x^3-x^6-6*x^5)/(15*x^2+1-6*x+15*x^4-20*x^3+x^6-6*x^5) ogf A008414 37.1331 -12/(x-1)/(x+1) lgdogf A008414 92.8328 12-6*x ogf_with_Euler_Transform A008414 12.1086 {(n+2)*a(n+2)-12*a(n+1)-n*a(n),a(0)=1,a(1)=12} ogf A008414 23.2082 {a(n+2),a(0)=12,a(1)=-6} ogf_with_Euler_Transform A008415 5.39927 -(-1-7*x-21*x^2-35*x^4-x^7-35*x^3-7*x^6-21*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008415 31.3832 -(x+1)^7/(x-1)^7 ogf A008415 33.4755 -14/(x-1)/(x+1) lgdogf A008415 83.6886 14-7*x ogf_with_Euler_Transform A008415 10.9159 {(n+2)*a(n+2)-14*a(n+1)-n*a(n),a(0)=1,a(1)=14} ogf A008415 20.9222 {a(n+2),a(0)=14,a(1)=-7} ogf_with_Euler_Transform A008416 35.806 (x+1)^8/(x-1)^8 ogf A008416 5.01954 -(1+8*x+28*x^2+70*x^4+8*x^7+56*x^3+28*x^6+x^8+56*x^5)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A008416 35.806 -16/(x-1)/(x+1) lgdogf A008416 89.5151 16-8*x ogf_with_Euler_Transform A008416 11.6759 {(n+2)*a(n+2)-16*a(n+1)-n*a(n),a(0)=1,a(1)=16} ogf A008416 22.3788 {a(n+2),a(0)=16,a(1)=-8} ogf_with_Euler_Transform A008417 7.48965 -(-1-8*x-28*x^2-70*x^4-8*x^7-56*x^3-28*x^6-x^8-56*x^5)/(36*x^2+1-9*x+9*x^8+126*x^4-x^9-84*x^3+84*x^6-126*x^5-36*x^7) ogf A008417 45.7263 -(17+x)/(x-1)/(x+1) lgdogf A008417 54.3 -(x+1)^8/(x-1)^9 ogf A008417 144.8 17-8*x ogf_with_Euler_Transform A008417 14.0129 {(-n-3)*a(n+3)+17*a(n+2)+(n+2)*a(n+1),a(0)=1,a(1)=17,a(2)=145} ogf A008417 36.2 {a(n+2),a(0)=17,a(1)=-8} ogf_with_Euler_Transform A008418 33.3146 -(x+1)^9/(x-1)^9 ogf A008418 33.3146 -18+(1-x^2)*f(x) lgdogf A008418 35.5356 -18/(x-1)/(x+1) lgdogf A008418 88.8389 18-9*x ogf_with_Euler_Transform A008418 11.5877 {(n+2)*a(n+2)-18*a(n+1)-n*a(n),a(0)=1,a(1)=18} ogf A008418 22.2097 {a(n+2),a(0)=18,a(1)=-9} ogf_with_Euler_Transform A008419 45.5238 (x+1)^9/(x-1)^10 ogf A008419 38.3358 -(19+x)/(x-1)/(x+1) lgdogf A008419 40.4656 -19-x+(1-x^2)*f(x) lgdogf A008419 121.397 19-9*x ogf_with_Euler_Transform A008419 11.7481 {(-n-3)*a(n+3)+19*a(n+2)+(n+2)*a(n+1),a(0)=1,a(1)=19,a(2)=181} ogf A008419 30.3492 {a(n+2),a(0)=19,a(1)=-9} ogf_with_Euler_Transform A008420 28.2961 (x+1)^10/(x-1)^10 ogf A008420 32.0689 -20/(x-1)/(x+1) lgdogf A008420 68.7192 20-10*x ogf_with_Euler_Transform A008420 10.4573 {(n+2)*a(n+2)-20*a(n+1)-n*a(n),a(0)=1,a(1)=20} ogf A008420 19.2414 {a(n+2),a(0)=20,a(1)=-10} ogf_with_Euler_Transform A008421 37.8968 -(21+x)/(x-1)/(x+1) lgdogf A008421 40.0022 -(x+1)^10/(x-1)^11 ogf A008421 40.0022 -21-x+(1-x^2)*f(x) lgdogf A008421 102.863 21-10*x ogf_with_Euler_Transform A008421 11.6136 {(-n-3)*a(n+3)+21*a(n+2)+(n+2)*a(n+1),a(0)=1,a(1)=21,a(2)=221} ogf A008421 28.8016 {a(n+2),a(0)=21,a(1)=-10} ogf_with_Euler_Transform A008437 74.8214 3*x^7/(1+x^8) ogf_with_Euler_Transform A008438 92.6311 -4/(-1-x) ogf_with_Euler_Transform A008438 39.6991 {-a(n+1)-a(n),a(0)=4} ogf_with_Euler_Transform A008439 65.1941 -5/(-1-x) ogf_with_Euler_Transform A008439 27.9403 {-a(n+1)-a(n),a(0)=5} ogf_with_Euler_Transform A008440 86.8423 -6/(-1-x) ogf_with_Euler_Transform A008440 37.2181 {-a(n+1)-a(n),a(0)=6} ogf_with_Euler_Transform A008441 108.075 -2/(-1-x) ogf_with_Euler_Transform A008441 46.318 {-a(n+1)-a(n),a(0)=2} ogf_with_Euler_Transform A008442 74.8214 2*x^3/(1+x^4) ogf_with_Euler_Transform A008442 23.7238 {a(n+4)+a(n),a(0)=0,a(1)=0,a(2)=0,a(3)=2} ogf_with_Euler_Transform A008443 99.5264 -3/(-1-x) ogf_with_Euler_Transform A008443 42.6542 {-a(n+1)-a(n),a(0)=3} ogf_with_Euler_Transform A008451 24.0728 -(14-7*x+7*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A008451 13.6261 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=14,a(1)=-21,a(2)=14} ogf_with_Euler_Transform A008452 23.567 -(18-9*x+9*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A008452 13.3398 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=18,a(1)=-27,a(2)=18} ogf_with_Euler_Transform A008453 21.677 -(22-11*x+11*x^2)/(-x^2-1-x-x^3) ogf_with_Euler_Transform A008453 13.088 {-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=22,a(1)=-33,a(2)=22} ogf_with_Euler_Transform A008458 46.3552 (1+4*x+x^2)/(x-1)^2 ogf A008458 22.5833 -(1+4*x+x^2-6*x^23+6*x^22)/(-x^2-1+2*x) ogf A008458 33.8749 -6*(x+1)/(x-1)/(x^2+4*x+1) lgdogf A008458 32.6203 1+4*x+x^2+(-x^2-1+2*x)*f(x) ogf A008458 18.7393 {-a(n+3)+2*a(n+2)-a(n+1),a(0)=1,a(1)=6,a(2)=12} ogf A008460 7.0695 -(-6-36*x-50*x^5-41*x^3-45*x^2-25*x^6-17*x^4-29*x^7+46*x^13-3*x^12-x^11-100*x^10-8*x^15-79*x^8-53*x^9+27*x^16+9*x^14)/(1-x^8) ogf A008461 20.2863 (-7-42*x-48*x^2-33*x^3+120*x^4+9*x^5)/(x-1) ogf A008461 10.6379 (49+96*x+315*x^4+36*x^5-546*x^3+51*x^2)/(x-1)/(9*x^5+120*x^4-33*x^3-48*x^2-42*x-7) lgdogf A008461 19.8253 -(-7-42*x+9*x^5-33*x^3-48*x^2+120*x^4)/(1-x) ogf A008462 9.22131 -(8+64*x+89*x^5+29*x^3+52*x^2+145*x^6+85*x^4+42*x^7-27*x^12+8*x^11-36*x^10+12*x^8-60*x^9)/(-1+x^8) ogf A008463 8.35895 (-9-81*x-65*x^2-61*x^3-37*x^4-58*x^5-89*x^6-145*x^7-33*x^8+61*x^9+61*x^10+45*x^11)/(x-1)/(x+1)/(1+x^2)/(x^4+1) ogf A008463 10.1042 -(9+81*x+58*x^5+61*x^3+65*x^2+89*x^6+37*x^4+145*x^7-45*x^11-61*x^10+33*x^8-61*x^9)/(-1+x^8) ogf A008464 14.7869 -(-1+3*x-4*x^2)/(20*x^2+1-8*x-16*x^3) ogf A008464 10.1317 -(-5+22*x+32*x^3-32*x^2)/(2*x-1)/(4*x-1)/(4*x^2-3*x+1) lgdogf A008464 17.0973 -(1-3*x+4*x^2)/(4*x-1)/(2*x-1)^2 ogf A008464 6.28867 41-123*x+164*x^2+(152-251*x+656*x^3-48*x^2)*f(x)+(-3860*x^2-193+1544*x+3088*x^3)*f(x)^2 ogf A008464 9.59849 {a(n+3)-8*a(n+2)+20*a(n+1)-16*a(n),a(0)=1,a(1)=5,a(2)=24} ogf A008465 7.99205 (-1+14*x-104*x^2+464*x^3-1104*x^4+1056*x^5)/(4*x-1)^4/(2*x-1)^5 ogf A008465 3.96456 -(1-14*x-1056*x^5-464*x^3+104*x^2+1104*x^4)/(44032*x^7-1+26*x+8192*x^9-296*x^2+1936*x^3-8016*x^4+21792*x^5-38912*x^6-28672*x^8) ogf A008465 4.41666 -4*(3-36*x+4800*x^4+8448*x^6-9984*x^5-1280*x^3+240*x^2)/(2*x-1)/(4*x-1)/(1056*x^5-1104*x^4+464*x^3-104*x^2+14*x-1) lgdogf A008465 3.67518 {(-2880-1056*n-96*n^2)*a(n+1)+(640*n+960+80*n^2)*a(n+2)+(-110*n-168-18*n^2)*a(n+3)+(7*n+12+n^2)*a(n+4),a(0)=1,a(1)=12,a(2)=120,a(3)=1040} ogf A008466 23.1885 -(-3+2*x+6*x^2)/(2*x-1)/(x^2+x-1) lgdogf A008466 28.3415 -x^2+(1-3*x+x^2+2*x^3)*f(x) ogf A008466 33.2704 -x^2/(-1+3*x-x^2-2*x^3) ogf A008466 40.2747 1/(2*x-1)/(x^2+x-1) ogf A008466 14.4381 {-a(n+3)+3*a(n+2)-a(n+1)-2*a(n),a(0)=0,a(1)=0,a(2)=1} ogf A008483 56.0022 -x^2/(-1+x) ogf_with_Euler_Transform A008483 61.6024 -x^2/(x-1) ogf_with_Euler_Transform A008483 16.6493 {-a(n+3)+a(n+2),a(0)=0,a(1)=0,a(2)=1} ogf_with_Euler_Transform A008484 57.6134 -x^3/(-1+x) ogf_with_Euler_Transform A008484 63.3747 -x^3/(x-1) ogf_with_Euler_Transform A008484 14.4033 {-a(n+4)+a(n+3),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf_with_Euler_Transform A008486 51.911 (1+x^2+x)/(x-1)^2 ogf A008486 38.369 -(1+x+x^2)/(-x^2-1+2*x) ogf A008486 36.7703 -3*(x+1)/(x-1)/(x^2+x+1) lgdogf A008486 35.2995 1+x+x^2+(-x^2-1+2*x)*f(x) ogf A008486 176.497 3-x^2 ogf_with_Euler_Transform A008486 19.1845 {-a(n+3)+2*a(n+2)-a(n+1),a(0)=1,a(1)=3,a(2)=6} ogf A008486 29.4162 {a(n+3),a(0)=3,a(1)=0,a(2)=-1} ogf_with_Euler_Transform A008487 13.5259 (-1-x-x^4-x^3-x^2)*f(x)+(6*x^2+1-4*x+x^4-4*x^3)*f(x)^2 ogf A008487 29.2159 (x^4+x^3+x^2+x+1)/(x-1)^4 ogf A008487 16.986 -(-1-x-x^4-x^3-x^2)/(6*x^2+1-4*x+x^4-4*x^3) ogf A008487 18.26 -5*(x+1)*(1+x^2)/(x-1)/(x^4+x^3+x^2+x+1) lgdogf A008487 146.08 5-x^4 ogf_with_Euler_Transform A008487 7.09125 {(5*n+n^2)*a(n)+(18-2*n^2-4*n)*a(n+1)+(-n-6+n^2)*a(n+2),a(0)=1,a(1)=5,a(2)=15,a(3)=35,a(4)=70,a(5)=125} ogf A008487 16.6 {a(n+5),a(0)=5,a(1)=0,a(2)=0,a(3)=0,a(4)=-1} ogf_with_Euler_Transform A008488 10.1771 -(-1-x-x^4-x^5-x^3-x^2)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A008488 16.463 -(x+1)*(1-x+x^2)*(1+x^2+x)/(x-1)^5 ogf A008488 10.7642 -6*(x^4+x^3+x^2+x+1)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) lgdogf A008488 111.948 6-x^5 ogf_with_Euler_Transform A008488 4.86731 {(6*n+n^2)*a(n)+(28-2*n^2-4*n)*a(n+1)+(-2*n-8+n^2)*a(n+2),a(0)=1,a(1)=6,a(2)=21,a(3)=56,a(4)=126,a(5)=252,a(6)=461} ogf A008488 10.9753 {a(n+6),a(0)=6,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=-1} ogf_with_Euler_Transform A008489 17.4183 (1+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^6 ogf A008489 8.70913 -(-1-x-x^4-x^5-x^3-x^2-x^6)/(15*x^2+1-6*x+15*x^4-20*x^3+x^6-6*x^5) ogf A008489 9.58005 -7*(x+1)*(x^2+x+1)*(x^2-x+1)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008489 114.961 7-x^6 ogf_with_Euler_Transform A008489 4.56193 {(7*n+n^2)*a(n)+(40-2*n^2-4*n)*a(n+1)+(-3*n-10+n^2)*a(n+2),a(0)=1,a(1)=7,a(2)=28,a(3)=84,a(4)=210,a(5)=462,a(6)=924,a(7)=1715} ogf A008489 9.91039 {a(n+7),a(0)=7,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=-1} ogf_with_Euler_Transform A008490 6.8485 -(-1-x-x^4-x^5-x^3-x^2-x^6-x^7)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008490 17.5778 -(x+1)*(1+x^2)*(x^4+1)/(x-1)^7 ogf A008490 9.41669 -8*(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)/(x+1)/(1+x^2)/(1+x^4) lgdogf A008490 105.467 8-x^7 ogf_with_Euler_Transform A008490 3.82126 {(8*n+n^2)*a(n)+(54-2*n^2-4*n)*a(n+1)+(-4*n-12+n^2)*a(n+2),a(0)=1,a(1)=8,a(2)=36,a(3)=120,a(4)=330,a(5)=792,a(6)=1716,a(7)=3432,a(8)=6434} ogf A008490 8.11284 {a(n+8),a(0)=8,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=-1} ogf_with_Euler_Transform A008491 19.4341 (1+x^2+x)*(1+x^3+x^6)/(x-1)^8 ogf A008491 6.40442 -(1+x+x^4+x^5+x^3+x^2+x^6+x^7+x^8)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A008491 10.8382 -9*(x+1)*(1+x^2)*(1+x^4)/(x-1)/(x^2+x+1)/(x^6+x^3+1) lgdogf A008491 112.718 9-x^8 ogf_with_Euler_Transform A008491 7.93787 {-a(n),a(0)=9,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=-1} ogf_with_Euler_Transform A008492 10.3648 -(x+1)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)/(x-1)^9 ogf A008492 7.09917 -10*(x^2+x+1)*(x^6+x^3+1)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) lgdogf A008492 86.3733 10-x^9 ogf_with_Euler_Transform A008492 6.56 {-a(n),a(0)=10,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=-1} ogf_with_Euler_Transform A008493 9.90804 (x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^10 ogf A008493 5.37564 -11*(x+1)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)/(x-1)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) lgdogf A008493 72.1871 11-x^10 ogf_with_Euler_Transform A008493 5.80816 {-a(n),a(0)=11,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A008494 9.64972 -(x+1)*(1+x^2)*(1+x^2+x)*(1-x+x^2)*(x^4-x^2+1)/(x-1)^11 ogf A008494 9.64972 -(x+1)*(x^2+1)*(1+x+x^2)*(x^2-x+1)*(x^4-x^2+1)/(x-1)^11 ogf A008494 75.8192 12-x^11 ogf_with_Euler_Transform A008494 5.58668 {-a(n),a(0)=12,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=0,a(11)=-1} ogf_with_Euler_Transform A008495 8.96106 (x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^12 ogf A008495 30.368 13*exp(-1/13*x^12) ogf_with_Euler_Transform A008495 14.3849 169+(-26+26*x)*f(x)+(x^2+1-2*x)*f(x)^2 lgdogf A008495 5.30703 {-a(n),a(0)=13,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=0,a(11)=0,a(12)=-1} ogf_with_Euler_Transform A008496 11.5196 (x^2+x+1)*(x^6-x^5+2*x^3-x+1)/(x^4+x^3+x^2+x+1)^3/(x-1)^4 ogf A008496 5.05089 -(1+x+24*x^4+4*x^6+4*x^5+10*x^3+x^10+4*x^2+x^11+8*x^12+24*x^7+12*x^9+26*x^8)/(x-1)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x^6-x^5+2*x^3-x+1) lgdogf A008496 9.51617 -(x^5+x^13+x^10+x^8+2*x^9)/(-1+x+3*x^5-3*x^10-3*x^6+3*x^11+x^15-x^16) ogf A008497 9.27221 -(1+x+12*x^4+x^6+x^5+5*x^3+x^2+x^7+7*x^8)/(x-1)/(x^4+x^3+x^2+x+1)/(x^4+1) lgdogf A008497 18.802 -(1+x^4)/(x^4+x^3+x^2+x+1)^2/(x-1)^3 ogf A008497 17.3557 -(x^5+x^9)/(-1+x+2*x^5+x^11-2*x^6-x^10) ogf A008497 45.1248 1+x^3+2*x^4-x^7 ogf_with_Euler_Transform A008498 10.8406 -(-1-x-x^4-x^3-x^2)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A008498 11.5182 -(6+6*x+6*x^2+6*x^3+x^4)/(x^4+x^3+x^2+x+1)/(x-1) lgdogf A008498 21.2643 -(x^4+x^3+x^2+x+1)/(x-1)^5 ogf A008498 110.574 6-x^4 ogf_with_Euler_Transform A008498 5.07222 {(14+9*n+n^2)*a(n+1)+(12-10*n-2*n^2)*a(n+2)+(n-6+n^2)*a(n+3),a(0)=1,a(1)=6,a(2)=21,a(3)=56,a(4)=126,a(5)=251} ogf A008498 12.5653 {a(n+5),a(0)=6,a(1)=0,a(2)=0,a(3)=0,a(4)=-1} ogf_with_Euler_Transform A008499 17.3152 (x+1)*(x^2+x+1)*(x^2-x+1)/(x-1)^6 ogf A008499 9.21615 -(1+x+x^4+x^5+x^3+x^2)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008499 9.21615 -(7+7*x+7*x^2+7*x^3+7*x^4+x^5)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) lgdogf A008499 114.28 7-x^5 ogf_with_Euler_Transform A008499 4.84239 {(16+10*n+n^2)*a(n+1)+(23-10*n-2*n^2)*a(n+2)+(-9+n^2)*a(n+3),a(0)=1,a(1)=7,a(2)=28,a(3)=84,a(4)=210,a(5)=462,a(6)=923} ogf A008499 11.204 {a(n+6),a(0)=7,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=-1} ogf_with_Euler_Transform A008500 9.03186 -(1+x+x^4+x^5+x^3+x^2+x^6)/(-21*x^2-1+7*x-35*x^4+35*x^3-7*x^6+21*x^5+x^7) ogf A008500 9.69597 -(8+8*x+8*x^2+8*x^3+8*x^4+8*x^5+x^6)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008500 19.3919 -(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^7 ogf A008500 131.865 8-x^6 ogf_with_Euler_Transform A008500 4.95734 {(18+11*n+n^2)*a(n+1)+(36-10*n-2*n^2)*a(n+2)+(-n-12+n^2)*a(n+3),a(0)=1,a(1)=8,a(2)=36,a(3)=120,a(4)=330,a(5)=792,a(6)=1716,a(7)=3431} ogf A008500 11.3677 {a(n+7),a(0)=8,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=-1} ogf_with_Euler_Transform A008501 19.3204 (x+1)*(x^2+1)*(1+x^4)/(x-1)^8 ogf A008501 6.67015 -(1+x+x^4+x^5+x^3+x^2+x^6+x^7)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A008501 8.00418 -(9+9*x+9*x^2+9*x^3+9*x^4+9*x^5+9*x^6+x^7)/(x-1)/(x+1)/(x^2+1)/(x^4+1) lgdogf A008501 112.059 9-x^7 ogf_with_Euler_Transform A008501 8.61989 {a(n+8),a(0)=9,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=-1} ogf_with_Euler_Transform A008502 6.16952 -(10+10*x+10*x^2+10*x^3+10*x^4+10*x^5+10*x^6+10*x^7+x^8)/(x-1)/(x^2+x+1)/(x^6+x^3+1) lgdogf A008502 17.2747 -(x^2+x+1)*(x^6+x^3+1)/(x-1)^9 ogf A008502 7.09917 -1000+(300-300*x)*f(x)+(-30+60*x-30*x^2)*f(x)^2+(-3*x+3*x^2-x^3+1)*f(x)^3 lgdogf A008502 86.3733 10-x^8 ogf_with_Euler_Transform A008502 7.19777 {-a(n),a(0)=10,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=-1} ogf_with_Euler_Transform A008503 10.1062 (x+1)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)/(x-1)^10 ogf A008503 4.55234 -(11+11*x+11*x^2+11*x^3+11*x^4+11*x^5+11*x^6+11*x^7+11*x^8+x^9)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) lgdogf A008503 84.2183 11-x^9 ogf_with_Euler_Transform A008503 6.39633 {-a(n),a(0)=11,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=-1} ogf_with_Euler_Transform A008504 10.2064 -(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)/(x-1)^11 ogf A008504 4.42279 -(12+12*x+12*x^2+12*x^3+12*x^4+12*x^5+12*x^6+12*x^7+12*x^8+12*x^9+x^10)/(x-1)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) lgdogf A008504 75.8192 12-x^10 ogf_with_Euler_Transform A008504 6.10039 {-a(n),a(0)=12,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A008505 10.1227 (x+1)*(x^2+1)*(x^2+x+1)*(x^2-x+1)*(x^4-x^2+1)/(x-1)^12 ogf A008505 78.0892 13-x^11 ogf_with_Euler_Transform A008505 5.75394 {-a(n),a(0)=13,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=0,a(11)=-1} ogf_with_Euler_Transform A008506 8.54674 -(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^13 ogf A008506 29.4388 14*exp(-1/14*x^12) ogf_with_Euler_Transform A008506 13.9447 196+(-28+28*x)*f(x)+(x^2+1-2*x)*f(x)^2 lgdogf A008506 5.14464 {-a(n),a(0)=14,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=0,a(11)=0,a(12)=-1} ogf_with_Euler_Transform A008511 19.0012 (x^2+10*x+1)*(x+1)^2/(x-1)^4 ogf A008511 10.2314 -(1+12*x+x^4+12*x^3+22*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A008511 13.3008 -16*(1+4*x+x^2)/(x-1)/(x+1)/(x^2+10*x+1) lgdogf A008511 4.32547 -581-6972*x-581*x^4-6972*x^3-12782*x^2+(506-3224*x+506*x^4-3224*x^3+1836*x^2)*f(x)+(450*x^2+75-300*x+75*x^4-300*x^3)*f(x)^2 ogf A008511 3.9704 {(-238*n-67*n^2)*a(n)+(-6135-4046*n-647*n^2)*a(n+1)+(-14100-3644*n+67*n^2)*a(n+2)+(3644*n+5109+647*n^2)*a(n+3),a(0)=1,a(1)=16,a(2)=80} ogf A008512 8.07231 -(-1-27*x-27*x^4-x^5-92*x^3-92*x^2)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A008512 13.1913 -(x+1)*(x^4+26*x^3+66*x^2+26*x+1)/(x-1)^5 ogf A008512 7.61753 -4*(8+73*x+8*x^4+73*x^3+138*x^2)/(x-1)/(x+1)/(x^4+26*x^3+66*x^2+26*x+1) lgdogf A008512 4.09731 {(-146*n-241*n^2)*a(n)+(789-2308*n-57*n^2)*a(n+1)+(-7200-1966*n+57*n^2)*a(n+2)+(1300*n+1731+241*n^2)*a(n+3),a(0)=1,a(1)=32,a(2)=242} ogf A008513 11.9586 (x^4+56*x^3+246*x^2+56*x+1)*(x+1)^2/(x-1)^6 ogf A008513 6.12167 -(1+58*x+359*x^4+58*x^5+604*x^3+x^6+359*x^2)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008513 7.04411 -16*(4+59*x+4*x^4+59*x^3+144*x^2)/(x-1)/(x+1)/(x^4+56*x^3+246*x^2+56*x+1) lgdogf A008514 9.10801 -(-1-12*x-x^4-12*x^3-22*x^2)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A008514 11.88 -(17+75*x+x^3+27*x^2)/(x-1)/(x+1)/(x^2+10*x+1) lgdogf A008514 18.8442 -(x^2+10*x+1)*(x+1)^2/(x-1)^5 ogf A008515 26.1906 (x+1)*(x^4+26*x^3+66*x^2+26*x+1)/(x-1)^6 ogf A008515 14.1571 -(1+27*x+27*x^4+x^5+92*x^3+92*x^2)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008515 13.6055 -(33+319*x+59*x^4+x^5+384*x^3+644*x^2)/(x-1)/(x+1)/(x^4+26*x^3+66*x^2+26*x+1) lgdogf A008515 6.98417 {(1162+1035*n+227*n^2)*a(n+1)+(4422+2871*n+99*n^2)*a(n+2)+(9240+1683*n-99*n^2)*a(n+3)+(-1689*n-3124-227*n^2)*a(n+4),a(0)=1,a(1)=33,a(2)=275,a(3)=1267} ogf A008516 5.92642 -(-1-58*x-359*x^4-58*x^5-604*x^3-x^6-359*x^2)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008516 6.57688 -(65+1001*x+121*x^4+x^5+1246*x^3+2606*x^2)/(x-1)/(x+1)/(x^4+56*x^3+246*x^2+56*x+1) lgdogf A008516 12.2569 -(x^4+56*x^3+246*x^2+56*x+1)*(x+1)^2/(x-1)^7 ogf A008522 14.8337 (3+7*x-5*x^4+3*x^5+3*x^3-9*x^2)/(x-1)/(x^5+3*x^3-4*x^2+x-2) lgdogf A008522 28.232 -(-2+x-4*x^2+3*x^3+x^5)/(x-1)^2 ogf A008522 25.0055 -(2-x-x^5-3*x^3+4*x^2)/(-x^2-1+2*x) ogf A008527 15.69 -(-1-7*x-x^3-7*x^2)/(3*x^2+1-3*x-x^3) ogf A008527 22.3281 -(x+1)*(x^2+6*x+1)/(x-1)^3 ogf A008527 6.11084 -161-1127*x-161*x^3-1127*x^2+(205-175*x-117*x^3+791*x^2)*f(x)+(-132*x^2-44+132*x+44*x^3)*f(x)^2 ogf A008527 14.1593 -2*(5+14*x+5*x^2)/(x-1)/(x+1)/(x^2+6*x+1) lgdogf A008527 9.07079 {a(4+n)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=10,a(2)=34,a(3)=74} ogf A008528 16.1432 (1+14*x+36*x^2+14*x^3+x^4)/(x-1)^4 ogf A008528 10.5552 -(-1-14*x-x^4-14*x^3-36*x^2)/(6*x^2+1-4*x+x^4-4*x^3) ogf A008528 9.80125 -6*(x+1)*(3*x^2+16*x+3)/(x-1)/(x^4+14*x^3+36*x^2+14*x+1) lgdogf A008528 4.0657 2713+37982*x+2713*x^4+37982*x^3+97668*x^2+(-2504+13778*x-2504*x^4+13778*x^3-8754*x^2)*f(x)+(-1254*x^2-209+836*x-209*x^4+836*x^3)*f(x)^2 ogf A008528 3.61099 {(16739*n+11101*n^2)*a(n)+(396798+370053*n+74739*n^2)*a(n+1)+(-138150-72419*n-80701*n^2)*a(n+2)+(-8133*n+21852-5139*n^2)*a(n+3),a(0)=1,a(1)=18,a(2)=102} ogf A008529 20.4072 (x^2+8*x+1)*(x+1)^2/(x-1)^4 ogf A008529 10.596 -(1+10*x+x^4+10*x^3+18*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A008529 4.1742 -1319-13190*x-1319*x^4-13190*x^3-23742*x^2+(1099-7476*x+1099*x^4-7476*x^3+3954*x^2)*f(x)+(220-880*x+1320*x^2-880*x^3+220*x^4)*f(x)^2 ogf A008529 13.4389 -2*(7+26*x+7*x^2)/(x-1)/(x+1)/(x^2+8*x+1) lgdogf A008529 3.42233 {(-51657*n-13820*n^2)*a(n)+(-1125681-702708*n-106745*n^2)*a(n+1)+(-2437788-588813*n+13820*n^2)*a(n+2)+(619788*n+898659+106745*n^2)*a(n+3),a(0)=1,a(1)=14,a(2)=68} ogf A008530 26.0759 (x^2+4*x+1)^2/(x-1)^4 ogf A008530 10.9519 -(1+8*x+x^4+8*x^3+18*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A008530 20.2812 -12*(x+1)/(x-1)/(x^2+4*x+1) lgdogf A008530 4.60162 -139-1112*x-139*x^4-1112*x^3-2502*x^2+(114-756*x+114*x^4-756*x^3+384*x^2)*f(x)+(150*x^2+25-100*x+25*x^4-100*x^3)*f(x)^2 ogf A008530 7.1116 {(n+3)*a(n+3)+(-6+3*n)*a(n+2)+(-15-3*n)*a(n+1)-a(n)*n,a(0)=1,a(1)=12,a(2)=60} ogf A008531 24.3264 (1+6*x+16*x^2+6*x^3+x^4)/(x-1)^4 ogf A008531 15.5689 -(1+6*x+x^4+6*x^3+16*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A008531 14.9701 -10*(x+1)*(x^2+4*x+1)/(x-1)/(x^4+6*x^3+16*x^2+6*x+1) lgdogf A008531 7.07677 -67-402*x-67*x^4-402*x^3-1072*x^2+(52-358*x+52*x^4-358*x^3+162*x^2)*f(x)+(15-60*x+90*x^2-60*x^3+15*x^4)*f(x)^2 ogf A008531 5.44367 {(-5281*n-699*n^2)*a(n)+(-44850+7639*n+6669*n^2)*a(n+1)+(37626+42325*n-1689*n^2)*a(n+2)+(-16027*n-9552-4281*n^2)*a(n+3),a(0)=1,a(1)=10,a(2)=50} ogf A008532 30.604 (x^2+4*x+1)*(x+1)^2/(x-1)^4 ogf A008532 20.1539 -2*(5+14*x+5*x^2)/(x-1)/(x+1)/(x^2+4*x+1) lgdogf A008532 5.98775 -2939-17634*x-2939*x^4-17634*x^3-29390*x^2+(1799-18596*x+1799*x^4-18596*x^3+6234*x^2)*f(x)+(1140-4560*x+6840*x^2-4560*x^3+1140*x^4)*f(x)^2 ogf A008532 6.50637 {(-105*n-20*n^2)*a(n)+(-1437-666*n-79*n^2)*a(n+1)+(-2328-369*n+20*n^2)*a(n+2)+(546*n+927+79*n^2)*a(n+3),a(0)=1,a(1)=10,a(2)=44} ogf A008533 8.45866 -(-1-7*x-7*x^4-x^5-22*x^3-22*x^2)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A008533 14.0978 -(x+1)*(1+6*x+16*x^2+6*x^3+x^4)/(x-1)^5 ogf A008533 10.1817 -12*(x^2+3*x+1)^2/(x-1)/(x+1)/(x^4+6*x^3+16*x^2+6*x+1) lgdogf A008533 5.39032 {(n+n^2)*a(n)+(18*n+16+2*n^2)*a(n+1)+(6*n+20-2*n^2)*a(n+2)+(-5*n-6-n^2)*a(n+3),a(0)=1,a(1)=12,a(2)=72} ogf A008534 11.8991 (1+8*x+29*x^2+64*x^3+29*x^4+8*x^5+x^6)/(x-1)^6 ogf A008534 6.92862 -(1+8*x+29*x^4+8*x^5+64*x^3+x^6+29*x^2)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A008534 6.92862 -14*(x+1)*(x^4+6*x^3+16*x^2+6*x+1)/(x-1)/(x^6+8*x^5+29*x^4+64*x^3+29*x^2+8*x+1) lgdogf A008534 4.63865 {(4*n+n^2)*a(n)+(57+14*n-n^2)*a(n+1)+(6-20*n-n^2)*a(n+2)+(2*n-3+n^2)*a(n+3),a(0)=1,a(1)=14,a(2)=98,a(3)=462,a(4)=1596} ogf A008535 5.6043 -(-1-9*x-93*x^4-37*x^5-93*x^3-9*x^6-x^7-37*x^2)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008535 9.83397 -(x+1)*(1+8*x+29*x^2+64*x^3+29*x^4+8*x^5+x^6)/(x-1)^7 ogf A008535 5.42917 -8*(2+16*x+58*x^4+2*x^6+16*x^5+93*x^3+58*x^2)/(x-1)/(x+1)/(x^6+8*x^5+29*x^4+64*x^3+29*x^2+8*x+1) lgdogf A008542 32.162 -1+(1-6*x)*f(x) lgdegf A008542 48.2431 -1/(6*x-1) lgdegf A008542 11.4864 -1/6*(1-5*x)^(1/5)+5/6*(1-5*x)^(1/5)*x+1/6 revegf A008542 32.162 1/(1-6*x)^(1/6) egf A008542 12.6955 {(-6*n-7)*a(n+1)+a(n+2),a(0)=1,a(1)=1} ogf A008543 15.4123 -1/6*x*(x-2)*(x^2-x+1)*(x^2-3*x+3) revegf A008543 34.9346 -5+(1-6*x)*f(x) lgdegf A008543 52.402 -5/(6*x-1) lgdegf A008543 34.9346 1/(1-6*x)^(5/6) egf A008543 13.4364 {(-6*n-11)*a(n+1)+a(n+2),a(0)=1,a(1)=5} ogf A008544 21.3107 -1+(1-6*x+9*x^2)*f(x)^3 egf A008544 49.0145 -2/(3*x-1) lgdegf A008544 32.6764 1/(1-3*x)^(2/3) egf A008544 28.8321 1/3*x*(x^2-3*x+3) revegf A008544 12.8986 {(-3*n-5)*a(n+1)+a(n+2),a(0)=1,a(1)=2} ogf A008545 26.2542 -1/4*x*(x-2)*(x^2-2*x+2) revegf A008545 42.0067 -3+(1-4*x)*f(x) lgdegf A008545 63.0101 -3/(4*x-1) lgdegf A008545 39.3813 1/(-4*x+1)^(3/4) egf A008545 42.0067 1/(1-4*x)^(3/4) egf A008545 16.5816 {(-4*n-7)*a(n+1)+a(n+2),a(0)=1,a(1)=3} ogf A008546 33.2711 -4+(1-5*x)*f(x) lgdegf A008546 49.9066 -4/(5*x-1) lgdegf A008546 33.2711 1/(1-5*x)^(4/5) egf A008546 16.0989 1/5*x*(5-10*x+10*x^2-5*x^3+x^4) revegf A008546 13.1333 {(-5*n-9)*a(n+1)+a(n+2),a(0)=1,a(1)=4} ogf A008548 35.6984 -1+(1-5*x)*f(x) lgdegf A008548 53.5477 -1/(5*x-1) lgdegf A008548 12.7494 -1/5*(1-4*x)^(1/4)+4/5*(1-4*x)^(1/4)*x+1/5 revegf A008548 35.6984 1/(1-5*x)^(1/5) egf A008548 14.0915 {(-5*n-6)*a(n+1)+a(n+2),a(0)=1,a(1)=1} ogf A008549 16.2197 -x+(1-6*x+8*x^2)*f(x)+(-x+8*x^2-16*x^3)*f(x)^2 ogf A008549 10.6586 {(-16*n-40)*a(n+1)+(8*n+26)*a(n+2)+(-n-4)*a(n+3),a(0)=0,a(1)=1,a(2)=6} ogf A008553 28.4607 -(-10-x+(100+x)^(1/2))/(19+x) revogf A008553 43.4401 -(-20+19*x)/(x-1)^2 ogf A008553 30.5689 -(-21+19*x)/(x-1)/(19*x-20) lgdogf A008553 35.8853 -(20-19*x)/(-x^2-1+2*x) ogf A008553 14.2304 -8020+7619*x+(361-764*x+401*x^2)*f(x)+(2-4*x+2*x^2)*f(x)^2 ogf A008553 21.1631 {-a(n+2)+2*a(n+1)-a(n),a(0)=20,a(1)=21} ogf A008574 56.2701 (x+1)^2/(x-1)^2 ogf A008574 33.762 -(1+2*x+x^2)/(-x^2-1+2*x) ogf A008574 60.2893 -4/(x-1)/(x+1) lgdogf A008574 31.2611 1+2*x+x^2+(-x^2-1+2*x)*f(x) ogf A008574 168.81 4-2*x ogf_with_Euler_Transform A008574 18.3489 {-a(n+3)+2*a(n+2)-a(n+1),a(0)=1,a(1)=4,a(2)=8} ogf A008574 36.6979 {a(n+2),a(0)=4,a(1)=-2} ogf_with_Euler_Transform A008576 19.1826 (x^2+1)*(x+1)^2/(x^2+x+1)/(x-1)^2 ogf A008576 16.2314 -(-1-2*x-x^4-2*x^3-2*x^2)/(1-x+x^4-x^3) ogf A008576 11.1057 -(3+4*x+3*x^4+4*x^3+10*x^2)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1) lgdogf A008576 6.8807 -2-4*x-2*x^4-4*x^3-4*x^2+(-21-48*x-21*x^4-48*x^3-46*x^2)*f(x)+(23-23*x^3-23*x+23*x^4)*f(x)^2 ogf A008576 57.5477 3-x+x^2-x^3 ogf_with_Euler_Transform A008576 16.6585 {a(n+4),a(0)=3,a(1)=-1,a(2)=1,a(3)=-1} ogf_with_Euler_Transform A008577 11.573 -(-1-2*x-x^4-2*x^3-2*x^2)/(x^2+1-2*x+2*x^4-x^3-x^5) ogf A008577 9.67575 -(4+6*x+5*x^4+x^5+7*x^3+13*x^2)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1) lgdogf A008577 17.3594 -(x^2+1)*(x+1)^2/(x^2+x+1)/(x-1)^3 ogf A008577 53.6564 4-x+x^2-x^3 ogf_with_Euler_Transform A008577 15.5321 {a(n+4),a(0)=4,a(1)=-1,a(2)=1,a(3)=-1} ogf_with_Euler_Transform A008579 12.7893 -(1+4*x+3*x^4-2*x^5+6*x^3+6*x^2)/(-1-x^4+2*x^2) ogf A008579 12.5228 -(2*x+1)*(x^4-2*x^3-2*x^2-2*x-1)/(x-1)^2/(x+1)^2 ogf A008579 7.80645 2*(2+8*x-2*x^4+x^6+12*x^3+15*x^2)/(x-1)/(2*x+1)/(x+1)/(x^4-2*x^3-2*x^2-2*x-1) lgdogf A008579 5.13758 {(-n+n^2)*a(n)+(n^2+3*n-6)*a(n+1)+(-6+3*n-n^2)*a(n+2)+(-n^2-n+6)*a(n+3),a(0)=1,a(1)=4,a(2)=8,a(3)=14,a(4)=18,a(5)=22} ogf A008580 12.7835 (2*x+1)*(x^4-2*x^3-2*x^2-2*x-1)/(x+1)^2/(x-1)^3 ogf A008580 7.90558 (5+21*x+5*x^4+x^5+36*x^3+40*x^2)/(x-1)/(2*x+1)/(x+1)/(x^4-2*x^3-2*x^2-2*x-1) lgdogf A008580 10.0137 -(-1-4*x-3*x^4+2*x^5-6*x^3-6*x^2)/(-2*x^2+1-x+x^4+2*x^3-x^5) ogf A008581 32.2671 1+x+x^2+x^3+x^4+x^6 ogf_with_Euler_Transform A008582 28.3962 1+x^3+x^5+x^6+x^8+x^9+x^11+x^14 ogf_with_Euler_Transform A008585 100.409 -2/(x-1) lgdogf A008585 32.131 12*x/(3+(9+12*x)^(1/2))^2 revogf A008585 38.2512 3*x+(-x^2-1+2*x)*f(x) ogf A008585 53.5517 3*x/(1-2*x+x^2) ogf A008585 89.2528 3/(x-1)^2 ogf A008585 22.3132 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=3} ogf A008586 103.034 -2/(x-1) lgdogf A008586 39.2509 4*x+(-x^2-1+2*x)*f(x) ogf A008586 54.9513 4*x/(1-2*x+x^2) ogf A008586 91.5855 4/(x-1)^2 ogf A008586 43.3826 x/(1+(1+x)^(1/2))^2 revogf A008586 22.8964 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=4} ogf A008587 101.137 -2/(x-1) lgdogf A008587 31.1191 20*x/(5+(20*x+25)^(1/2))^2 revogf A008587 38.5284 5*x+(-x^2-1+2*x)*f(x) ogf A008587 53.9397 5*x/(1-2*x+x^2) ogf A008587 89.8995 5/(x-1)^2 ogf A008587 22.4749 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=5} ogf A008588 26.6894 -(6*x-6*x^23+6*x^22)/(-1+2*x-x^2) ogf A008588 110.094 -2/(x-1) lgdogf A008588 41.9404 6*x+(-x^2-1+2*x)*f(x) ogf A008588 38.2934 6*x/(3+(9+6*x)^(1/2))^2 revogf A008588 97.861 6/(x-1)^2 ogf A008588 24.4652 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=6} ogf A008589 101.185 -2/(x-1) lgdogf A008589 31.1339 28*x/(7+(49+28*x)^(1/2))^2 revogf A008589 38.5467 7*x+(-x^2-1+2*x)*f(x) ogf A008589 53.9654 7*x/(1-2*x+x^2) ogf A008589 89.9423 7/(x-1)^2 ogf A008589 22.4856 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=7} ogf A008590 102.187 -2/(x-1) lgdogf A008590 35.5433 2*x/(2+(4+2*x)^(1/2))^2 revogf A008590 38.9283 8*x+(-x^2-1+2*x)*f(x) ogf A008590 54.4997 8*x/(1-2*x+x^2) ogf A008590 90.8328 8/(x-1)^2 ogf A008590 22.7082 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=8} ogf A008591 100.223 -2/(x-1) lgdogf A008591 34.8602 4*x/(3+(9+4*x)^(1/2))^2 revogf A008591 38.1802 9*x+(-x^2-1+2*x)*f(x) ogf A008591 53.4523 9*x/(1-2*x+x^2) ogf A008591 89.0872 9/(x-1)^2 ogf A008591 22.2718 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=9} ogf A008592 101.719 -2/(x-1) lgdogf A008592 36.9887 10*x+(-x^2-1+2*x)*f(x) ogf A008592 50.8595 10*x/(1-2*x+x^2) ogf A008592 31.2982 10*x/(5+(10*x+25)^(1/2))^2 revogf A008592 81.3752 10/(x-1)^2 ogf A008592 21.9933 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=10} ogf A008593 101.719 -2/(x-1) lgdogf A008593 36.9887 11*x+(-x^2-1+2*x)*f(x) ogf A008593 50.8595 11*x/(1-2*x+x^2) ogf A008593 81.3752 11/(x-1)^2 ogf A008593 29.0626 44*x/(11+(121+44*x)^(1/2))^2 revogf A008593 21.9933 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=11} ogf A008594 102.218 -2/(x-1) lgdogf A008594 37.17 12*x+(-x^2-1+2*x)*f(x) ogf A008594 51.1088 12*x/(1-2*x+x^2) ogf A008594 81.7741 12/(x-1)^2 ogf A008594 35.554 3*x/(3+(9+3*x)^(1/2))^2 revogf A008594 22.1011 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=12} ogf A008595 100.25 -2/(x-1) lgdogf A008595 36.4545 13*x+(-x^2-1+2*x)*f(x) ogf A008595 50.1249 13*x/(1-2*x+x^2) ogf A008595 80.1999 13/(x-1)^2 ogf A008595 28.6428 52*x/(13+(169+52*x)^(1/2))^2 revogf A008595 21.6756 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=13} ogf A008596 100.25 -2/(x-1) lgdogf A008596 36.4545 14*x+(-x^2-1+2*x)*f(x) ogf A008596 50.1249 14*x/(1-2*x+x^2) ogf A008596 30.8461 14*x/(7+(49+14*x)^(1/2))^2 revogf A008596 80.1999 14/(x-1)^2 ogf A008596 21.6756 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=14} ogf A008597 100.746 -2/(x-1) lgdogf A008597 36.6349 15*x+(-x^2-1+2*x)*f(x) ogf A008597 50.3731 15*x/(1-2*x+x^2) ogf A008597 80.5969 15/(x-1)^2 ogf A008597 28.7846 60*x/(15+(225+60*x)^(1/2))^2 revogf A008597 21.7829 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=15} ogf A008598 100.746 -2/(x-1) lgdogf A008598 36.6349 16*x+(-x^2-1+2*x)*f(x) ogf A008598 50.3731 16*x/(1-2*x+x^2) ogf A008598 80.5969 16/(x-1)^2 ogf A008598 42.4194 x/(2+(4+x)^(1/2))^2 revogf A008598 21.7829 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=16} ogf A008599 101.242 -2/(x-1) lgdogf A008599 36.8154 17*x+(-x^2-1+2*x)*f(x) ogf A008599 50.6212 17*x/(1-2*x+x^2) ogf A008599 80.9939 17/(x-1)^2 ogf A008599 28.9264 68*x/(17+(289+68*x)^(1/2))^2 revogf A008599 21.8902 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=17} ogf A008600 101.242 -2/(x-1) lgdogf A008600 36.8154 18*x+(-x^2-1+2*x)*f(x) ogf A008600 50.6212 18*x/(1-2*x+x^2) ogf A008600 80.9939 18/(x-1)^2 ogf A008600 35.2147 2*x/(3+(9+2*x)^(1/2))^2 revogf A008600 21.8902 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=18} ogf A008601 101.242 -2/(x-1) lgdogf A008601 36.8154 19*x+(-x^2-1+2*x)*f(x) ogf A008601 50.6212 19*x/(1-2*x+x^2) ogf A008601 80.9939 19/(x-1)^2 ogf A008601 28.9264 76*x/(19+(361+76*x)^(1/2))^2 revogf A008601 21.8902 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=19} ogf A008602 97.3128 -2/(x-1) lgdogf A008602 35.3865 20*x+(-x^2-1+2*x)*f(x) ogf A008602 48.6564 20*x/(1-2*x+x^2) ogf A008602 77.8502 20/(x-1)^2 ogf A008602 32.4376 5*x/(5+(25+5*x)^(1/2))^2 revogf A008602 21.0406 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=20} ogf A008603 89.5215 -2/(x-1) lgdogf A008603 32.5533 21*x+(-x^2-1+2*x)*f(x) ogf A008603 44.7608 21*x/(1-2*x+x^2) ogf A008603 71.6172 21/(x-1)^2 ogf A008603 25.5776 84*x/(21+(441+84*x)^(1/2))^2 revogf A008603 19.356 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=21} ogf A008604 84.7087 -2/(x-1) lgdogf A008604 30.8031 22*x+(-x^2-1+2*x)*f(x) ogf A008604 42.3543 22*x/(1-2*x+x^2) ogf A008604 24.2025 22*x/(11+(121+22*x)^(1/2))^2 revogf A008604 67.7669 22/(x-1)^2 ogf A008604 18.3154 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=22} ogf A008605 100.262 -2/(x-1) lgdogf A008605 36.4588 23*x+(-x^2-1+2*x)*f(x) ogf A008605 50.1308 23*x/(1-2*x+x^2) ogf A008605 80.2093 23/(x-1)^2 ogf A008605 28.6462 92*x/(23+(529+92*x)^(1/2))^2 revogf A008605 21.6782 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=23} ogf A008606 101.245 -2/(x-1) lgdogf A008606 36.8162 24*x+(-x^2-1+2*x)*f(x) ogf A008606 50.6223 24*x/(1-2*x+x^2) ogf A008606 80.9957 24/(x-1)^2 ogf A008606 33.7482 6*x/(6+(36+6*x)^(1/2))^2 revogf A008606 21.8907 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=24} ogf A008607 99.7565 -2/(x-1) lgdogf A008607 36.2751 25*x+(-x^2-1+2*x)*f(x) ogf A008607 49.8783 25*x/(1-2*x+x^2) ogf A008607 79.8052 25/(x-1)^2 ogf A008607 33.2522 4*x/(5+(25+4*x)^(1/2))^2 revogf A008607 21.569 {a(n+2)-2*a(n+1)+a(n),a(0)=0,a(1)=25} ogf A008609 7.16151 -(-1-2*x^4-x^12+2*x^11-4*x^10+x^5+4*x^9-x^6+2*x^7-x^2-2*x^8+2*x^3)/(1-2*x+x^2-3*x^3+6*x^4-3*x^5) ogf A008609 8.28319 -(1+x^2-2*x^3+2*x^4-x^5+x^6-2*x^7-4*x^9+4*x^10-2*x^11+x^12+2*x^8)/(3*x^3-1)/(x-1)^2 ogf A008610 16.159 (1-x+x^2+x^3)/(x^2+1)/(x+1)^2/(x-1)^4 ogf A008610 8.42091 -(1+4*x-x^4+5*x^6+8*x^5+12*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(x^3+x^2-x+1) lgdogf A008610 11.7232 -(1-x+x^2+x^3)/(-2*x^5-1+2*x+2*x^4-2*x^3-x^8+2*x^7) ogf A008611 35.417 (x^2-x+1)/(x^2+x+1)/(x-1)^2 ogf A008611 20.7882 -2*x*(1+x^3-x^2+2*x)/(x-1)/(1+x+x^2)/(x^2-x+1) lgdogf A008611 11.5212 23-23*x+23*x^2+(-12+12*x-23*x^4+23*x^3+11*x^2)*f(x)+(-11+11*x+11*x^3-11*x^4)*f(x)^2 ogf A008611 86.9326 x+2*x^2-x^5 ogf_with_Euler_Transform A008611 13.6608 {(-n-4)*a(n+1)-a(n+2)-a(n+3)+(n+3)*a(n+4),a(0)=1,a(1)=0,a(2)=1,a(3)=2} ogf A008611 8.53802 {6*a(n+2)+4*a(n+2)*n-2*a(n+2)*n^2-12*a(n+1)+15*a(n+1)*n-3*a(n+1)*n^2,a(0)=0,a(1)=1,a(2)=2,a(3)=0,a(4)=0,a(5)=-1} ogf_with_Euler_Transform A008612 16.3398 (x^4-x^2+1)/(x+1)/(x^2+x+1)/(x-1)^2 ogf A008612 19.063 -(-1-x^4+x^2)/(-x^3+1-x^2+x^5) ogf A008612 30.0995 -x^11+x^2*(1+x+x^3) ogf_with_Euler_Transform A008612 9.22406 -x^2*(x^2+x^4-x^3+7*x+3+x^5)/(x-1)/(x+1)/(1+x+x^2)/(x^4-x^2+1) lgdogf A008613 9.12643 -(-1-x+x^4+x^5-x^7-x^8+x^3)/(-x^2+1+x-x^11+2*x^8-2*x^3+x^7-x^4+x^9-x^10) ogf A008613 9.38719 -(1+x-x^3-x^4-x^5+x^7+x^8)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x+1)^2/(x-1)^3 ogf A008614 9.8189 -(1+x-x^3-x^4+x^6-x^9+x^11+x^12-x^8)/(x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x^2+1)/(x+1)^2/(x-1)^3 ogf A008614 11.2216 -(1+x-x^4+x^12+x^11-x^9+x^6-x^8-x^3)/(-2*x^11-1-x-x^12+x^3+x^15+2*x^4+x^5+x^14-x^10) ogf A008615 24.2719 -x*(2+5*x^2+5*x)/(x-1)/(x+1)/(1+x+x^2) lgdogf A008615 28.8229 -x^2*f(x)+(1-x^2-x^3+x^5)*f(x)^2 ogf A008615 36.8933 1/(x+1)/(x^2+x+1)/(x-1)^2 ogf A008615 184.466 x+x^2 ogf_with_Euler_Transform A008615 46.1166 x^2/(-x^3+1-x^2+x^5) ogf A008616 16.4357 -x*(2+7*x^3+7*x^4+2*x^2+2*x)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1) lgdogf A008616 56.0747 1/(1-x^2-x^5+x^7) ogf A008616 28.887 1/(x+1)/(x^4+x^3+x^2+x+1)/(x-1)^2 ogf A008616 190.654 x+x^4 ogf_with_Euler_Transform A008616 22.1691 {a(n+5),a(0)=0,a(1)=1,a(2)=0,a(3)=0,a(4)=1} ogf_with_Euler_Transform A008617 75.0322 (1+x^5)*x ogf_with_Euler_Transform A008617 8.65756 -x*(2+2*x^3+9*x^5+2*x^4+2*x^2+2*x+9*x^6)/(x-1)/(x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008617 39.7229 1/(1-x^2-x^7+x^9) ogf A008617 16.4705 1/(x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A008617 11.8472 {a(n+1),a(0)=0,a(1)=1,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=1} ogf_with_Euler_Transform A008618 7.67375 -x*(2+2*x^3+2*x^5+2*x^4+2*x^2+2*x+2*x^6+11*x^8+11*x^7)/(x-1)/(x+1)/(1+x+x^2)/(x^6+x^3+1) lgdogf A008618 37.5161 1/(1-x^2-x^9+x^11) ogf A008618 18.2511 1/(x+1)/(x^2+x+1)/(x^6+x^3+1)/(x-1)^2 ogf A008618 135.058 x+x^8 ogf_with_Euler_Transform A008618 9.51113 {a(n+1),a(0)=0,a(1)=1,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=1} ogf_with_Euler_Transform A008619 44.4701 -(3*x+1)/(x-1)/(x+1) lgdogf A008619 42.3525 1+(-1+x+x^2-x^3)*f(x) ogf A008619 59.2935 1/(1-x-x^2+x^3) ogf A008619 59.2935 1/(x+1)/(x-1)^2 ogf A008619 296.468 x+1 ogf_with_Euler_Transform A008619 40.4274 {a(n+2),a(0)=1,a(1)=1} ogf_with_Euler_Transform A008619 18.5292 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=1,a(1)=1,a(2)=2} ogf A008620 32.0529 -(1+x+4*x^2)/(x-1)/(1+x+x^2) lgdogf A008620 52.7931 -1/(-1+x+x^3-x^4) ogf A008620 47.2359 1/(x^2+x+1)/(x-1)^2 ogf A008620 34.5185 f(x)+(-1+x+x^3-x^4)*f(x)^2 ogf A008620 179.496 x^2+1 ogf_with_Euler_Transform A008620 16.0265 {-a(n+4)+a(n+3)+a(n+1)-a(n),a(0)=1,a(1)=1,a(2)=1,a(3)=2} ogf A008620 30.9477 {a(n+3),a(0)=1,a(1)=0,a(2)=1} ogf_with_Euler_Transform A008621 25.5835 -(1+x+x^2+5*x^3)/(x-1)/(x+1)/(1+x^2) lgdogf A008621 54.1767 -1/(-1+x+x^4-x^5) ogf A008621 184.201 1+x^3 ogf_with_Euler_Transform A008621 40.0437 1/(x+1)/(x^2+1)/(x-1)^2 ogf A008621 35.4232 f(x)+(-1+x+x^4-x^5)*f(x)^2 ogf A008621 21.9287 {-a(n+4)+a(n),a(0)=1,a(1)=1,a(2)=1,a(3)=5} lgdogf A008621 25.5835 {a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=1} ogf_with_Euler_Transform A008622 24.1617 -1/(-1+x^4+x^6+x^7-x^10-x^11-x^13+x^17) ogf A008622 13.0876 -1/(x^2+x+1)/(x^2-x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x^2+1)/(x+1)^2/(x-1)^3 ogf A008622 85.6643 x^3+x^5+x^6 ogf_with_Euler_Transform A008622 8.41346 {-6*a(n+2)+8*a(n+2)*n-2*a(n+2)*n^2-30*a(n+1)+21*a(n+1)*n-3*a(n+1)*n^2,a(0)=0,a(1)=0,a(2)=0,a(3)=1,a(4)=0,a(5)=1} ogf_with_Euler_Transform A008623 6.6185 (1+x^4+x^5+x^6+x^9+x^10+x^8+x^14)/(x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x^2+1)/(x+1)^2/(x-1)^4 ogf A008624 21.1413 (x^2-x+1)/(x+1)/(x^2+1)/(x-1)^2 ogf A008624 26.2152 -(-1+x-x^2)/(1-x-x^4+x^5) ogf A008624 11.7032 -x*(2-3*x^3+3*x^4+5*x^2+x)/(x-1)/(x+1)/(1+x^2)/(x^2-x+1) lgdogf A008624 50.4138 x+x^2+x^3-x^5 ogf_with_Euler_Transform A008624 5.16047 {-16*a(n+3)+4*a(n+3)*n^2-9*a(n+2)*n+3*a(n+2)*n^2+16*a(n+1)-12*a(n+1)*n+2*a(n+1)*n^2,a(0)=0,a(1)=1,a(2)=1,a(3)=1,a(4)=0,a(5)=-1} ogf_with_Euler_Transform A008625 17.6199 -(1-x+x^4-x^7+x^8)/(x^3-1+x+x^7+x^11-x^4-x^10-x^8) ogf A008625 11.9053 -(x^4-x^3+x^2-x+1)*(x^4-x^2+1)/(x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008627 15.8527 (x^4-x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^4 ogf A008627 11.067 -(-1-x^4+x^2)/(x^5+1-x-2*x^2+x^3+2*x^4+x^8-2*x^6-x^7) ogf A008627 8.14652 -(1+4*x-2*x^4+5*x^6+6*x^3+6*x^2+4*x^7)/(x-1)/(x+1)/(1+x+x^2)/(x^4-x^2+1) lgdogf A008627 29.3275 1+x+x^2+x^3+x^5-x^11 ogf_with_Euler_Transform A008628 7.71528 -(1+x^4-x^6-x^2+x^8)/(x^10-1+x+2*x^2+x^6-x^3-2*x^4-x^12+2*x^9-x^7+x^13-2*x^11) ogf A008628 9.403 -(x^8-x^6+x^4-x^2+1)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x+1)^2/(x-1)^5 ogf A008628 25.0747 1+x+x^2+x^3+x^4+x^9-x^19 ogf_with_Euler_Transform A008629 6.39792 (x^4-x^3+x^2-x+1)*(1+x-x^3-x^4-x^5+x^7+x^8)/(x^2+1)/(x^4+x^3+x^2+x+1)/(x+1)^2/(x^2+x+1)^2/(x-1)^6 ogf A008630 23.4698 -1/(x-1)+1/(x-1)*x^7+x^20 ogf_with_Euler_Transform A008634 47.5723 (-1/x^11+1)/(x-1)*x^11 ogf_with_Euler_Transform A008634 10.3623 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf_with_Euler_Transform A008635 27.1636 (-1/x^12+1)/(x-1)*x^12 ogf_with_Euler_Transform A008635 5.48256 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=0} ogf_with_Euler_Transform A008636 34.1803 1+x+x^2+x^3+x^4+x^5+x^6 ogf_with_Euler_Transform A008636 11.0725 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=0} ogf_with_Euler_Transform A008637 37.0529 (x+1)*(x^2+1)*(x^4+1) ogf_with_Euler_Transform A008637 9.97578 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=0} ogf_with_Euler_Transform A008638 37.7903 (1+x^2+x)*(x^6+x^3+1) ogf_with_Euler_Transform A008638 37.7903 (x^2+x+1)*(x^6+x^3+1) ogf_with_Euler_Transform A008638 9.33642 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=0} ogf_with_Euler_Transform A008639 35.0014 (-1/x^10+1)/(x-1)*x^10 ogf_with_Euler_Transform A008639 8.27989 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=0} ogf_with_Euler_Transform A008640 32.8757 (-1/x^11+1)/(x-1)*x^11 ogf_with_Euler_Transform A008640 7.16104 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf_with_Euler_Transform A008641 35.7014 (-1/x^12+1)/(x-1)*x^12 ogf_with_Euler_Transform A008641 7.20579 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=0} ogf_with_Euler_Transform A008642 17.7405 -(1+3*x+x^2+7*x^3)/(x-1)/(x+1)/(1+x^2) lgdogf A008642 25.9284 -1/(x^2+1)/(x+1)^2/(x-1)^3 ogf A008642 96.3054 1+x+x^3 ogf_with_Euler_Transform A008642 21.7464 1/(1-x-x^2+x^3-x^4+x^5+x^6-x^7) ogf A008642 18.2199 {-a(n+4),a(0)=1,a(1)=1,a(2)=0,a(3)=1} ogf_with_Euler_Transform A008643 9.07132 -(1+3*x+x^2+7*x^3+x^4+3*x^5+x^6+15*x^7)/(x-1)/(x+1)/(1+x^2)/(x^4+1) lgdogf A008643 8.56026 -1/(-1+x+x^2-x^3+x^4-x^5-x^6+x^7+x^8-x^9-x^10+x^11-x^12+x^13+x^14-x^15) ogf A008643 55.2526 1+x+x^3+x^7 ogf_with_Euler_Transform A008643 17.3651 1/(1+x^4)/(x^2+1)^2/(x+1)^3/(x-1)^4 ogf A008644 8.00662 -(1+3*x+x^2+7*x^3+x^4+3*x^5+x^6+15*x^7+x^8+3*x^9+x^10+7*x^11+x^12+3*x^13+x^14+31*x^15)/(x-1)/(x+1)/(1+x^2)/(x^4+1)/(x^8+1) lgdogf A008644 61.0505 1+x+x^3+x^7+x^15 ogf_with_Euler_Transform A008645 14.4709 (1+x^8)/(x^2+1)/(2*x^16-1)/(x+1)^2/(x-1)^3 ogf A008646 10.1921 -(-1+3*x-x^4-5*x^2+3*x^3)/(4*x^8+1-4*x+4*x^6+6*x^2-4*x^3+x^4-x^5-6*x^7-x^9) ogf A008646 7.56838 -(1+2*x+9*x^4+27*x^6-12*x^5+4*x^3+3*x^2-14*x^7+5*x^8)/(x-1)/(x^4+x^3+x^2+x+1)/(x^4-3*x^3+5*x^2-3*x+1) lgdogf A008646 15.2881 -(1-3*x+5*x^2-3*x^3+x^4)/(x^4+x^3+x^2+x+1)/(x-1)^5 ogf A008647 15.7044 (1-x^3+x^6)/(x+1)/(x^2+1)/(x^2+x+1)/(x-1)^2 ogf A008647 22.5097 -(-1-x^6+x^3)/(-x^4+1-x^3+x^7) ogf A008647 7.58753 -x^3*(4*x+2*x^3+10*x^2+4+x^7+x^8+2*x^4+x^6-x^5)/(x-1)/(x+1)/(1+x^2)/(x^2+x+1)/(x^6-x^3+1) lgdogf A008647 42.2056 x^3+x^5+x^8-x^17 ogf_with_Euler_Transform A008648 17.9386 -1/(-1+x+x^5-x^6+x^25-x^26-x^30+x^31) ogf A008648 12.5232 -1/(x^20+x^15+x^10+x^5+1)/(x^4+x^3+x^2+x+1)^2/(x-1)^3 ogf A008648 66.3728 1+x^4+x^24 ogf_with_Euler_Transform A008649 9.55346 -(1+x+4*x^2+x^3+x^4+4*x^5+x^6+x^7+13*x^8)/(x-1)/(x^2+x+1)/(x^6+x^3+1) lgdogf A008649 19.3879 -1/(x^6+x^3+1)/(x^2+x+1)^2/(x-1)^3 ogf A008649 73.2432 1+x^2+x^8 ogf_with_Euler_Transform A008649 19.3879 1/(1-x-x^3+x^4-x^9+x^10+x^12-x^13) ogf A008651 10.079 (1+x-x^3-x^4-x^5+x^7+x^8)/(x+1)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x-1)^2 ogf A008651 11.6429 -(-x+x^3+x^4+x^5-x^7-1-x^8)/(-x^3+1+x-x^5-x^4+x^8-x^6+x^9) ogf A008652 5.88025 -(1+x+x^2+5*x^3+x^4+x^5+x^6+5*x^7+x^8+x^9+x^10+5*x^11+x^12+x^13+x^14+21*x^15)/(x-1)/(x+1)/(x^2+1)/(x^4+1)/(x^8+1) lgdogf A008652 17.9586 -1/(-1+x+x^4-x^5+x^16-x^17-x^20+x^21) ogf A008652 15.1015 -1/(1+x^4)/(1+x^8)/(x+1)^2/(x^2+1)^2/(x-1)^3 ogf A008652 66.4468 1+x^3+x^15 ogf_with_Euler_Transform A008666 8.76236 -1/(x^2-x+1)/(x^4+x^3+x^2+x+1)/(x^6+x^3+1)/(x+1)^2/(x^2+x+1)^3/(x-1)^5 ogf A008666 36.0803 x+x^2+x^4+x^5+x^8 ogf_with_Euler_Transform A008667 7.89905 -x*(2+32*x^3+49*x^5+46*x^4+18*x^2+7*x+44*x^6+14*x^8+28*x^7)/(x-1)/(x+1)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x^2+1) lgdogf A008667 16.5725 1/(1-x^2-x^3-x^4+x^6+2*x^7+x^8-x^10-x^11-x^12+x^14) ogf A008667 15.9471 1/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x^2+1)/(x+1)^2/(x-1)^4 ogf A008667 32.5076 1/24*x*(24+12*x+4*x^2+x^3) egf_with_Euler_Transform A008667 19.2091 {-a(n+5),a(0)=0,a(1)=1,a(2)=1,a(3)=1,a(4)=1} ogf_with_Euler_Transform A008668 46.9814 1+x^5+x^9+x^14 ogf_with_Euler_Transform A008669 9.16425 -(1+5*x+23*x^4+23*x^6+27*x^5+18*x^3+12*x^2+11*x^7)/(x^4+x^3+x^2+x+1)/(x^2+x+1)/(x-1)/(x+1) lgdogf A008669 74.9802 1+x+x^2+x^4 ogf_with_Euler_Transform A008669 24.9934 1/(1-x-x^2+x^4+x^7-x^9-x^10+x^11) ogf A008669 19.181 1/(x+1)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x-1)^4 ogf A008669 18.7451 {-a(n+5),a(0)=1,a(1)=1,a(2)=1,a(3)=0,a(4)=1} ogf_with_Euler_Transform A008670 10.7115 -(1+x+5*x^4+x^6+15*x^5+6*x^3+5*x^2+14*x^7)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1)/(x^2-x+1) lgdogf A008670 67.5649 1+x^2+x^3+x^5 ogf_with_Euler_Transform A008670 18.2988 1/(1-x-x^3+x^5-x^6+2*x^7-x^8+x^9-x^11-x^13+x^14) ogf A008670 18.6882 1/(x^2+1)/(x^2-x+1)/(x+1)^2/(x^2+x+1)^2/(x-1)^4 ogf A008670 7.02675 {13*a(n+3)*n-24*a(n+3)+7*a(n+3)*n^2+4*a(n+2)*n+24*a(n+2)-4*a(n+2)*n^2-4*a(n+1)-27*a(n+1)*n+7*a(n+1)*n^2,a(0)=1,a(1)=0,a(2)=1} ogf_with_Euler_Transform A008671 81.7426 (1+x+x^5)*x ogf_with_Euler_Transform A008671 24.3019 -1/(-1+x^2+x^3-x^5+x^7-x^9-x^10+x^12) ogf A008671 17.2917 -1/(x+1)/(x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008671 8.40345 -x*(2+12*x^3+19*x^5+12*x^4+12*x^2+7*x+26*x^6+12*x^8+24*x^7)/(x-1)/(x+1)/(x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008671 7.49307 {20*a(n+2)+15*a(n+2)*n-5*a(n+2)*n^2-20*a(n+1)+24*a(n+1)*n-4*a(n+1)*n^2,a(0)=0,a(1)=1,a(2)=1,a(3)=0,a(4)=0,a(5)=0,a(6)=1} ogf_with_Euler_Transform A008672 11.5345 -(1+2*x+11*x^4+9*x^6+10*x^5+6*x^3+6*x^2)/(x-1)/(x^2+x+1)/(x^4+x^3+x^2+x+1) lgdogf A008672 22.4619 -1/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008672 94.8391 1+x^2+x^4 ogf_with_Euler_Transform A008672 27.5339 1/(1-x-x^3+x^4-x^5+x^6+x^8-x^9) ogf A008672 19.3989 {-a(n+5),a(0)=1,a(1)=0,a(2)=1,a(3)=0,a(4)=1} ogf_with_Euler_Transform A008673 8.84457 -1/(-1+x+x^3-x^4+x^5-x^6+x^7-2*x^8+x^9-x^10+x^11-x^12+x^13+x^15-x^16) ogf A008673 46.9442 1+x^2+x^4+x^6 ogf_with_Euler_Transform A008673 9.68691 1/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^4 ogf A008673 7.82404 {a(n+3)-a(n+1),a(0)=1,a(1)=0,a(2)=1,a(3)=0,a(4)=1,a(5)=0,a(6)=1,a(7)=0,a(8)=0} ogf_with_Euler_Transform A008674 21.961 (-1/x^10+1)/(x+1)/(x-1)*x^10 ogf_with_Euler_Transform A008674 6.61191 {a(n+3)-a(n+1),a(0)=1,a(1)=0,a(2)=1,a(3)=0,a(4)=1,a(5)=0,a(6)=1,a(7)=0,a(8)=1,a(9)=0,a(10)=0} ogf_with_Euler_Transform A008675 31.4387 (-1/x^12+1)/(x+1)/(x-1)*x^12 ogf_with_Euler_Transform A008675 8.07599 {a(n+3)-a(n+1),a(0)=1,a(1)=0,a(2)=1,a(3)=0,a(4)=1,a(5)=0,a(6)=1,a(7)=0,a(8)=1,a(9)=0,a(10)=1,a(11)=0,a(12)=0} ogf_with_Euler_Transform A008676 10.5514 -x^2*(8*x^2+8*x^4+8*x^3+3*x+3)/(x-1)/(x^2+x+1)/(x^4+x^3+x^2+x+1) lgdogf A008676 39.7229 1/(1-x^3-x^5+x^8) ogf A008676 18.2511 1/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x-1)^2 ogf A008676 96.47 x^2+x^4 ogf_with_Euler_Transform A008676 15.3475 {-a(n+5),a(0)=0,a(1)=0,a(2)=1,a(3)=0,a(4)=1} ogf_with_Euler_Transform A008677 10.4087 -1/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008677 18.5043 1/(1-x^3-x^5-x^7+x^8+x^10+x^12-x^15) ogf A008677 60.5595 x^2+x^4+x^6 ogf_with_Euler_Transform A008677 8.65136 {-a(n+2)+a(n),a(0)=0,a(1)=0,a(2)=1,a(3)=0,a(4)=1,a(5)=0,a(6)=1,a(7)=0,a(8)=0} ogf_with_Euler_Transform A008678 9.05676 1/(1-x^3-x^5-x^7+x^8-x^9+x^10+2*x^12+x^14-x^15+x^16-x^17-x^19-x^21+x^24) ogf A008678 8.46866 1/(x^4+x^3+x^2+x+1)/(x^6+x^3+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x^2+x+1)^2/(x-1)^4 ogf A008678 43.4724 x^2+x^4+x^6+x^8 ogf_with_Euler_Transform A008678 7.0879 {-a(n+2)+a(n),a(0)=0,a(1)=0,a(2)=1,a(3)=0,a(4)=1,a(5)=0,a(6)=1,a(7)=0,a(8)=1,a(9)=0,a(10)=0} ogf_with_Euler_Transform A008679 14.1054 -x^2*(7*x^2+7*x^3+7*x+3)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1) lgdogf A008679 44.8055 1/(1-x^3-x^4+x^7) ogf A008679 23.0816 1/(x+1)/(x^2+1)/(x^2+x+1)/(x-1)^2 ogf A008679 108.813 x^2+x^3 ogf_with_Euler_Transform A008679 21.1582 {a(n+4),a(0)=0,a(1)=0,a(2)=1,a(3)=1} ogf_with_Euler_Transform A008680 17.1755 -1/(x+1)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x^2+1)/(x-1)^3 ogf A008680 8.67112 -x^2*(22*x^2+39*x^4+34*x^3+10*x+3+36*x^5+12*x^7+24*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^4+x^3+x^2+x+1)/(x^2+1) lgdogf A008680 26.2684 1/(1-x^3-x^4-x^5+x^7+x^8+x^9-x^12) ogf A008680 81.1932 x^2+x^3+x^4 ogf_with_Euler_Transform A008680 20.7704 {a(n+5),a(0)=0,a(1)=0,a(2)=1,a(3)=1,a(4)=1} ogf_with_Euler_Transform A008681 9.07959 -1/(-1+x^3+x^4+x^5+x^6-x^7-x^8-2*x^9-x^10-x^11+x^12+x^13+x^14+x^15-x^18) ogf A008681 5.18834 -x^2*(15*x^2+33*x^4+28*x^3+7*x+18*x^8+3+18*x^9+43*x^5+36*x^7+39*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^4+x^3+x^2+x+1)/(x^2+1) lgdogf A008681 10.0574 1/(x^2-x+1)/(x^4+x^3+x^2+x+1)/(x^2+1)/(x+1)^2/(x^2+x+1)^2/(x-1)^4 ogf A008681 22.5424 1/120*x^2*(60+20*x+5*x^2+x^3) egf_with_Euler_Transform A008681 10.2145 {a(n+2)-a(n+1),a(0)=0,a(1)=0,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=0} ogf_with_Euler_Transform A008682 10.3803 -1/(x^2+x+1)/(x^2-x+1)/(x^4+x^3+x^2+x+1)/(x^2+1)/(x+1)^2/(x-1)^3 ogf A008682 5.5827 -x^3*(9*x+24*x^3+19*x^2+4+15*x^7+15*x^8+34*x^4+30*x^6+30*x^5)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^4+x^3+x^2+x+1)/(x^2+1) lgdogf A008682 18.4539 1/(1-x^4-x^5-x^6+x^9+x^10+x^11-x^15) ogf A008682 30.1973 1/120*x^3*(20+5*x+x^2) egf_with_Euler_Transform A008682 8.85788 {-a(n+3)*n+2*a(n+2)-a(n+2)*n+4*a(n+1)-a(n+1)*n,a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf_with_Euler_Transform A008684 11.4939 -(-31+961*x^31-961*x^32+28*x^28)/(-28*x^28+31-62*x+31*x^2+56*x^29-28*x^30) ogf A008684 16.3566 -(31-961*x^31+961*x^32-28*x^28)/(28*x^28-31)/(x-1)^2 ogf A008706 31.455 (x^2+3*x+1)/(x-1)^2 ogf A008706 23.9058 -(1+3*x+x^2)/(-x^2-1+2*x) ogf A008706 22.9864 -5*(x+1)/(x-1)/(x^2+3*x+1) lgdogf A008706 22.135 1+3*x+x^2+(-x^2-1+2*x)*f(x) ogf A008706 12.7159 {-a(n+3)+2*a(n+2)-a(n+1),a(0)=1,a(1)=5,a(2)=10} ogf A008711 1.91932 100-180*x+81*x^2+(-20+58*x+18*x^3-56*x^2)*f(x)+(x^4+6*x^2+1-4*x-4*x^3)*f(x)^2 ogf A008712 2.08312 -100+180*x-81*x^2+(20-58*x-18*x^3+56*x^2)*f(x)+(-1-6*x^2+4*x+4*x^3-x^4)*f(x)^2 ogf A008713 2.34604 -100+180*x-81*x^2+(20-58*x-18*x^3+56*x^2)*f(x)+(-1-6*x^2+4*x+4*x^3-x^4)*f(x)^2 ogf A008714 2.54262 -100+180*x-81*x^2+(20-58*x-18*x^3+56*x^2)*f(x)+(-1-6*x^2+4*x+4*x^3-x^4)*f(x)^2 ogf A008715 2.74215 -100+180*x-81*x^2+(20-58*x-18*x^3+56*x^2)*f(x)+(-1-6*x^2+4*x+4*x^3-x^4)*f(x)^2 ogf A008718 11.4513 (1-x^3+x^6)/(x^2-x+1)/(x^4-x^2+1)/(x+1)^2/(x^2+1)^2/(x^2+x+1)^2/(x-1)^4 ogf A008718 12.7038 -(1-x^3+x^6)/(x^19-1+x+x^3+x^8-x^5-x^13-x^7+x^17+x^12-x^20-x^15) ogf A008718 35.3498 1+x^3+x^5+x^8+x^11-x^17 ogf_with_Euler_Transform A008719 5.84555 -(1+x+x^2+5*x^3+x^4+7*x^5+x^6+5*x^7+x^8+x^9+x^10+23*x^11)/(x^2-x+1)/(1+x^2+x)/(x^2+1)/(x-1)/(x+1)/(x^4-x^2+1) lgdogf A008719 45.5118 1+x^3+x^5+x^11 ogf_with_Euler_Transform A008719 8.72829 1/(1-x-x^4+x^5-x^6+x^7+x^10-x^11-x^12+x^13+x^16-x^17+x^18-x^19-x^22+x^23) ogf A008719 10.1137 1/(x^4-x^2+1)/(x^2+1)^2/(x^2+x+1)^2/(x^2-x+1)^2/(x+1)^3/(x-1)^4 ogf A008720 18.2357 -1/(x^4+x^3+x^2+x+1)/(x+1)^2/(x-1)^3 ogf A008720 11.3187 -x*(4+9*x^3+9*x^4+4*x^2+4*x)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1) lgdogf A008720 22.6374 1/(1-2*x^2+x^4-x^5+2*x^7-x^9) ogf A008720 93.7834 2*x+x^4 ogf_with_Euler_Transform A008720 15.2671 {a(n+5),a(0)=0,a(1)=2,a(2)=0,a(3)=0,a(4)=1} ogf_with_Euler_Transform A008721 14.8885 -1/(x^6+x^5+x^4+x^3+x^2+x+1)/(x+1)^2/(x-1)^3 ogf A008721 8.18868 -x*(4+4*x^3+11*x^5+4*x^4+4*x^2+4*x+11*x^6)/(x-1)/(x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008721 21.8365 1/(1-2*x^2+x^4-x^7+2*x^9-x^11) ogf A008721 72.7883 x*(2+x^5) ogf_with_Euler_Transform A008721 11.4929 {a(n+1),a(0)=0,a(1)=2,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=1} ogf_with_Euler_Transform A008722 19.9315 -1/(-1+2*x^2-x^4+x^9-2*x^11+x^13) ogf A008722 16.4435 -1/(x^2+x+1)/(x^6+x^3+1)/(x+1)^2/(x-1)^3 ogf A008722 7.47431 -x*(4+4*x^3+4*x^5+4*x^4+4*x^2+4*x+4*x^6+13*x^8+13*x^7)/(x-1)/(x+1)/(1+x^2+x)/(x^6+x^3+1) lgdogf A008722 93.9627 2*x+x^8 ogf_with_Euler_Transform A008722 9.26393 {a(n+1),a(0)=0,a(1)=2,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=1} ogf_with_Euler_Transform A008723 19.2244 -1/(-1+2*x^2-x^4+x^11-2*x^13+x^15) ogf A008723 10.7152 -1/(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)/(x+1)^2/(x-1)^3 ogf A008723 5.35761 -x*(4+4*x^3+4*x^5+4*x^4+4*x^2+15*x^9+4*x+15*x^10+4*x^6+4*x^8+4*x^7)/(x-1)/(x+1)/(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008723 81.7035 2*x+x^10 ogf_with_Euler_Transform A008723 7.60033 {a(n+1),a(0)=0,a(1)=2,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=1} ogf_with_Euler_Transform A008724 25.2543 -1/(x+1)/(x^2+x+1)/(x^2-x+1)/(x-1)^3 ogf A008724 15.6751 -2*(1+x+x^2+x^3+x^4+4*x^5)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) lgdogf A008724 181.831 2+x^5 ogf_with_Euler_Transform A008725 12.1456 -(2+2*x+2*x^2+2*x^3+2*x^4+2*x^5+9*x^6)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008725 29.3169 -1/(-1+2*x-x^2+x^7-2*x^8+x^9) ogf A008725 23.6164 -1/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008725 170.038 2+x^6 ogf_with_Euler_Transform A008725 14.9156 {a(n+7),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=1} ogf_with_Euler_Transform A008726 28.7257 -1/(-1+2*x-x^2+x^8-2*x^9+x^10) ogf A008726 26.9303 -1/(x+1)/(x^2+1)/(1+x^4)/(x-1)^3 ogf A008726 13.8995 -2*(1+x+x^2+x^3+x^4+x^5+x^6+5*x^7)/(x-1)/(x+1)/(x^2+1)/(1+x^4) lgdogf A008726 172.354 2+x^7 ogf_with_Euler_Transform A008726 13.4652 {a(n+8),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=1} ogf_with_Euler_Transform A008727 10.7512 -(2+2*x+2*x^2+2*x^3+2*x^4+2*x^5+2*x^6+2*x^7+11*x^8)/(x-1)/(1+x^2+x)/(x^6+x^3+1) lgdogf A008727 27.3981 -1/(-1+2*x-x^2+x^9-2*x^10+x^11) ogf A008727 26.5419 -1/(x^2+x+1)/(x^6+x^3+1)/(x-1)^3 ogf A008727 169.868 2+x^8 ogf_with_Euler_Transform A008727 12.3093 {a(n),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=1} ogf_with_Euler_Transform A008728 16.5555 -1/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x-1)^3 ogf A008728 9.56542 -2*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+6*x^9)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) lgdogf A008728 28.6963 1/(1-2*x+x^2-x^10+2*x^11-x^12) ogf A008728 172.178 2+x^9 ogf_with_Euler_Transform A008728 11.3275 {a(n),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=1} ogf_with_Euler_Transform A008729 7.54487 -(2+2*x+2*x^2+2*x^3+2*x^4+2*x^5+2*x^6+2*x^7+2*x^8+2*x^9+13*x^10)/(x-1)/(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008729 26.6428 -1/(-1+2*x-x^2+x^11-2*x^12+x^13) ogf A008729 16.0862 -1/(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)/(x-1)^3 ogf A008729 142.095 2+x^10 ogf_with_Euler_Transform A008729 10.1496 {a(n),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=1} ogf_with_Euler_Transform A008730 15.1502 -1/(x+1)/(x^2+1)/(x^2+x+1)/(x^2-x+1)/(x^4-x^2+1)/(x-1)^3 ogf A008730 8.1578 -2*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+7*x^11)/(x^2-x+1)/(1+x^2+x)/(x^2+1)/(x-1)/(x+1)/(x^4-x^2+1) lgdogf A008730 28.2804 1/(1-2*x+x^2-x^12+2*x^13-x^14) ogf A008730 141.402 2+x^11 ogf_with_Euler_Transform A008730 9.22186 {a(n),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=0,a(11)=1} ogf_with_Euler_Transform A008731 23.0421 -1/(x^2+x+1)/(x+1)^2/(x-1)^3 ogf A008731 16.9784 -x*(4+7*x^2+7*x)/(x-1)/(1+x^2+x)/(x+1) lgdogf A008731 22.2476 1/(1-2*x^2-x^3+x^4+2*x^5-x^7) ogf A008731 92.1686 2*x+x^2 ogf_with_Euler_Transform A008731 21.506 {-a(n+3),a(0)=0,a(1)=2,a(2)=1} ogf_with_Euler_Transform A008732 12.376 -(2+2*x+2*x^2+2*x^3+7*x^4)/(x-1)/(x^4+x^3+x^2+x+1) lgdogf A008732 22.1 -1/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008732 22.9185 1/(1-2*x+x^2-x^5+2*x^6-x^7) ogf A008732 123.76 2+x^4 ogf_with_Euler_Transform A008732 14.3907 {a(n+5),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=1} ogf_with_Euler_Transform A008733 20.0405 -(1-x+x^2)/(x^2-1+x+x^4-x^5-x^6-x^3+x^7) ogf A008733 23.577 -(x^2-x+1)/(x^2+1)/(x+1)^2/(x-1)^3 ogf A008733 14.3146 -x*(4-5*x^3+5*x^4+9*x^2-x)/(x-1)/(x+1)/(x^2+1)/(x^2-x+1) lgdogf A008733 53.4413 2*x+x^2+x^3-x^5 ogf_with_Euler_Transform A008733 6.31197 {-32*a(n+3)+8*a(n+3)*n^2-9*a(n+2)*n+3*a(n+2)*n^2+16*a(n+1)-12*a(n+1)*n+2*a(n+1)*n^2,a(0)=0,a(1)=2,a(2)=1,a(3)=1,a(4)=0,a(5)=-1} ogf_with_Euler_Transform A008734 12.3624 -(-1+x+x^3-x^4-x^2)/(-x^2+1-x+x^10-x^11-x^8+x^3+x^9) ogf A008734 12.8569 -(x^4-x^3+x^2-x+1)/(x^2+1)/(1+x^4)/(x+1)^2/(x-1)^3 ogf A008734 5.63899 -x*(4-3*x^3-3*x^5+7*x^4+8*x^2-7*x^9-4*x+7*x^10+15*x^6+11*x^8-11*x^7)/(x-1)/(x+1)/(x^2+1)/(x^4-x^3+x^2-x+1)/(1+x^4) lgdogf A008734 42.8563 2*x+x^4+x^7-x^9 ogf_with_Euler_Transform A008735 7.90645 -(1-x+x^2-x^3+x^4-x^5+x^6)/(x^2+1)/(x^2+x+1)/(x^2-x+1)/(x^4-x^2+1)/(x+1)^2/(x-1)^3 ogf A008735 10.6283 -(1-x-x^3-x^5+x^6+x^4+x^2)/(-x^14-1+x+x^12+x^2-x^3-x^13+x^15) ogf A008736 9.3 -(-1+x+x^3+x^5-x^6-x^4-x^2-x^8+x^7)/(-x^16+1-x-x^19-x^2+x^3+x^18+x^17) ogf A008736 10.5 -(x^2-x+1)*(1-x^3+x^6)/(x^2+1)/(1+x^4)/(1+x^8)/(x+1)^2/(x-1)^3 ogf A008736 38.2941 2*x+x^8+x^15-x^17 ogf_with_Euler_Transform A008737 16.8546 -1/(x+1)/(x^2+x+1)^2/(x^2-x+1)^2/(x-1)^3 ogf A008737 12.9651 -2*(1+x^2+x^4+6*x^5)/(x-1)/(x+1)/(1+x^2+x)/(x^2-x+1) lgdogf A008737 9.11058 -x^6/(-1+2*x-2*x^2+2*x^3-2*x^4+2*x^5-2*x^7+2*x^8-2*x^9+2*x^10-2*x^11+x^12) ogf A008737 74.9092 2-x+2*x^5 ogf_with_Euler_Transform A008738 23.8827 -(-x-x^4)/(1-2*x+x^2-x^5+2*x^6-x^7) ogf A008738 9.95114 -(2+2*x+9*x^4+2*x^6+2*x^5+4*x^3+5*x^2+4*x^7)/(x-1)/(x+1)/(x^2-x+1)/(x^4+x^3+x^2+x+1) lgdogf A008738 19.9023 -(x+1)*(x^2-x+1)/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008738 64.2997 2+x^2+x^4-x^5 ogf_with_Euler_Transform A008739 17.2707 -(1+x^4)/(-1+2*x-x^2+x^7-2*x^8+x^9) ogf A008739 14.3922 -(1+x^4)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008739 5.81225 -(2+2*x+4*x^4+11*x^6+4*x^5+6*x^3+5*x^10+2*x^2+2*x^7+2*x^9+2*x^8)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(1+x^4) lgdogf A008739 46.498 2+x^3+x^6-x^7 ogf_with_Euler_Transform A008740 16.4264 -(-1-x^5)/(1-2*x+x^2-x^9+2*x^10-x^11) ogf A008740 11.2552 -(x+1)*(x^4-x^3+x^2-x+1)/(x^2+x+1)/(x^6+x^3+1)/(x-1)^3 ogf A008740 46.7522 2+x^4+x^8-x^9 ogf_with_Euler_Transform A008742 15.9291 -(1+x^4-x^2)/(x^3-1+2*x^2-2*x^5+x^7-x^4) ogf A008742 16.7675 -(x^4-x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^3 ogf A008742 9.10236 -x*(2-x^3+3*x^5-x^4+7*x^2+5*x+3*x^6)/(x-1)/(x+1)/(1+x^2+x)/(x^4-x^2+1) lgdogf A008742 30.3412 -x^11+x*(1+x+x^2+x^4) ogf_with_Euler_Transform A008743 17.7833 -(-1+x^3-x^6)/(1-x^2-x^3-x^4+x^5+x^6+x^7-x^9) ogf A008743 17.3967 -(1-x^3+x^6)/(x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^3 ogf A008743 7.5495 -x*(2+4*x^3-2*x^5+10*x^4+8*x^2+3*x^9+2*x+3*x^10+2*x^6+5*x^8-x^7)/(x-1)/(x+1)/(x^2+1)/(1+x^2+x)/(x^6-x^3+1) lgdogf A008747 10.045 -(1+4*x+5*x^4+3*x^6+4*x^5+10*x^3+7*x^2+2*x^7)/(x-1)/(x+1)/(1+x^2+x)/(x^4+1) lgdogf A008747 24.3025 -(1+x^4)/(-x^4-1+x+x^2-x^5+x^6) ogf A008747 23.5431 -(1+x^4)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A008747 50.2252 1+x+x^2+x^3-x^7 ogf_with_Euler_Transform A008748 18.4848 -(-1+x+x^3-x^4-x^2)/(x^2+1-2*x+2*x^4-x^3-x^5) ogf A008748 14.3417 -(1+2*x+3*x^4+x^6+2*x^2)/(x-1)/(1+x^2+x)/(x^4-x^3+x^2-x+1) lgdogf A008748 23.1061 -(x^4-x^3+x^2-x+1)/(x^2+x+1)/(x-1)^3 ogf A008748 55.4545 1+x+x^2+x^4-x^9 ogf_with_Euler_Transform A008749 7.28154 -(1+4*x+7*x^6+6*x^5+6*x^3+7*x^2+4*x^7+x^8)/(x-1)/(x+1)/(x^2+1)/(1+x^2+x)/(x^4-x^2+1) lgdogf A008749 19.7306 -(1+x^6)/(-x^4-1+x+x^2-x^5+x^6) ogf A008749 13.9011 -(x^2+1)*(x^4-x^2+1)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A008749 38.2281 1+x+x^2+x^5-x^11 ogf_with_Euler_Transform A008750 7.45914 (-1-2*x+2*x^4-x^6-4*x^5-2*x^2-2*x^7+x^8)/(x-1)/(1+x^2+x)/(x^6-x^5+x^4-x^3+x^2-x+1) lgdogf A008750 11.5406 -(-1+x+x^3+x^5-x^6-x^4-x^2)/(x^2+1-2*x+2*x^4-x^3-x^5) ogf A008750 13.9011 -(1-x+x^2-x^3+x^4-x^5+x^6)/(x^2+x+1)/(x-1)^3 ogf A008750 38.2281 1+x+x^2+x^6-x^13 ogf_with_Euler_Transform A008751 7.59723 (-1-4*x-6*x^3+x^10-7*x^2+2*x^11-8*x^7-4*x^9-9*x^8)/(x-1)/(x+1)/(1+x^2+x)/(x^8+1) lgdogf A008751 19.6058 -(-1-x^8)/(1-x-x^2+x^4+x^5-x^6) ogf A008751 18.9931 -(1+x^8)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A008751 37.9862 1+x+x^2+x^7-x^15 ogf_with_Euler_Transform A008752 6.53525 (-1-2*x+2*x^4+6*x^6-4*x^5+3*x^10-2*x^2-8*x^7-4*x^9+x^8)/(x-1)/(1+x^2+x)/(x^2-x+1)/(x^6-x^3+1) lgdogf A008752 9.96358 -(1-x-x^3-x^5+x^6+x^4+x^2+x^8-x^7)/(-x^2-1+2*x-2*x^4+x^3+x^5) ogf A008752 15.1945 -(x^2-x+1)*(1-x^3+x^6)/(x^2+x+1)/(x-1)^3 ogf A008752 37.9862 1+x+x^2+x^8-x^17 ogf_with_Euler_Transform A008753 5.73376 (-1-4*x-6*x^3-11*x^10-7*x^2-4*x^11+3*x^12-10*x^9+4*x^13)/(x-1)/(x+1)/(1+x^2+x)/(x^2+1)/(x^8-x^6+x^4-x^2+1) lgdogf A008753 18.9931 -(1+x^10)/(-x^4-1+x+x^2-x^5+x^6) ogf A008753 11.688 -(x^2+1)*(x^8-x^6+x^4-x^2+1)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A008753 37.9862 1+x+x^2+x^9-x^19 ogf_with_Euler_Transform A008754 4.57505 (-1+6*x^6-4*x^5+3*x^10-2*x^2-6*x^11+5*x^12-8*x^7-12*x^9+10*x^8-2*x+2*x^4)/(x-1)/(1+x^2+x)/(x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1) lgdogf A008754 8.62725 -(-1+x+x^3+x^5-x^6-x^4-x^2-x^8+x^7-x^10+x^9)/(x^2+1-2*x+2*x^4-x^3-x^5) ogf A008754 9.90012 -(1-x+x^2-x^3+x^4-x^5+x^6-x^7-x^9+x^10+x^8)/(x^2+x+1)/(x-1)^3 ogf A008754 35.524 1+x+x^2+x^10-x^21 ogf_with_Euler_Transform A008755 6.10007 (-1-4*x-6*x^3-7*x^2-12*x^11-13*x^12+5*x^14-4*x^13+6*x^15)/(x-1)/(x+1)/(1+x^2+x)/(x^4+1)/(x^8-x^4+1) lgdogf A008755 18.8721 -(1+x^12)/(-x^4-1+x+x^2-x^5+x^6) ogf A008755 13.7252 -(1+x^4)*(x^8-x^4+1)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A008755 35.524 1+x+x^2+x^11-x^23 ogf_with_Euler_Transform A008756 8.45121 -(1-x+x^2-x^3+x^4-x^5+x^6-x^7-x^9+x^10-x^11+x^12+x^8)/(x^2+x+1)/(x-1)^3 ogf A008757 5.12851 (-1-4*x-6*x^3-7*x^2+7*x^16+8*x^17-15*x^14-14*x^13-4*x^15)/(x-1)/(x+1)/(x^2+1)/(1+x^2+x)/(x^12-x^10+x^8-x^6+x^4-x^2+1) lgdogf A008757 18.7511 -(1+x^14)/(-x^4-1+x+x^2-x^5+x^6) ogf A008757 9.678 -(x^2+1)*(x^12-x^10+x^8-x^6+x^4-x^2+1)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A008758 8.33383 -(x^2-x+1)*(x^4-x^3+x^2-x+1)*(1+x-x^3-x^4-x^5+x^7+x^8)/(x^2+x+1)/(x-1)^3 ogf A008759 6.90907 (-1-4*x-6*x^3-7*x^2-17*x^16-4*x^17+9*x^18-16*x^15+10*x^19)/(x-1)/(x+1)/(1+x^2+x)/(x^16+1) lgdogf A008759 19.2159 -(-1-x^16)/(1-x-x^2+x^4+x^5-x^6) ogf A008759 18.6336 -(1+x^16)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A008760 6.75723 -(1-x+x^2-x^3+x^4-x^5+x^6-x^7-x^9+x^10-x^11+x^12-x^13+x^14+x^8-x^15+x^16)/(x^2+x+1)/(x-1)^3 ogf A008761 5.39393 (-1-4*x-6*x^3-7*x^2-18*x^17+11*x^20-19*x^18+12*x^21-4*x^19)/(x-1)/(x+1)/(x^2+1)/(1+x^2+x)/(x^4-x^2+1)/(x^12-x^6+1) lgdogf A008761 19.2159 -(1+x^18)/(-x^4-1+x+x^2-x^5+x^6) ogf A008761 10.7879 -(x^2+1)*(x^4-x^2+1)*(x^12-x^6+1)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A008762 9.16793 -(2+4*x+11*x^4+9*x^5+13*x^3+9*x^2)/(1+x^2+x)/(x^2+1)/(x-1)/(x+1) lgdogf A008762 13.0388 -1/(-1+2*x-x^2+x^3-x^4-x^5+x^6-x^7+2*x^8-x^9) ogf A008762 17.7802 1/(x+1)/(x^2+1)/(x^2+x+1)/(x-1)^4 ogf A008762 65.1941 2+x^2+x^3 ogf_with_Euler_Transform A008762 16.2985 {a(n+4),a(0)=2,a(1)=0,a(2)=1,a(3)=1} ogf_with_Euler_Transform A008763 20.4078 -(1+6*x+8*x^3+9*x^2)/(1+x^2+x)/(x-1)/(x+1) lgdogf A008763 19.0473 -x^4/(-1+x+2*x^2-x^3-2*x^4-x^8-x^5+2*x^6+x^7) ogf A008763 31.7454 1/(x^2+x+1)/(x+1)^2/(x-1)^4 ogf A008763 95.2363 x^2+1+2*x ogf_with_Euler_Transform A008764 20.2368 (x^2-x+1)/(x+1)/(x^2+1)/(x^2+x+1)/(x-1)^4 ogf A008764 9.87747 -(1+3*x+8*x^4+x^6+10*x^5+10*x^3+8*x^2+7*x^7)/(x-1)/(x+1)/(x^2+1)/(1+x^2+x)/(x^2-x+1) lgdogf A008764 15.6549 -(1-x+x^2)/(-1+2*x-x^2+x^3-x^4-x^5+x^6-x^7+2*x^8-x^9) ogf A008764 48.8063 1+x+2*x^2+x^3-x^5 ogf_with_Euler_Transform A008765 14.4907 (1+x^4)/(x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^4 ogf A008765 6.06243 -(1+4*x+16*x^4+8*x^6+18*x^5+18*x^3+8*x^2+10*x^7+6*x^9+7*x^8)/(x-1)/(x+1)/(x^2+1)/(1+x^2+x)/(x^4+1) lgdogf A008765 15.6347 -(1+x^4)/(-1+x+x^2-2*x^5+x^8+x^9-x^10) ogf A008765 34.9481 1+x+x^2+2*x^3-x^7 ogf_with_Euler_Transform A008766 12.0476 (x^4-x^3+x^2-x+1)/(x+1)/(x^2+1)/(x^2+x+1)/(x-1)^4 ogf A008766 6.14931 -(1+3*x+7*x^4+9*x^5+9*x^3+5*x^2+8*x^7+5*x^9+x^8)/(x-1)/(x+1)/(1+x^2+x)/(x^4-x^3+x^2-x+1)/(x^2+1) lgdogf A008766 9.6776 -(1-x-x^3+x^4+x^2)/(-1+2*x-x^2+x^3-x^4-x^5+x^6-x^7+2*x^8-x^9) ogf A008766 31.0702 1+x+x^2+x^3+x^4-x^9 ogf_with_Euler_Transform A008767 16.0172 -(x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)^2/(x-1)^3 ogf A008767 17.2493 -(x^8+x^7)/(-1+x+2*x^7+x^15-2*x^8-x^14) ogf A008767 9.09084 -2*(1+x+x^4+8*x^6+x^5+x^3+x^2+7*x^7)/(x-1)/(x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008767 74.7469 2-x+2*x^6 ogf_with_Euler_Transform A008768 14.2763 (1-x+x^2-x^3+x^4-x^5+x^6)/(x+1)/(x^2+1)/(x^2+x+1)/(x-1)^4 ogf A008768 6.6701 -(1+3*x+2*x^4-x^6+8*x^5+9*x^3+x^10+5*x^2+3*x^11+9*x^7+6*x^9+2*x^8)/(x-1)/(x+1)/(1+x^2+x)/(x^6-x^5+x^4-x^3+x^2-x+1)/(x^2+1) lgdogf A008768 11.7935 -(1-x-x^3-x^5+x^6+x^4+x^2)/(-1+2*x-x^2+x^3-x^4-x^5+x^6-x^7+2*x^8-x^9) ogf A008768 40.6876 1+x+x^2+x^3+x^6-x^13 ogf_with_Euler_Transform A008769 14.6696 (1+x^8)/(x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^4 ogf A008769 15.8277 -(-1-x^8)/(2*x^5+1-x-x^2+x^10-x^8-x^9) ogf A008769 5.0121 -(1+4*x+11*x^4+10*x^5+8*x^10+8*x^2+3*x^12+12*x^9+9*x^8+2*x^13+8*x^7+6*x^11+14*x^3)/(x-1)/(x+1)/(x^2+1)/(1+x^2+x)/(x^8+1) lgdogf A008769 30.0726 1+x+x^2+x^3+x^7-x^15 ogf_with_Euler_Transform A008770 11.3482 (x^2-x+1)*(1-x^3+x^6)/(x+1)/(x^2+1)/(x^2+x+1)/(x-1)^4 ogf A008770 7.81107 -(-1+x+x^3+x^5-x^6-x^4-x^2-x^8+x^7)/(x^2+1-2*x-2*x^8+x^4+x^9-x^3-x^6+x^5+x^7) ogf A008770 4.62656 -(1+3*x+2*x^4-8*x^6+8*x^5+9*x^3+4*x^10+5*x^2+4*x^11+x^12+8*x^7+9*x^9+x^8+x^13)/(x-1)/(x+1)/(x^2+1)/(1+x^2+x)/(x^2-x+1)/(x^6-x^3+1) lgdogf A008770 30.0726 1+x+x^2+x^3+x^8-x^17 ogf_with_Euler_Transform A008771 13.698 (x^8-x^6+x^4-x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^4 ogf A008771 10.1051 -(-1+x^6-x^4+x^2-x^8)/(x^5+1-x-2*x^2+x^8+x^3+2*x^4-x^7-2*x^6) ogf A008771 5.98457 -(1+4*x-2*x^4-2*x^6-6*x^5+6*x^3+x^10+6*x^2+6*x^7+4*x^9+6*x^8)/(x-1)/(x+1)/(1+x^2+x)/(x^8-x^6+x^4-x^2+1) lgdogf A008771 30.8206 1+x+x^2+x^3+x^9-x^19 ogf_with_Euler_Transform A008772 8.32988 (1-x+x^2-x^3+x^4-x^5+x^6-x^7-x^9+x^10+x^8)/(x+1)/(x^2+1)/(x^2+x+1)/(x-1)^4 ogf A008772 29.3529 1+x+x^2+x^3+x^10-x^21 ogf_with_Euler_Transform A008773 15.5757 (1+x^4)*(x^8-x^4+1)/(x^2+1)/(x^2+x+1)/(x+1)^2/(x-1)^4 ogf A008773 21.1669 -(1+x^12)/(-1+x+x^2-2*x^5+x^8+x^9-x^10) ogf A008773 39.31 1+x+x^2+x^3+x^11-x^23 ogf_with_Euler_Transform A008776 31.9336 -1/3*ln(2)+1/3*ln(3*x+2) revegf A008776 51.0937 -2+(1-3*x)*f(x) ogf A008776 69.6733 -2/(-1+3*x) ogf A008776 76.6406 -3/(3*x-1) lgdogf A008776 85.1562 2/(1-3*x) ogf A008776 85.1562 x/(2+3*x) revogf A008776 34.8366 {a(n+1)-3*a(n),a(0)=2} ogf A008778 31.781 -(-1-x+x^2)/(x-1)^4 ogf A008778 20.8221 -(-5-x+2*x^2)/(x-1)/(x^2-x-1) lgdogf A008778 17.2526 -(1+x-x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A008778 5.86252 -515-515*x+515*x^2+(461-2114*x+515*x^4-2060*x^3+3144*x^2)*f(x)+(54*x^4+324*x^2+54-216*x-216*x^3)*f(x)^2 ogf A008778 7.27518 {(-n-4)*a(n+4)+5*a(n+3)+(5+2*n)*a(n+2)+(-3-n)*a(n+1),a(0)=1,a(1)=5,a(2)=13,a(3)=26} ogf A008779 23.8928 (-1-2*x+x^2+x^3)/(x-1)^5 ogf A008779 11.7026 -(-1-2*x+x^3+x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A008779 13.3355 -(-7-6*x+2*x^3+6*x^2)/(x-1)/(x^3+x^2-2*x-1) lgdogf A008779 6.51622 {(-6+n+n^2)*a(n+1)+(-72-21*n-3*n^2)*a(n+2)+(16*n+30+2*n^2)*a(n+3),a(0)=1,a(1)=7,a(2)=24} ogf A008780 19.7035 -(-1-5*x+3*x^2+2*x^3)/(x-1)^6 ogf A008780 11.428 -(-11-19*x+6*x^3+18*x^2)/(x-1)/(2*x^3+3*x^2-5*x-1) lgdogf A008780 9.52336 -(1+5*x-2*x^3-3*x^2)/(-15*x^2-1+6*x-15*x^4+6*x^5+20*x^3-x^6) ogf A008780 4.53493 {(-116796-61307*n-8027*n^2)*a(n+1)+(256490+121344*n+17290*n^2)*a(n+2)+(-53857*n-78204-9263*n^2)*a(n+3),a(0)=1,a(1)=11,a(2)=48} ogf A008785 11.9917 1/9*3^(2/3)*(ln(3)+ln(x+1/3))/(x+1/3)^(1/3) revegf A008786 11.7106 1/8*2^(1/2)*(2*ln(2)+ln(x+1/4))/(x+1/4)^(1/4) revegf A008787 12.2987 1/25*5^(4/5)*(ln(5)+ln(x+1/5))/(x+1/5)^(1/5) revegf A008794 18.0799 -(-x^4-x^2)/(1-x-2*x^2-x^5+2*x^3+x^4) ogf A008794 17.6041 -(1+7*x+x^2+3*x^3)/(x-1)/(x+1)/(1+x^2) lgdogf A008794 27.8731 -(x^2+1)/(x+1)^2/(x-1)^3 ogf A008794 74.3284 1+3*x-x^3 ogf_with_Euler_Transform A008794 6.08141 41*x^4+41*x^2+(-41+41*x+71*x^4-82*x^3+41*x^5+194*x^2)*f(x)+(-112+112*x+224*x^2+112*x^5-224*x^3-112*x^4)*f(x)^2 ogf A008794 4.95523 {(532+484*n+109*n^2)*a(n+1)+(566+248*n+13*n^2)*a(n+2)+(26-144*n-109*n^2)*a(n+3)+(-148-100*n-13*n^2)*a(n+4),a(0)=0,a(1)=0,a(2)=1,a(3)=1} ogf A008795 17.4455 -(-1+x-x^2)/(1-x-2*x^2-x^5+2*x^3+x^4) ogf A008795 24.8263 -(x^2-x+1)/(x+1)^2/(x-1)^3 ogf A008795 17.9301 -3*x*(2+x^2-x)/(x-1)/(x+1)/(x^2-x+1) lgdogf A008795 58.6803 3*x+x^2-x^5 ogf_with_Euler_Transform A008795 6.20657 {(3*n+n^2)*a(n)+(68+29*n+3*n^2)*a(n+1)+(10+3*n-n^2)*a(n+2)+(-19*n-30-3*n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=3} ogf A008795 6.20657 {(3*n+n^2)*a(n)+(68+29*n+3*n^2)*a(n+1)+(3*n+10-n^2)*a(n+2)+(-19*n-30-3*n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=3} ogf A008795 5.92187 {12*a(n+2)+8*a(n+2)*n-4*a(n+2)*n^2-4*a(n+1)+5*a(n+1)*n-a(n+1)*n^2,a(0)=0,a(1)=3,a(2)=1,a(3)=0,a(4)=0,a(5)=-1} ogf_with_Euler_Transform A008796 17.6204 -(-1-x^4)/(x^4+1-2*x^2-x^3+2*x^5-x^7) ogf A008796 38.3503 -(-2-x-x^2+x^6)*x ogf_with_Euler_Transform A008796 19.1751 -(1+x^4)/(x^2+x+1)/(x+1)^2/(x-1)^3 ogf A008796 9.18246 -x*(4+4*x^3+3*x^5+4*x^4+11*x^2+7*x+3*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^4+1) lgdogf A008797 13.7121 -(1-x-x^3+x^4+x^2)/(x^2-1+x-x^6+x^4-x^3+x^7-x^5) ogf A008797 15.671 -(x^4-x^3+x^2-x+1)/(x^2+1)/(x+1)^2/(x-1)^3 ogf A008797 8.33141 -x*(4-7*x^3-3*x^5+7*x^4+12*x^2-4*x+3*x^6)/(x-1)/(x+1)/(1+x^2)/(x^4-x^3+x^2-x+1) lgdogf A008797 43.8788 2*x+x^3+x^4-x^9 ogf_with_Euler_Transform A008798 17.6539 -(-1-x^6)/(1-2*x^2+x^4-x^5+2*x^7-x^9) ogf A008798 12.0962 -(x^2+1)*(x^4-x^2+1)/(x^4+x^3+x^2+x+1)/(x+1)^2/(x-1)^3 ogf A008798 5.63099 -x*(4+9*x^3+6*x^5+15*x^4+4*x^2+3*x^9+4*x+3*x^10+4*x^6+4*x^8+4*x^7)/(x-1)/(x+1)/(1+x^2)/(1+x+x^4+x^3+x^2)/(x^4-x^2+1) lgdogf A008798 34.3787 -x^11+x*(2+x^3+x^4) ogf_with_Euler_Transform A008799 10.4529 -(1-x+x^2-x^3+x^4-x^5+x^6)/(x^2+x+1)/(x^2-x+1)/(x+1)^2/(x-1)^3 ogf A008799 11.3698 -(1-x-x^3+x^6+x^4+x^2-x^5)/(-x^8-1+x+x^2-x^3-x^7+x^6+x^9) ogf A008799 5.1435 -x*(4-8*x^3-11*x^5+18*x^4+8*x^2-3*x^9-4*x+3*x^10+11*x^6+7*x^8-7*x^7)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^6-x^5+x^4-x^3+x^2-x+1) lgdogf A008799 34.1095 -x^13+x*(2+x^4+x^5) ogf_with_Euler_Transform A008800 17.1298 -(-1-x^8)/(1-2*x^2+x^4-x^7+2*x^9-x^11) ogf A008800 13.0186 -(1+x^8)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x+1)^2/(x-1)^3 ogf A008800 34.2595 -x^15+x^6*(x+1)+2*x ogf_with_Euler_Transform A008801 10.1321 -(1-x-x^3+x^6+x^4+x^2+x^8-x^7-x^5)/(x^2-1+x+x^11+x^8-x^3-x^10-x^9) ogf A008801 12.3836 -(x^2-x+1)*(1-x^3+x^6)/(x^2+1)/(1+x^4)/(x+1)^2/(x-1)^3 ogf A008801 35.1956 -x^17+x^7*(x+1)+2*x ogf_with_Euler_Transform A008802 16.4121 -(1+x^10)/(-1+2*x^2-x^4+x^9-2*x^11+x^13) ogf A008802 9.94673 -(x^2+1)*(x^8-x^6+x^4-x^2+1)/(x^2+x+1)/(x^6+x^3+1)/(x+1)^2/(x-1)^3 ogf A008802 41.0302 2*x+x^8+x^9-x^19 ogf_with_Euler_Transform A008803 7.13993 -(1-x+x^2-x^3+x^4-x^5+x^6-x^7-x^9+x^10+x^8)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x+1)^2/(x-1)^3 ogf A008803 8.80901 -(1-x-x^3+x^6+x^4+x^2+x^8-x^7-x^9-x^5+x^10)/(x^2-1+x-x^11+x^13-x^3-x^12+x^10) ogf A008803 39.8996 2*x+x^9+x^10-x^21 ogf_with_Euler_Transform A008804 20.5665 -1/(-1+2*x-2*x^3+2*x^4-2*x^5+2*x^7-x^8) ogf A008804 20.0523 -2*(1+2*x+x^2+4*x^3)/(x-1)/(x+1)/(1+x^2) lgdogf A008804 32.0837 1/(x^2+1)/(x+1)^2/(x-1)^4 ogf A008804 114.585 2+x+x^3 ogf_with_Euler_Transform A008804 21.6782 {-a(n+4),a(0)=2,a(1)=1,a(2)=0,a(3)=1} ogf_with_Euler_Transform A008805 31.7183 -(1+5*x)/(x-1)/(x+1) lgdogf A008805 35.2426 -1/(x+1)^2/(x-1)^3 ogf A008805 23.4951 1/(1-x-2*x^2-x^5+2*x^3+x^4) ogf A008805 126.873 2*x+1 ogf_with_Euler_Transform A008805 11.328 {(n+3)*a(n+3)-a(n+2)+(-6-n)*a(n+1),a(0)=1,a(1)=1,a(2)=3} ogf A008805 28.8348 {a(n+2),a(0)=1,a(1)=2} ogf_with_Euler_Transform A008806 19.1751 -(-1+x-x^2)/(-x^2+1-x+x^5-x^6+x^4) ogf A008806 19.1751 -(x^2-x+1)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A008806 11.642 -2*x*(2+3*x+2*x^2+2*x^4)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) lgdogf A008806 50.1504 2*x+2*x^2-x^5 ogf_with_Euler_Transform A008806 5.76951 {12*a(n+2)+8*a(n+2)*n-4*a(n+2)*n^2-12*a(n+1)+15*a(n+1)*n-3*a(n+1)*n^2,a(0)=0,a(1)=2,a(2)=2,a(3)=0,a(4)=0,a(5)=-1} ogf_with_Euler_Transform A008807 13.144 -(-1+x+x^3-x^4-x^2)/(-x^2+1-x+x^7-x^8-x^5+x^3+x^6) ogf A008807 13.144 -(x^4-x^3+x^2-x+1)/(x+1)/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008807 7.64189 -2*x*(2+2*x^2+5*x^3+2*x^4+2*x^6+2*x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) lgdogf A008807 50.554 2*x+2*x^4-x^9 ogf_with_Euler_Transform A008807 8.31901 {a(n+1),a(0)=0,a(1)=2,a(2)=0,a(3)=0,a(4)=2,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=-1} ogf_with_Euler_Transform A008808 11.2927 -(-1+x+x^3-x^6-x^4-x^2+x^5)/(x^9+1-x-x^7-x^2+x^3+x^8-x^10) ogf A008808 9.92385 -(1-x+x^2-x^3+x^4-x^5+x^6)/(x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008808 5.64633 -2*x*(2+2*x^2+2*x^4+7*x^5+2*x^6+2*x^8+2*x^10+2*x^12)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x+1)/(1-x+x^2-x^3+x^4-x^5+x^6) lgdogf A008808 46.7839 2*x+2*x^6-x^13 ogf_with_Euler_Transform A008809 9.73147 -(-1+x+x^3-x^6-x^4-x^2-x^8+x^7+x^5)/(-x^9+1-x-x^12-x^2+x^3+x^11+x^10) ogf A008809 11.5771 -(x^2-x+1)*(1-x^3+x^6)/(x+1)/(x^2+x+1)/(x^6+x^3+1)/(x-1)^3 ogf A008809 5.50387 -2*x*(2+2*x^2+2*x^4+2*x^6+9*x^7+2*x^8+2*x^10+2*x^12+2*x^14+2*x^16)/(x-1)/(x^2+x+1)/(x^6+x^3+1)/(x+1)/(x^2-x+1)/(x^6-x^3+1) lgdogf A008809 47.9623 2*x+2*x^8-x^17 ogf_with_Euler_Transform A008810 23.6807 -(-x-x^4)/(1-2*x+x^2-x^3+2*x^4-x^5) ogf A008810 24.3772 -(x+1)*(x^2-x+1)/(x^2+x+1)/(x-1)^3 ogf A008810 14.2901 -2*(1+x+4*x^2+x^3+x^4+x^5)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) lgdogf A008810 75.3478 2+2*x^2-x^5 ogf_with_Euler_Transform A008810 8.37197 {(n^2+6*n+11)*a(n+1)+(2*n+5)*a(n+2)+(2*n+5)*a(n+3)+(-n^2-4*n-6)*a(n+4),a(0)=0,a(1)=1,a(2)=2,a(3)=3} ogf A008811 21.9239 -(1+x^4)/(x+1)/(x^2+1)/(x-1)^3 ogf A008811 18.7919 -(x+x^5)/(-1+2*x-x^2+x^4-2*x^5+x^6) ogf A008811 10.2768 -2*(x^3-x^2+x+1)*(x^4+2*x^3+2*x^2+1)/(x-1)/(x+1)/(x^2+1)/(x^4+1) lgdogf A008811 59.7925 2+2*x^3-x^7 ogf_with_Euler_Transform A008812 17.5279 -(-1-x^5)/(-x^5+1-2*x+x^2+2*x^6-x^7) ogf A008812 12.6201 -(x+1)*(x^4-x^3+x^2-x+1)/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008812 7.01117 -2*(1+x+x^2+x^3+6*x^4+x^5+x^6+x^7+x^8+x^9)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) lgdogf A008812 57.3641 2+2*x^4-x^9 ogf_with_Euler_Transform A008812 8.08982 {-a(n),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=2,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=-1} ogf_with_Euler_Transform A008813 19.33 -(1+x^6)/(x^6-1+2*x-x^2-2*x^7+x^8) ogf A008813 12.1707 -(x^2+1)*(x^4-x^2+1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x-1)^3 ogf A008813 6.31942 -2*(1+x+x^2+x^3+x^4+7*x^5+x^6+x^7+x^8+x^9+x^10+x^11)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^2+1)/(x^4-x^2+1) lgdogf A008813 54.7683 2+2*x^5-x^11 ogf_with_Euler_Transform A008813 6.9917 {-a(n),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=2,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=0,a(11)=-1} ogf_with_Euler_Transform A008814 19.0999 -(1+x^7)/(x^7-1+2*x-x^2-2*x^8+x^9) ogf A008814 9.83932 -(x+1)*(1-x+x^2-x^3+x^4-x^5+x^6)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008814 5.15393 -2*(1+x+x^2+x^3+x^4+x^5+8*x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x+1)/(1-x+x^2-x^3+x^4-x^5+x^6) lgdogf A008814 54.1163 2+2*x^6-x^13 ogf_with_Euler_Transform A008814 5.90359 {-a(n),a(0)=2,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=2,a(7)=0,a(8)=0,a(9)=0,a(10)=0,a(11)=0,a(12)=0,a(13)=-1} ogf_with_Euler_Transform A008815 17.3398 -(-1-x^8)/(-x^8+1-2*x+x^2+2*x^9-x^10) ogf A008815 16.8835 -(1+x^8)/(x+1)/(x^2+1)/(1+x^4)/(x-1)^3 ogf A008815 5.94047 -2*(1+x+x^2+x^3+x^4+x^5+x^6+9*x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15)/(x-1)/(x+1)/(x^2+1)/(x^4+1)/(x^8+1) lgdogf A008815 53.4643 2+2*x^7-x^15 ogf_with_Euler_Transform A008816 17.0724 -(-1-x^9)/(-x^9+1-2*x+x^2+2*x^10-x^11) ogf A008816 11.1854 -(x+1)*(x^2-x+1)*(1-x^3+x^6)/(x^2+x+1)/(x^6+x^3+1)/(x-1)^3 ogf A008816 54.0627 2+2*x^8-x^17 ogf_with_Euler_Transform A008817 16.0222 -(-1-x^10)/(-x^10+1-2*x+x^2+2*x^11-x^12) ogf A008817 8.21652 -(x^2+1)*(x^8-x^6+x^4-x^2+1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x-1)^3 ogf A008817 53.4074 2+2*x^9-x^19 ogf_with_Euler_Transform A008818 17.2794 -(1-x+x^2+x^3)/(x^2+1)/(x+1)^2/(x-1)^3 ogf A008818 14.9231 -(1-x+x^3+x^2)/(x^2-1+x+x^7+x^4-x^5-x^3-x^6) ogf A008818 9.94872 -2*x*(2-x^3+2*x^5+3*x^4+5*x^2+x)/(x-1)/(x+1)/(x^2+1)/(x^3+x^2-x+1) lgdogf A008819 10.6802 -(1-x+x^2-x^3+x^4+x^5-x^6+x^7)/(x^2+1)/(1+x^4)/(x+1)^2/(x-1)^3 ogf A008819 10.5106 -(1-x-x^3-x^6+x^4+x^2+x^7+x^5)/(-x^9-1+x+x^11+x^2-x^3+x^8-x^10) ogf A008820 6.41445 -(1-x+x^2-x^3+x^4-x^5+x^6+x^7+x^9-x^8-x^10+x^11)/(x^2+1)/(x^2+x+1)/(x^2-x+1)/(x^4-x^2+1)/(x+1)^2/(x-1)^3 ogf A008821 6.19182 -(1-x+x^2-x^3+x^4-x^5+x^6-x^12+x^13-x^14+x^15-x^7+x^9+x^8-x^10+x^11)/(x^2+1)/(1+x^4)/(1+x^8)/(x+1)^2/(x-1)^3 ogf A008822 15.3214 -(-1-x^3-2*x^2)/(1-2*x+x^2-x^3+2*x^4-x^5) ogf A008822 19.6305 -(1+2*x^2+x^3)/(x^2+x+1)/(x-1)^3 ogf A008822 10.1319 -2*(1+3*x+4*x^4+x^5+3*x^3+6*x^2)/(x-1)/(x^2+x+1)/(x^3+2*x^2+1) lgdogf A008822 5.76308 {(2*n^2+15*n+30)*a(n+1)+(4*n+13)*a(n+2)+(4*n+13)*a(n+3)+(-2*n^2-11*n-17)*a(n+4),a(0)=1,a(1)=2,a(2)=5,a(3)=10} ogf A008823 15.3089 -(-1-2*x^3-x^5)/(-x^5+1-2*x+x^2+2*x^6-x^7) ogf A008823 16.0744 -(1+2*x^3+x^5)/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008823 7.14417 -2*(1+x+8*x^4+3*x^6+3*x^5+3*x^3+4*x^2+5*x^7+x^9+x^8)/(x-1)/(x^4+x^3+x^2+x+1)/(x^5+2*x^3+1) lgdogf A008824 15.4848 -(-1-2*x^4-x^7)/(-x^9+1-2*x+x^2-x^7+2*x^8) ogf A008824 11.2131 -(x^3-x+1)*(x^4+x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A008824 4.88994 -2*(1+x+3*x^4+10*x^6+3*x^5+5*x^3+6*x^10+x^2+x^11+x^12+3*x^7+3*x^9+3*x^8+x^13)/(x-1)/(x^3-x+1)/(x^4+x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A008825 18.3775 -(1+2*x^5+x^9)/(x^2+x+1)/(x^6+x^3+1)/(x-1)^3 ogf A008825 19.2526 -(1+x^9+2*x^5)/(x^11-1+2*x-x^2+x^9-2*x^10) ogf A008836 166.804 1/(1-x) ogf A008838 18.7592 -1/(x+1)/(x^2+1)^2/(1+x^4)^2/(x-1)^3 ogf A008838 12.9871 -2*(1+x^2+x^4+x^6+8*x^7)/(x-1)/(x+1)/(x^2+1)/(x^4+1) lgdogf A008838 6.62088 -x^8/(-1+2*x-2*x^2+2*x^3-2*x^4+2*x^5-2*x^6+2*x^7-2*x^9+2*x^10-2*x^11+2*x^12-2*x^13+2*x^14-2*x^15+x^16) ogf A008838 75.0367 2-x+2*x^7 ogf_with_Euler_Transform A008843 14.735 -(-1-14*x-x^2)/(35*x^2+1-35*x-x^3) ogf A008843 15.6559 -(1+14*x+x^2)/(x-1)/(x^2-34*x+1) ogf A008843 8.21294 -(49-68*x+x^4+28*x^3-522*x^2)/(x-1)/(x^2-34*x+1)/(x^2+14*x+1) lgdogf A008843 4.28196 -8537-119518*x-8537*x^2+(170240+1965047*x-8537*x^3+460498*x^2)*f(x)+(-5659605*x^2-161703+5659605*x+161703*x^3)*f(x)^2 ogf A008843 8.63775 {a(n+3)-35*a(n+2)+35*a(n+1)-a(n),a(0)=1,a(1)=49,a(2)=1681} ogf A008844 14.4164 -(1-10*x+x^2)/(-35*x^2-1+35*x+x^3) ogf A008844 15.3174 -(1-10*x+x^2)/(x-1)/(x^2-34*x+1) ogf A008844 8.03536 -(25-68*x+x^4-20*x^3+318*x^2)/(x-1)/(x^2-10*x+1)/(x^2-34*x+1) lgdogf A008844 4.22549 -1814+18140*x-1814*x^2+(163517-1680520*x-1814*x^3+225193*x^2)*f(x)+(-5659605*x^2-161703+5659605*x+161703*x^3)*f(x)^2 ogf A008844 8.45098 {-a(n+3)+35*a(n+2)-35*a(n+1)+a(n),a(0)=1,a(1)=25,a(2)=841} ogf A008845 14.314 -(35-70*x+3*x^2)/(x^2-34*x+1)/(x-1) lgdogf A008845 22.7722 -48/(x-1)/(x^2-34*x+1) ogf A008845 16.6996 48*x+(-1+35*x-35*x^2+x^3)*f(x) ogf A008845 20.8746 48*x/(35*x^2+1-35*x-x^3) ogf A008845 8.63775 {a(n+3)-35*a(n+2)+35*a(n+1)-a(n),a(0)=0,a(1)=48,a(2)=1680} ogf A008851 39.8956 (1+4*x)/(x+1)/(x-1)^2 ogf A008851 33.5123 -(-x-4*x^2)/(1-x-x^2+x^3) ogf A008851 24.6414 -(5+7*x+8*x^2)/(x-1)/(4*x+1)/(x+1) lgdogf A008851 10.4726 -703*x-2812*x^2+(703-788*x+703*x^3-1043*x^2)*f(x)+(85-85*x-85*x^2+85*x^3)*f(x)^2 ogf A008851 17.4543 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=0,a(1)=1,a(2)=5} ogf A008852 18.0486 (1+24*x+51*x^2+24*x^3)/(x+1)/(x^2+1)/(x-1)^2 ogf A008852 8.53914 -(25+127*x+171*x^4+48*x^6+177*x^5+104*x^3+148*x^2)/(x-1)/(x+1)/(x^2+1)/(24*x^3+51*x^2+24*x+1) lgdogf A008852 19.8535 -(x+51*x^3+24*x^4+24*x^2)/(-1+x-x^5+x^4) ogf A008853 15.5654 (1+375*x+249*x^2+375*x^3)/(x+1)/(x^2+1)/(x-1)^2 ogf A008853 17.0133 -(x+249*x^3+375*x^4+375*x^2)/(-1+x-x^5+x^4) ogf A008853 7.2433 -2*(188+437*x+1062*x^4+375*x^6+561*x^5+502*x^3+875*x^2)/(x-1)/(x+1)/(x^2+1)/(375*x^3+249*x^2+375*x+1) lgdogf A008854 28.4607 (x^2+3*x+1)/(x^2+x+1)/(x-1)^2 ogf A008854 28.4607 -(-x-x^3-3*x^2)/(1-x+x^4-x^3) ogf A008854 15.2845 -2*(2+3*x+x^4+5*x^3+4*x^2)/(x-1)/(x+x^2+1)/(x^2+3*x+1) lgdogf A008854 26.6245 -x-x^3-3*x^2+(1-x+x^4-x^3)*f(x) ogf A008854 11.7909 {(-n-3)*a(n+1)-a(n+2)-a(n+3)+(n+2)*a(n+4),a(0)=0,a(1)=1,a(2)=4,a(3)=5} ogf A008856 10.0577 (1+23*x+x^2+24*x^3+2*x^4+24*x^5+x^6+23*x^7+x^8)/(x^2+x+1)/(x^6+x^3+1)/(x-1)^2 ogf A008856 11.734 -(-x-x^3-24*x^6-24*x^4-23*x^2-23*x^8-x^7-x^9-2*x^5)/(1-x-x^9+x^10) ogf A008857 16.5341 -(-x^9-x^10)/(1-x-2*x^9-x^19+2*x^10+x^18) ogf A008857 16.9474 -(x+1)/(x^2+x+1)^2/(x^6+x^3+1)^2/(x-1)^3 ogf A008857 8.58098 -2*(1+x+x^4+x^6+x^5+x^3+x^2+x^7+9*x^9+10*x^8)/(x-1)/(x+1)/(x+x^2+1)/(x^6+x^3+1) lgdogf A008857 75.3219 2-x+2*x^8 ogf_with_Euler_Transform A008859 8.22102 -(-1+5*x+13*x^3-x^6-9*x^4-11*x^2+3*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008859 15.191 -(1-5*x+11*x^2-13*x^3+9*x^4-3*x^5+x^6)/(x-1)^7 ogf A008859 9.07515 -(2-8*x+12*x^4+x^6-16*x^3+16*x^2)/(x-1)/(x^6-3*x^5+9*x^4-13*x^3+11*x^2-5*x+1) lgdogf A008859 6.59232 {(2*n+4)*a(n+1)+(-3*n+6)*a(n+2)+(n-4)*a(n+3),a(0)=1,a(1)=2,a(2)=4,a(3)=8,a(4)=16,a(5)=32,a(6)=64,a(7)=127} ogf A008860 14.7509 (2*x^2-2*x+1)*(2*x^4-4*x^3+6*x^2-4*x+1)/(x-1)^8 ogf A008860 7.2218 -(1-6*x-24*x^3+4*x^6+22*x^4+16*x^2-12*x^5)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A008860 7.78981 -2*(1-5*x+14*x^4+4*x^6-6*x^5-16*x^3+12*x^2)/(x-1)/(2*x^2-2*x+1)/(2*x^4-4*x^3+6*x^2-4*x+1) lgdogf A008860 5.97667 {(2*n+4)*a(n+1)+(-3*n+8)*a(n+2)+(-5+n)*a(n+3),a(0)=1,a(1)=2,a(2)=4,a(3)=8,a(4)=16,a(5)=32,a(6)=64,a(7)=128,a(8)=255} ogf A008861 5.98873 -(-1+7*x+40*x^3-16*x^6-46*x^4-22*x^2-x^8+4*x^7+34*x^5)/(36*x^2+1-9*x+9*x^8+126*x^4-x^9-84*x^3+84*x^6-126*x^5-36*x^7) ogf A008861 6.74459 -(2-12*x+60*x^4+20*x^6-40*x^5-56*x^3+34*x^2+x^8)/(x-1)/(x^2-x+1)/(x^6-3*x^5+12*x^4-19*x^3+15*x^2-6*x+1) lgdogf A008861 12.1876 -(x^2-x+1)*(x^6-3*x^5+12*x^4-19*x^3+15*x^2-6*x+1)/(x-1)^9 ogf A008861 5.55754 {(2*n+4)*a(n+1)+(-3*n+10)*a(n+2)+(n-6)*a(n+3),a(0)=1,a(1)=2,a(2)=4,a(3)=8,a(4)=16,a(5)=32,a(6)=64,a(7)=128,a(8)=256,a(9)=511} ogf A008862 11.8721 (x^4-2*x^3+4*x^2-3*x+1)*(5*x^4-10*x^3+10*x^2-5*x+1)/(x-1)^10 ogf A008862 5.3964 -(1-8*x-62*x^3+50*x^6+86*x^4+29*x^2+5*x^8-20*x^7-80*x^5)/(-45*x^2-1+10*x-45*x^8-210*x^4+10*x^9+120*x^3-x^10-210*x^6+252*x^5+120*x^7) ogf A008862 6.14073 -2*(1-7*x+58*x^4+30*x^6-50*x^5-45*x^3+23*x^2-10*x^7+5*x^8)/(x-1)/(x^4-2*x^3+4*x^2-3*x+1)/(5*x^4-10*x^3+10*x^2-5*x+1) lgdogf A008862 5.19945 {(-2*n-4)*a(n+1)+(3*n-12)*a(n+2)+(-n+7)*a(n+3),a(0)=1,a(1)=2,a(2)=4,a(3)=8,a(4)=16,a(5)=32,a(6)=64,a(7)=128,a(8)=256,a(9)=512,a(10)=1023} ogf A008863 9.68833 -(1-9*x+x^10+37*x^2-91*x^3+148*x^4-166*x^5+130*x^6-70*x^7-5*x^9+25*x^8)/(x-1)^11 ogf A008865 38.3751 (1-5*x+2*x^2)/(x-1)^3 ogf A008865 21.7804 -(-1+x+2*x^3-4*x^2)/(3*x^2+1-3*x-x^3) ogf A008865 25.1836 -(1-5*x+2*x^2)/(3*x^2+1-3*x-x^3) ogf A008865 23.025 -2*(-1-3*x+x^2)/(x-1)/(2*x^2-5*x+1) lgdogf A008865 8.75952 1097-5485*x+2194*x^2+(829-1951*x-1097*x^3+2755*x^2)*f(x)+(-268+804*x-804*x^2+268*x^3)*f(x)^2 ogf A008865 15.2052 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=-1,a(1)=2,a(2)=7} ogf A008885 7.06498 30+42*x+54*x^2+66*x^3+78*x^4+90*x^5+144*x^6+259*x^7+45*x^8+33*x^9+15*x^10+9*x^11+4*x^12+3*x^13+x^14 ogf A008886 7.63864 42+54*x+66*x^2+78*x^3+90*x^4+144*x^5+259*x^6+45*x^7+33*x^8+15*x^9+9*x^10+4*x^11+3*x^12+x^13 ogf A008887 9.62438 60+108*x+172*x^2+136*x^3+134*x^4+70*x^5+74*x^6+40*x^7+50*x^8+43*x^9+x^10 ogf A008893 14.9051 -(8*x+8*x^3+26*x^2)/(-1+5*x-10*x^2+x^5+10*x^3-5*x^4) ogf A008893 31.0027 -2*(4+13*x+4*x^2)/(x-1)^5 ogf A008893 19.8735 -3*(11+20*x+4*x^2)/(x-1)/(4*x^2+13*x+4) lgdogf A008893 7.82895 {(12+4*n)*a(n+4)+(-15+9*n)*a(n+3)+(-69-9*n)*a(n+2)+(-12-4*n)*a(n+1),a(0)=0,a(1)=8,a(2)=66,a(3)=258} ogf A008894 6.11566 (-36-18*x+31*x^10-x^11-9*x^2-26*x^3-13*x^4-2*x^5-x^6+46*x^12+23*x^13-47*x^7-x^9-2*x^8)/(x-1)/(x^4+x^3+x^2+x+1) ogf A008894 7.08129 -(-36-18*x-26*x^3-x^6-13*x^4-9*x^2-2*x^8-47*x^7-x^9-2*x^5+31*x^10+46*x^12-x^11+23*x^13)/(1-x^5) ogf A008909 2.62472 -1+2*x-x^4+x^3-2*x^2+(1-3*x+2*x^4-3*x^3+3*x^2)*f(x)+(-x^2+2*x^3-x^4)*f(x)^2 ogf A008911 15.7887 -(-2*x^3-2*x^2)/(1-5*x+10*x^2-x^5-10*x^3+5*x^4) ogf A008911 33.7304 -2*(3+2*x)/(x-1)/(x+1) lgdogf A008911 46.3793 -2*(x+1)/(x-1)^5 ogf A008911 12.7943 {(n+1)*a(n+3)-6*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=0,a(2)=2} ogf A008921 5.19175 -(-1-49*x-2263*x^3-625*x^6-3703*x^4-567*x^2-x^7-2583*x^5)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A008921 8.76639 -(x+1)*(x^6+624*x^5+1959*x^4+1744*x^3+519*x^2+48*x+1)/(x-1)^7 ogf A008921 4.60991 -4*(14+357*x+6006*x^4+158*x^6+2229*x^5+5966*x^3+2406*x^2)/(x-1)/(x+1)/(x^6+624*x^5+1959*x^4+1744*x^3+519*x^2+48*x+1) lgdogf A008922 9.2216 (x+1)*(x^6+624*x^5+1959*x^4+1744*x^3+519*x^2+48*x+1)/(x-1)^8 ogf A008922 5.02997 -(1+49*x+2263*x^3+625*x^6+3703*x^4+567*x^2+x^7+2583*x^5)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A008922 4.46207 -(57+1477*x+27727*x^4+1257*x^6+11499*x^5+26127*x^3+10191*x^2+x^7)/(x-1)/(x+1)/(x^6+624*x^5+1959*x^4+1744*x^3+519*x^2+48*x+1) lgdogf A008931 13.3384 -3+(1-36*x)*f(x)+(3*x-108*x^2)*f(x)^2 lgdogf A008931 15.4225 2^(1/3)/(1+(1-36*x)^(1/2))^(1/3) ogf A008931 14.1006 6/(1-36*x)^(1/2)/(1+(1-36*x)^(1/2)) lgdogf A008931 7.47759 {(-210-306*n-108*n^2)*a(n+1)+(13*n+14+3*n^2)*a(n+2),a(0)=1,a(1)=3} ogf A008936 26.8747 -(-1+2*x+x^4)/(2*x-1)^2 ogf A008936 22.8933 -(-1+2*x+x^4)/(4*x^2+1-4*x) ogf A008936 9.50951 -17+34*x+17*x^4+(19-72*x-2*x^4+68*x^2)*f(x)+(-2-8*x^2+8*x)*f(x)^2 ogf A008936 15.0761 2*(1-2*x+2*x^4-2*x^3)/(2*x-1)/(x^4+2*x-1) lgdogf A008936 9.8114 {-a(n+5)+4*a(n+4)-4*a(n+3),a(0)=1,a(1)=2,a(2)=4,a(3)=8,a(4)=15} ogf A008937 23.4558 -2*(-1+2*x^3)/(x-1)/(x^3+x^2+x-1) lgdogf A008937 40.739 -x+(1-2*x+x^4)*f(x) ogf A008937 36.8591 1/(x-1)/(x^3+x^2+x-1) ogf A008937 59.5416 x/(1-2*x+x^4) ogf A008954 8.89737 -(1+3*x+6*x^10+3*x^11+6*x^2+5*x^4+5*x^6+x^12+5*x^8)/(x-1)/(x^2+1)/(x^4+x^3+x^2+x+1)/(x^8-x^6+x^4-x^2+1) ogf A008954 12.7282 -(x+6*x^3+3*x^2+5*x^7+5*x^9+5*x^5+3*x^12+6*x^11+x^13)/(-1+x^5-x^10+x^15) ogf A008959 7.36986 -(1+4*x+9*x^2+6*x^3+5*x^4+6*x^5+9*x^6+4*x^7+x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A008959 11.7918 -(x+4*x^2+9*x^3+6*x^4+5*x^5+6*x^6+9*x^7+4*x^8+x^9)/(-1+x^10) ogf A008960 7.21945 -(1+8*x+7*x^2+4*x^3+5*x^4+6*x^5+3*x^6+2*x^7+9*x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A008960 11.4114 -(x+8*x^2+7*x^3+4*x^4+5*x^5+6*x^6+3*x^7+2*x^8+9*x^9)/(-1+x^10) ogf A008977 5.86732 {(840+1712*n+1152*n^2+256*n^3)*a(n+1)+(-n^3-6*n^2-12*n-8)*a(n+2),a(0)=1,a(1)=24} ogf A008987 1.34552 1+(-2+2*x)*f(x)+(x^2+1-2*x)*f(x)^2 egf A008988 1.34552 1+(-2+2*x)*f(x)+(x^2+1-2*x)*f(x)^2 egf A008989 1.34552 1+(-2+2*x)*f(x)+(x^2+1-2*x)*f(x)^2 egf A008998 32.5478 -(2+3*x^2)/(-1+2*x+x^3) lgdogf A008998 19.1949 -1+(2-2*x-x^3)*f(x)+(-1+2*x+x^3)*f(x)^2 ogf A008998 49.9067 -1/(-1+2*x+x^3) ogf A008998 17.0136 {-a(n+3)+2*a(n+2)+a(n),a(0)=1,a(1)=2,a(2)=4} ogf A008999 39.0607 -1/(-1+2*x+x^4) ogf A008999 23.4364 -2*(1+2*x^3)/(-1+2*x+x^4) lgdogf A008999 15.0233 1+(-2+2*x+x^4)*f(x)+(-x^4+1-2*x)*f(x)^2 ogf A008999 11.2675 {-a(n+4)+2*a(n+3)+a(n),a(0)=2,a(1)=4,a(2)=8,a(3)=20} lgdogf A009001 44.7217 -(-1-x-x^2+x^3)/(x^2+1)^2 ogf A009001 38.5532 -(1+x-x^2+x^3)/(-1-x^4+2*x^2) ogf A009001 26.62 -(x^2-4*x+1)*(x+1)^2/(x^2+1)/(x^3-x^2-x-1) lgdogf A009001 16.94 3+3*x-3*x^3+3*x^2+(-4-x-3*x^4+x^3-7*x^2)*f(x)+(1+x^4+2*x^2)*f(x)^2 ogf A009001 8.94433 {(62+51*n+10*n^2)*a(n+1)+(116+60*n+7*n^2)*a(n+2)+(6+31*n+10*n^2)*a(n+3)+(46*n+72+7*n^2)*a(n+4),a(0)=1,a(1)=1,a(2)=-1,a(3)=-3} ogf A009005 48.704 -(-3+x+x^2)/(x-1)^2 ogf A009005 37.015 -(-5+3*x)/(x-1)/(x^2+x-3) lgdogf A009005 15.9547 -57+19*x+19*x^2+(13-36*x+21*x^2)*f(x)+(2-4*x+2*x^2)*f(x)^2 ogf A009005 20.1168 {-a(n+3)+2*a(n+2)-a(n+1),a(0)=3,a(1)=5,a(2)=6} ogf A009014 27.9971 -(2*x+2)/(-x^2-2-2*x) egf A009014 23.5176 -(4+2*x^2+2*x^3)/(-4+x^4) egf A009014 25.5626 -2*x-2+(x^2+2+2*x)*f(x) egf A009014 22.613 -x*(x+2)/(x+1)/(x^2+2*x+2) lgdegf A009014 30.9442 2*(x+1)/(x^2+2+2*x) egf A009014 4.62944 {(-12-16*n-7*n^2-n^3)*a(n+1)+(-60-50*n-13*n^2-n^3)*a(n+2)+(-18*n-36-2*n^2)*a(n+3)+(-2*n-8)*a(n+4),a(0)=1,a(1)=0,a(2)=-1,a(3)=3} ogf A009024 5.82196 {(-6-5*n-7*n^2-5*n^3-n^4)*a(n+1)+(-3-10*n-9*n^2-2*n^3)*a(n+2)+(-2-3*n-n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=0} ogf A009024 7.78782 {(n^2+1)*a(n+1)+(1+3*n+2*n^2)*a(n+2)+(2+3*n+n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=0} egf A009056 55.1115 -(-3+2*x)/(x-1)^2 ogf A009056 14.1954 -(3-2*x-6*x^23+4*x^24+x^26-x^27)/(-x^2-1+2*x-4*x^24+2*x^23+2*x^25) ogf A009056 28.3908 -1/2*(-3-2*x+(9+4*x)^(1/2))/(2+x) revogf A009056 20.3673 -15+10*x+(2-8*x+5*x^2)*f(x)+(1-2*x+x^2)*f(x)^2 ogf A009056 42.5862 -2*(x-2)/(x-1)/(2*x-3) lgdogf A009056 25.3215 {-a(n+2)+2*a(n+1)-a(n),a(0)=3,a(1)=4} ogf A009102 8.31883 {(n+2)*a(n+1)+a(n+2)+(n+4)*a(n+3)+a(n+4),a(0)=1,a(1)=-1,a(2)=1,a(3)=-3} ogf A009108 21.9939 2/(x^2+2+2*x)*(x+1)*cos(x) egf A009116 40.2705 (x+1)/(2*x^2+1+2*x) ogf A009116 33.2669 -(-1-x-2*x^3)/(1-4*x^4) ogf A009116 22.5041 -(1+4*x+2*x^2)/(x+1)/(2*x^2+2*x+1) lgdogf A009116 36.4352 -(x+1)/(-2*x^2-1-2*x) ogf A009116 33.2669 -1-x+(1+2*x+2*x^2)*f(x) ogf A009116 19.1285 {-a(n+2)-2*a(n+1)-2*a(n),a(0)=1,a(1)=-1} ogf A009117 51.9124 (2*x+1)/(1+4*x) ogf A009117 45.8051 -(-1+2*x)/(1-4*x) ogf A009117 5.76804 -(-1+2*x+32*x^3-128*x^4+512*x^5-8*x^2-18432*x^6+40960*x^7-163840*x^8+655360*x^9-2621440*x^10+10485760*x^11-41943040*x^12)/(1+16384*x^6) ogf A009117 40.9835 -1-2*x+(1+4*x)*f(x) ogf A009117 28.8402 -1/4+x+1/4*(1+16*x^2)^(1/2) revogf A009117 43.2603 -2/(2*x+1)/(4*x+1) lgdogf A009117 23.5965 {-a(n+2)-4*a(n+1),a(0)=1,a(1)=-2} ogf A009120 7.732 {(64*n^2+192*n+140)*a(n+1)-a(n+2),a(0)=1,a(1)=12} ogf A009132 16.7449 -(2+2*x+x^3+2*x^2)/(x+1)/(x^2+2*x+2) lgdegf A009132 7.53519 -46-46*x-23*x^3-46*x^2+(-40-86*x-20*x^3-63*x^2)*f(x)+(6+12*x+9*x^2+3*x^3)*f(x)^2 lgdegf A009132 20.7867 1/2*exp(-x)/(x+1)*(x^2+2+2*x) egf A009132 7.7284 {(n^2+4*n+4)*a(n+1)+(n^2+4*n+2)*a(n+2)+a(n+3)*n,a(0)=1,a(1)=-1,a(2)=2,a(3)=-7} ogf A009179 40.3906 1/(x+1)*cosh(x) egf A009179 8.41471 {(n+2)*a(n+1)+a(n+2)+(-n-4)*a(n+3)-a(n+4),a(0)=1,a(1)=-1,a(2)=3,a(3)=-9} ogf A009183 23.6904 2/(x^2+2+2*x)*(x+1)*cosh(x) egf A009189 41.116 -sin(x)*x+cos(x) lgdegf A009189 6.99847 {-a(n+1)+(-6-3*n-n^2)*a(n+3)+(-18*n-40-2*n^2)*a(n+5),a(0)=1,a(1)=0,a(2)=-3/2,a(3)=0,a(4)=5/24} lgdegf A009198 17.4927 -1/(x+1)*exp(-x)*(ln(x+1)*x+ln(x+1)-1) lgdegf A009198 5.44856 {(n+3)*a(n+1)+(12*n+16+2*n^2)*a(n+2)+(36*n+36+11*n^2+n^3)*a(n+3)+(26*n+24+9*n^2+n^3)*a(n+4),a(0)=1,a(1)=-3,a(2)=4,a(3)=-4} lgdegf A009199 38.1456 2/(x+1)*ln(x+1) lgdegf A009199 8.54007 {(-n-2)*a(n+1)+(-2*n-5)*a(n+2)+(-n-3)*a(n+3),a(0)=0,a(1)=2,a(2)=-3} lgdegf A009200 33.4863 cos(ln(x+1))/(x+1) lgdegf A009200 6.84946 {(-5-4*n-n^2)*a(n+1)+(-9*n-10-2*n^2)*a(n+2)+(-5*n-6-n^2)*a(n+3),a(0)=1,a(1)=-1,a(2)=1/2} lgdegf A009206 112.404 cos(x) lgdegf A009206 13.2241 {a(n+1)+(5*n+6+n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=-1/2} lgdegf A009209 76.5367 -1+cos(x) lgdegf A009209 13.5065 {-a(n)+(-2-3*n-n^2)*a(n+2),a(0)=0,a(1)=0,a(2)=-1/2} lgdegf A009210 80.3469 cos(2*x) lgdegf A009210 12.6034 {4*a(n+1)+(5*n+6+n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=-2} lgdegf A009212 28.2194 exp(x)*(sin(x)+cos(x)) lgdegf A009212 9.26607 {-2*a(n+1)+(2*n+4)*a(n+2)+(-5*n-6-n^2)*a(n+3),a(0)=1,a(1)=2,a(2)=1} lgdegf A009216 27.1458 -exp(-x)*(sin(x)-cos(x)) lgdegf A009216 9.87122 {2*a(n+1)+(2*n+4)*a(n+2)+(5*n+n^2+6)*a(n+3),a(0)=1,a(1)=-2,a(2)=1} lgdegf A009218 15.6179 (2+2*x+x^2)*f(x)+(-2-4*x-2*x^2)*f(x)^2 lgdegf A009218 25.8035 1/2*(2+2*x+x^2)/(x+1)^2 lgdegf A009218 16.4855 1/exp(-1/2)*exp(1/2*(x^2+x-1)/(x+1)) egf A009218 6.18208 {(5*n+n^2+6)*a(n+1)+(-8*n-2*n^2-6)*a(n+2)+(-10-4*n)*a(n+3)-2*a(n+4),a(0)=1,a(1)=1,a(2)=0,a(3)=1} ogf A009218 6.18208 {(n^2+5*n+6)*a(n+1)+(-8*n-2*n^2-6)*a(n+2)+(-10-4*n)*a(n+3)-2*a(n+4),a(0)=1,a(1)=1,a(2)=0,a(3)=1} ogf A009224 28.6773 1/2*exp(x)+1/2*exp(-x) lgdegf A009224 12.3706 {a(n+1)+(-5*n-6-n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=1/2} lgdegf A009227 24.9788 1/2*exp(x)+1/2*exp(-x)-1 lgdegf A009227 12.2345 {-a(n)+(2+3*n+n^2)*a(n+2),a(0)=0,a(1)=0,a(2)=1/2} lgdegf A009229 21.7562 1/2*exp(-2*x)+1/2*exp(2*x) lgdegf A009229 11.0914 {4*a(n+1)+(-5*n-6-n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=2} lgdegf A009235 74.8607 exp(-2*x) lgdegf A009235 17.2756 {(-n-2)*a(n+2)-2*a(n+1),a(0)=1,a(1)=-2} lgdegf A009257 21.2997 1/exp(-1)*exp(-2/(x^2+2+2*x)) egf A009257 8.34718 20+20*x+(-24-44*x-20*x^3-5*x^4-40*x^2)*f(x)+(8*x^2+4+8*x+x^4+4*x^3)*f(x)^2 lgdegf A009257 29.4139 4*(x+1)/(x^2+2*x+2)^2 lgdegf A009257 6.57119 {(-2*n-8)*a(n+4)+(-14-4*n)*a(n+3)+(-12-3*n)*a(n+2)+(-4-n)*a(n+1),a(0)=1,a(1)=-1,a(2)=0,a(3)=1} lgdegf A009281 15.8315 (2+6*x+x^3+4*x^2)/(x+1)/(x^2+2*x+2) lgdegf A009281 19.7894 1/2*exp(x)/(x+1)*(x^2+2+2*x) egf A009281 6.75735 58+174*x+29*x^3+116*x^2+(-64-134*x-32*x^3-99*x^2)*f(x)+(6+12*x+9*x^2+3*x^3)*f(x)^2 lgdegf A009282 94.3434 1+cos(x) lgdegf A009282 15.403 {a(n)+(2+3*n+n^2)*a(n+2),a(0)=2,a(1)=0,a(2)=-1/2} lgdegf A009283 31.0877 1/2*exp(x)+1/2*exp(-x)+1 lgdegf A009283 15.2266 {-a(n)+(2+3*n+n^2)*a(n+2),a(0)=2,a(1)=0,a(2)=1/2} lgdegf A009294 17.2004 (2+2*x+x^3+2*x^2)/(x+1)/(x^2+2*x+2) lgdegf A009294 7.52518 46+46*x+23*x^3+46*x^2+(-40-86*x-20*x^3-63*x^2)*f(x)+(-6-12*x-9*x^2-3*x^3)*f(x)^2 lgdegf A009294 4.89442 {(-30-31*n-10*n^2-n^3)*a(n+1)+(18+9*n^2+24*n+n^3)*a(n+2)+(22+14*n+2*n^2)*a(n+3)+(2*n+8)*a(n+4),a(0)=1,a(1)=1,a(2)=0,a(3)=1} ogf A009345 18.3774 (x^2+2+2*x)/(x+1)/(x^2+4*x+2) egf A009383 29.4838 2/(x+1)/(x^2+2+2*x) egf A009383 6.29429 {(n^3+3*n^2+2*n)*a(n)+(3*n^2+9*n+6)*a(n+1)+(4*n+8)*a(n+2)+2*a(n+3),a(0)=0,a(1)=1,a(2)=-2} ogf A009383 7.09103 {-a(n)*n+(-3*n-3)*a(n+1)+(-8-4*n)*a(n+2)+(-2*n-6)*a(n+3),a(0)=0,a(1)=1,a(2)=-1} egf A009430 6.3465 {(n+2)*a(n+1)+(3*n+8)*a(n+2)+(4*n+12)*a(n+3)+(2*n+8)*a(n+4),a(0)=0,a(1)=1,a(2)=-1/2,a(3)=-1/6} egf A009440 14.8251 -(16+180*x-90*x^2-14400*x^17+15300*x^16)/(-x^2-1+2*x) ogf A009440 16.7177 -2*(-8-90*x+45*x^2-7650*x^16+7200*x^17)/(x-1)^2 ogf A009440 9.58209 2*(53-114750*x^16+54000*x^17+61200*x^15)/(x-1)/(7200*x^17-7650*x^16+45*x^2-90*x-8) lgdogf A009441 16.1859 -(-17-180*x+90*x^2-13500*x^14+12600*x^15)/(x-1)^2 ogf A009441 14.9643 -(17+180*x+13500*x^14-90*x^2-12600*x^15)/(-x^2-1+2*x) ogf A009441 9.1162 2*(107-175500*x^14+94500*x^13+81900*x^15)/(x-1)/(12600*x^15-13500*x^14+90*x^2-180*x-17) lgdogf A009445 15.8346 {(4*n^2+18*n+20)*a(n+1)-a(n+2),a(0)=1,a(1)=6} ogf A009454 30.4452 cos(ln(x+1))/(x+1) egf A009454 8.30324 {(-2*n-n^2-2)*a(n+1)+(-2*n-3)*a(n+2)-a(n+3),a(0)=0,a(1)=1,a(2)=-1} ogf A009470 14.5851 -(18+180*x-90*x^2-10800*x^13+11700*x^12)/(-x^2-1+2*x) ogf A009470 17.178 -18*(-1-10*x+5*x^2-650*x^12+600*x^13)/(x-1)^2 ogf A009470 10.4461 4*(3+1950*x^11-3575*x^12+1650*x^13)/(x-1)/(600*x^13-650*x^12+5*x^2-10*x-1) lgdogf A009474 16.1807 -(-19-180*x+90*x^2-10800*x^11+9900*x^12)/(x-1)^2 ogf A009474 14.9361 -(19+180*x-90*x^2-9900*x^12+10800*x^11)/(-x^2-1+2*x) ogf A009474 9.0311 2*(109+59400*x^10-108000*x^11+49500*x^12)/(x-1)/(9900*x^12-10800*x^11+90*x^2-180*x-19) lgdogf A009531 61.2638 (x+1)^2/(x^2+1)^2 ogf A009531 37.1959 -(x^3-2*x^2-x)/(1+x^4-2*x^2) ogf A009531 13.5258 -11*x-11*x^3-22*x^2+(11+4*x+11*x^4+4*x^3+30*x^2)*f(x)+(-4-4*x^4-8*x^2)*f(x)^2 ogf A009531 35.9133 -2*(-1+2*x+x^2)/(x+1)/(1+x^2) lgdogf A009531 94.6804 2-4*x+2*x^3 ogf_with_Euler_Transform A009531 13.3524 {(n+3)*a(n+4)+n*a(n+3)+(5+n)*a(n+2)+(n+2)*a(n+1),a(0)=0,a(1)=1,a(2)=2,a(3)=-1} ogf A009545 39.646 -2*(2*x-1)/(2*x^2+1-2*x) lgdogf A009545 63.4335 1/(2*x^2-2*x+1) ogf A009545 45.3097 x+(-1+2*x-2*x^2)*f(x) ogf A009545 25.0395 {a(n+2)-2*a(n+1)+2*a(n),a(0)=0,a(1)=1} ogf A009551 17.2523 (-cos(x)*x+cos(x)+sin(x))/(x-1)^2 egf A009551 8.25109 {(n+2)*a(n+1)-a(n+2)+(n+4)*a(n+3)-a(n+4),a(0)=0,a(1)=1,a(2)=2,a(3)=5} ogf A009564 13.0299 {(64*n^2+256*n+252)*a(n+1)+a(n+2),a(0)=1,a(1)=-60} ogf A009572 4.17788 {(10+5*n+n^2)*a(n+1)+(2+n+n^2)*a(n+2)+(28+44*n+27*n^2+8*n^3+n^4)*a(n+3)+(36+48*n+27*n^2+8*n^3+n^4)*a(n+4),a(0)=0,a(1)=1,a(2)=-1/2,a(3)=0} egf A009573 4.33344 {(-2-5*n-n^2)*a(n+1)+(6-n-n^2)*a(n+2)+(-4+12*n+19*n^2+8*n^3+n^4)*a(n+3)+(-12+8*n+19*n^2+8*n^3+n^4)*a(n+4),a(0)=0,a(1)=1,a(2)=-1/2,a(3)=1} egf A009574 24.2238 (1+3*x+x^2)/(x+2)/(x+1) lgdegf A009574 15.4763 1/2*exp(x)/(x+1)^2*(x^3+4*x^2+4*x+2) egf A009574 7.52902 {(-8-6*n-n^2)*a(n+1)+(2+n^2+4*n)*a(n+2)+(n+2)*a(n+3),a(0)=0,a(1)=1,a(2)=1} ogf A009575 6.15117 {(n^2-2*n+1)*a(n)+(-1-3*n+2*n^2)*a(n+1)+(-2-n+n^2)*a(n+2),a(0)=0,a(1)=0,a(2)=1,a(3)=-1,a(4)=13/12} egf A009578 25.1173 -(3+3*x+x^2)/(x+2)/(x+1) lgdegf A009578 17.7299 -1/2*exp(-x)*(x^3+2*x^2-2)/(x+1)^2 egf A009578 5.48014 {(12+10*n+2*n^2)*a(n+1)+(27+18*n+3*n^2)*a(n+2)+(19+10*n+n^2)*a(n+3)+(n+3)*a(n+4),a(0)=0,a(1)=1,a(2)=-3,a(3)=9} ogf A009628 14.3527 1/2*(exp(x)*x+exp(-x)*x+2*exp(-x))/(x+1)^2 egf A009628 8.49035 {(n+2)*a(n+1)+a(n+2)+(-n-4)*a(n+3)-a(n+4),a(0)=0,a(1)=1,a(2)=-2,a(3)=7} ogf A009759 17.9817 (3-21*x+4*x^2)/(x-1)/(x^2-6*x+1) ogf A009759 16.4404 -(-3+21*x-4*x^2)/(-7*x^2-1+7*x+x^3) ogf A009759 14.0345 -(3-6*x^3+38*x^2-21*x)/(-7*x^2-1+7*x+x^3) ogf A009759 9.43302 -2*x*(-17+2*x^3-21*x^2+64*x)/(x-1)/(1-6*x+x^2)/(4*x^2-21*x+3) lgdogf A009759 4.16967 11650395-81552765*x+15533860*x^2+(-16370639+114594473*x-3883465*x^3+178783*x^2)*f(x)+(-47259576*x^2-6751368+47259576*x+6751368*x^3)*f(x)^2 ogf A009759 10.4621 {-a(n+3)+7*a(n+2)-7*a(n+1)+a(n),a(0)=-3,a(1)=0,a(2)=17} ogf A009769 28.4081 (2*x+1)/(2*x^2+1+2*x) egf A009769 22.0952 -(1+2*x^2+4*x^3)/(-1+4*x^4) egf A009769 23.8628 -1-2*x+(2*x^2+1+2*x)*f(x) egf A009769 18.6428 -4*(x+1)*x/(2*x+1)/(2*x^2+2*x+1) lgdegf A009769 4.48549 {(-48-64*n-28*n^2-4*n^3)*a(n+1)+(-120-100*n-26*n^2-2*n^3)*a(n+2)+(-18*n-36-2*n^2)*a(n+3)+(-n-4)*a(n+4),a(0)=1,a(1)=0,a(2)=-4,a(3)=24} ogf A009775 25.236 -(-2*x^2-4*x-x^4)/(4-x^4) egf A009775 21.03 -(2+4*x+x^2)/(x+2)/(x^2+2*x+2) lgdegf A009775 25.236 -2*x-x^2+(2+2*x+x^2)*f(x) egf A009775 30.0429 4*(x+1)/(x^2+2+2*x)^2 egf A009775 5.58319 {(-2*n-3*n^2-n^3)*a(n)+(-20*n-12-9*n^2-n^3)*a(n+1)+(-12-12*n-2*n^2)*a(n+2)+(-4-2*n)*a(n+3),a(0)=0,a(1)=1,a(2)=-1} ogf A009778 17.29 (2+2*x+x^3+3*x^2)/(x+2)/(x^2+2*x+2) lgdegf A009778 13.7534 exp(x)*(x^4+4*x^3+6*x^2+8*x+4)/(x^2+2+2*x)^2 egf A009778 4.96024 {(-30-31*n-10*n^2-n^3)*a(n+1)+(6+17*n+8*n^2+n^3)*a(n+2)+(14+2*n^2+12*n)*a(n+3)+(6+2*n)*a(n+4),a(0)=0,a(1)=1,a(2)=1,a(3)=0} ogf A009779 5.51375 {a(n)*n^2+(3*n^2+n-2)*a(n+1)+(4*n^2+2*n-4)*a(n+2)+(-4+2*n+2*n^2)*a(n+3),a(0)=0,a(1)=0,a(2)=1,a(3)=-1,a(4)=7/12} egf A009779 5.56387 {a(n)*n^2+(3*n^2+n-2)*a(n+1)+(4*n^2+2*n-4)*a(n+2)+(2*n+2*n^2-4)*a(n+3),a(0)=0,a(1)=0,a(2)=1,a(3)=-1,a(4)=7/12} egf A009782 16.3997 -(x+1)*(x^2+4*x+6)/(x+2)/(x^2+2*x+2) lgdegf A009782 14.0569 -exp(-x)*(x^4+4*x^3+6*x^2-4)/(x^2+2+2*x)^2 egf A009782 5.31882 {-n*a(n)+(2-3*n-n^2)*a(n+1)+(4-4*n-2*n^2)*a(n+2)+(4-2*n-2*n^2)*a(n+3),a(0)=0,a(1)=1,a(2)=-3/2,a(3)=1,a(4)=-1/6} egf A009866 8.7818 -(1+3*x^7+5*x^6+2*x+4*x^8+2*x^9+5*x^5+5*x^4+4*x^2+x^10+3*x^3)/(-2*x^9-1+2*x+x^8-x^2+x^10) ogf A009866 10.0203 -(x^4+x^3+x^2+x+1)*(x^6+x^5+2*x^4-x^3+2*x^2+x+1)/(x+1)/(x^2+1)/(1+x^4)/(x-1)^3 ogf A009923 8.21466 -(-1-8*x^7-29*x^6-8*x+5*x^8-6*x^9-82*x^5-88*x^4-35*x^2-68*x^3)/(-x^8+1+x^6-x^2+2*x^5-2*x^3) ogf A009923 8.59234 -(1+8*x+35*x^2+68*x^3+88*x^4+82*x^5+29*x^6-5*x^8+8*x^7+6*x^9)/(x+1)/(x^2+x+1)^2/(x-1)^3 ogf A009924 10.1523 -(-1-x^7-9*x^6-9*x-28*x^5-42*x^4-24*x^2-46*x^3)/(-x^7+1-x+2*x^4-2*x^3+x^6) ogf A009924 12.1173 -(x^3+4*x^2+2*x+1)*(x^4+5*x^3+6*x^2+7*x+1)/(x^2+x+1)^2/(x-1)^3 ogf A009924 6.2606 -2*(5+29*x+174*x^4+85*x^6+154*x^5+146*x^3+89*x^2+33*x^7+5*x^8)/(x-1)/(x^2+x+1)/(x^3+4*x^2+2*x+1)/(x^4+5*x^3+6*x^2+7*x+1) lgdogf A009925 14.1312 -(1+4*x+19*x^2+12*x^3+19*x^4+4*x^5+x^6)/(x-1)^3/(x+1)^3 ogf A009925 12.9536 -(1+x^6+4*x+4*x^5+19*x^4+19*x^2+12*x^3)/(-1-3*x^4+3*x^2+x^6) ogf A009925 8.26823 -4*(1+11*x+14*x^4+x^6+11*x^5+38*x^3+14*x^2)/(x-1)/(x+1)/(x^6+4*x^5+19*x^4+12*x^3+19*x^2+4*x+1) lgdogf A009926 13.0608 -(-1-x^6-8*x-8*x^5-9*x^4-9*x^2-24*x^3)/(1+3*x^4-3*x^2-x^6) ogf A009926 14.2929 -(1+8*x+9*x^2+24*x^3+9*x^4+8*x^5+x^6)/(x-1)^3/(x+1)^3 ogf A009926 8.51152 -8*(1+3*x+14*x^4+x^6+3*x^5+9*x^3+14*x^2)/(x-1)/(x+1)/(x^6+8*x^5+9*x^4+24*x^3+9*x^2+8*x+1) lgdogf A009928 5.76388 -(-1-124*x^7-146*x^6-13*x-57*x^8-4*x^13-33*x^9-150*x^5-122*x^4-37*x^2+11*x^10+4*x^12-76*x^3)/(-x^8+1-x+2*x^7+x^2-x^10-2*x^3+x^9) ogf A009940 19.4219 -1/exp(-1)/(x-1)*exp(1/(x-1)) egf A009940 28.1618 -x+(-1+2*x-x^2)*f(x) lgdegf A009940 56.3236 -x/(x-1)^2 lgdegf A009940 8.66517 {(n^2+4*n+4)*a(n+1)+(-2*n-4)*a(n+2)+a(n+3),a(0)=1,a(1)=0,a(2)=-1} ogf A009941 11.3692 -(1+10*x+35*x^2+40*x^3+35*x^4+10*x^5+x^6)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A009941 11.7302 -(1+x^6+10*x+10*x^5+35*x^4+35*x^2+40*x^3)/(x^2-1+x-x^4-x^5+x^6) ogf A009941 5.8189 -(11+94*x+610*x^4+272*x^6+506*x^5+506*x^3+272*x^2+94*x^7+11*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^6+10*x^5+35*x^4+40*x^3+35*x^2+10*x+1) lgdogf A009942 11.4264 -(-1-x^6-13*x-13*x^5-29*x^4-29*x^2-46*x^3)/(-x^2+1-x+x^4+x^5-x^6) ogf A009942 11.4264 -(1+13*x+29*x^2+46*x^3+29*x^4+13*x^5+x^6)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A009942 5.84814 -2*(7+44*x+302*x^4+142*x^6+250*x^5+250*x^3+142*x^2+44*x^7+7*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^6+13*x^5+29*x^4+46*x^3+29*x^2+13*x+1) lgdogf A009943 13.9093 -(-1-4*x-2*x^5+5*x^4-12*x^2-10*x^3)/(1-2*x-x^4+2*x^3) ogf A009943 15.3582 -(1+4*x+12*x^2+10*x^3-5*x^4+2*x^5)/(x+1)/(x-1)^3 ogf A009943 8.47351 2*(-3-18*x-5*x^4+x^6-2*x^5-12*x^3-33*x^2)/(x-1)/(x+1)/(2*x^5-5*x^4+10*x^3+12*x^2+4*x+1) lgdogf A009945 12.0148 -(1+x^6+4*x+4*x^5+7*x^4+7*x^2+12*x^3)/(-x^2-1+2*x+x^4-2*x^5+x^6) ogf A009945 14.2397 -(x^3+3*x^2+x+1)*(x^3+x^2+3*x+1)/(x+1)/(x^2+1)/(x-1)^3 ogf A009945 6.92744 -2*(3+12*x+46*x^4+30*x^6+40*x^5+40*x^3+30*x^2+12*x^7+3*x^8)/(x-1)/(x+1)/(x^2+1)/(x^3+3*x^2+x+1)/(x^3+x^2+3*x+1) lgdogf A009946 20.2354 -(1+4*x+8*x^2+4*x^3+x^4)/(x+1)/(x-1)^3 ogf A009946 17.8824 -(1+4*x+x^4+8*x^2+4*x^3)/(-1+2*x+x^4-2*x^3) ogf A009946 7.32329 -119-476*x-119*x^4-476*x^3-952*x^2+(99-318*x-139*x^4+158*x^3-160*x^2)*f(x)+(20-40*x-20*x^4+40*x^3)*f(x)^2 ogf A009946 11.4768 -2*(3+14*x+3*x^4+14*x^3+20*x^2)/(x-1)/(x+1)/(x^4+4*x^3+8*x^2+4*x+1) lgdogf A009947 19.0275 (1+2*x+x^2+x^3)/(x-1)^2/(x^2+x+1)^2 ogf A009947 11.4821 -(x+1)*(3*x^4+x^3+9*x^2+2)/(x-1)/(x^2+x+1)/(x^3+x^2+2*x+1) lgdogf A009947 19.0275 -(x^5+x^4+x^2+2*x^3)/(-1+2*x^3-x^6) ogf A009948 10.8677 -(-1-x^6-10*x-10*x^5-19*x^4-19*x^2-24*x^3)/(x^2+1-2*x-x^4+2*x^5-x^6) ogf A009948 11.7302 -(1+10*x+19*x^2+24*x^3+19*x^4+10*x^5+x^6)/(x+1)/(x^2+1)/(x-1)^3 ogf A009948 6.15834 -4*(3+15*x+56*x^4+33*x^6+47*x^5+47*x^3+33*x^2+15*x^7+3*x^8)/(x-1)/(x+1)/(x^2+1)/(x^6+10*x^5+19*x^4+24*x^3+19*x^2+10*x+1) lgdogf A009955 8.18637 -(-1-7*x^7-20*x^6-7*x-41*x^5-50*x^4-20*x^2-x^8-41*x^3)/(-x^7+1+x+2*x^6-2*x^2+3*x^5-3*x^3-x^8) ogf A009955 9.63711 -(1+7*x+20*x^2+41*x^3+50*x^4+41*x^5+20*x^6+x^8+7*x^7)/(x^2+x+1)/(x-1)^3/(x+1)^3 ogf A009956 6.95581 -(1+35*x^7+65*x^6+4*x+5*x^9+60*x^5+50*x^4+17*x^2+20*x^8-4*x^10+x^12+x^11+33*x^3)/(-x^8-1+x^10+x^2-2*x^6+2*x^4) ogf A009956 7.21829 -(1+4*x+17*x^2+33*x^3+50*x^4+60*x^5+65*x^6+20*x^8+x^11+x^12+35*x^7+5*x^9-4*x^10)/(x^2+1)^2/(x-1)^3/(x+1)^3 ogf A009957 12.8158 -(-1-x^6-6*x-6*x^5-17*x^4-15*x^2-26*x^3)/(1+3*x^4-3*x^2-x^6) ogf A009957 13.9808 -(1+6*x+15*x^2+26*x^3+17*x^4+6*x^5+x^6)/(x-1)^3/(x+1)^3 ogf A009957 8.00985 -2*(3+18*x+54*x^4+3*x^6+20*x^5+64*x^3+54*x^2)/(x-1)/(x+1)/(x^6+6*x^5+17*x^4+26*x^3+15*x^2+6*x+1) lgdogf A009964 31.1916 -1+(1-20*x)*f(x) ogf A009964 41.5889 -1/(-1+20*x) ogf A009964 38.3897 -20/(-1+20*x) lgdogf A009964 49.9066 1/(1-20*x) ogf A009964 33.2711 1/20*ln(1+20*x) revegf A009964 49.9066 x/(20*x+1) revogf A009964 21.6985 {a(n+1)-20*a(n),a(0)=1} ogf A009965 58.607 -1+(1-21*x)*f(x) ogf A009965 78.1427 -1/(-1+21*x) ogf A009965 72.1317 -21/(-1+21*x) lgdogf A009965 93.7712 1/(1-21*x) ogf A009965 62.5141 1/21*ln(1+21*x) revegf A009965 93.7712 x/(1+21*x) revogf A009965 40.7701 {a(n+1)-21*a(n),a(0)=1} ogf A009966 59.7487 -1+(1-22*x)*f(x) ogf A009966 79.6649 -1/(-1+22*x) ogf A009966 73.5369 -22/(-1+22*x) lgdogf A009966 95.5979 1/(1-22*x) ogf A009966 63.732 1/22*ln(1+22*x) revegf A009966 95.5979 x/(1+22*x) revogf A009966 41.5643 {a(n+1)-22*a(n),a(0)=1} ogf A009967 60.3196 -1+(1-23*x)*f(x) ogf A009967 80.4261 -1/(-1+23*x) ogf A009967 74.2394 -23/(-1+23*x) lgdogf A009967 96.5113 1/(1-23*x) ogf A009967 64.3409 1/23*ln(1+23*x) revegf A009967 96.5113 x/(1+23*x) revogf A009967 41.9614 {a(n+1)-23*a(n),a(0)=1} ogf A009968 61.0807 -1+(1-24*x)*f(x) ogf A009968 81.4409 -1/(-1+24*x) ogf A009968 75.1762 -24/(-1+24*x) lgdogf A009968 97.7291 1/(1-24*x) ogf A009968 65.1527 1/24*ln(1+24*x) revegf A009968 97.7291 x/(24*x+1) revogf A009968 42.4909 {a(n+1)-24*a(n),a(0)=1} ogf A009969 61.4612 -1+(1-25*x)*f(x) ogf A009969 81.9483 -1/(-1+25*x) ogf A009969 75.6446 -25/(-1+25*x) lgdogf A009969 98.338 1/(1-25*x) ogf A009969 65.5587 1/25*ln(1+25*x) revegf A009969 98.338 x/(1+25*x) revogf A009969 42.7557 {a(n+1)-25*a(n),a(0)=1} ogf A009970 62.4127 -1+(1-26*x)*f(x) ogf A009970 83.2169 -1/(-1+26*x) ogf A009970 76.8156 -26/(-1+26*x) lgdogf A009970 99.8603 1/(1-26*x) ogf A009970 66.5735 1/26*ln(1+26*x) revegf A009970 99.8603 x/(1+26*x) revogf A009970 43.4175 {a(n+1)-26*a(n),a(0)=1} ogf A009971 33.9642 -1+(1-27*x)*f(x) ogf A009971 45.2856 -1/(-1+27*x) ogf A009971 41.8021 -27/(-1+27*x) lgdogf A009971 54.3428 1/(1-27*x) ogf A009971 36.2285 1/27*ln(1+27*x) revegf A009971 54.3428 x/(27*x+1) revogf A009971 23.6273 {a(n+1)-27*a(n),a(0)=1} ogf A009972 34.1375 -1+(1-28*x)*f(x) ogf A009972 45.5167 -1/(-1+28*x) ogf A009972 42.0154 -28/(-1+28*x) lgdogf A009972 54.62 1/(1-28*x) ogf A009972 36.4133 1/28*ln(1+28*x) revegf A009972 54.62 x/(1+28*x) revogf A009972 23.7478 {a(n+1)-28*a(n),a(0)=1} ogf A009973 34.4841 -1+(1-29*x)*f(x) ogf A009973 45.9788 -1/(-1+29*x) ogf A009973 42.442 -29/(-1+29*x) lgdogf A009973 55.1745 1/(1-29*x) ogf A009973 36.783 1/29*ln(1+29*x) revegf A009973 55.1745 x/(1+29*x) revogf A009973 23.9889 {a(n+1)-29*a(n),a(0)=1} ogf A009974 34.6574 -1+(1-30*x)*f(x) ogf A009974 46.2098 -1/(-1+30*x) ogf A009974 42.6552 -30/(-1+30*x) lgdogf A009974 55.4518 1/(1-30*x) ogf A009974 36.9679 1/30*ln(1+30*x) revegf A009974 55.4518 x/(1+30*x) revogf A009974 24.1095 {a(n+1)-30*a(n),a(0)=1} ogf A009975 34.6574 -1+(1-31*x)*f(x) ogf A009975 46.2098 -1/(-1+31*x) ogf A009975 42.6552 -31/(-1+31*x) lgdogf A009975 55.4518 1/(1-31*x) ogf A009975 36.9679 1/31*ln(1+31*x) revegf A009975 55.4518 x/(1+31*x) revogf A009975 24.1095 {a(n+1)-31*a(n),a(0)=1} ogf A009976 30.9733 -1+(1-32*x)*f(x) ogf A009976 41.2978 -1/(-1+32*x) ogf A009976 38.121 -32/(-1+32*x) lgdogf A009976 49.5573 1/(1-32*x) ogf A009976 33.0382 1/32*ln(1+32*x) revegf A009976 49.5573 x/(1+32*x) revogf A009976 21.5467 {a(n+1)-32*a(n),a(0)=1} ogf A009977 30.9733 -1+(1-33*x)*f(x) ogf A009977 41.2978 -1/(-1+33*x) ogf A009977 38.121 -33/(-1+33*x) lgdogf A009977 49.5573 1/(1-33*x) ogf A009977 33.0382 1/33*ln(1+33*x) revegf A009977 49.5573 x/(1+33*x) revogf A009977 21.5467 {a(n+1)-33*a(n),a(0)=1} ogf A009978 30.9733 -1+(1-34*x)*f(x) ogf A009978 41.2978 -1/(-1+34*x) ogf A009978 38.121 -34/(-1+34*x) lgdogf A009978 49.5573 1/(1-34*x) ogf A009978 33.0382 1/34*ln(1+34*x) revegf A009978 49.5573 x/(1+34*x) revogf A009978 21.5467 {a(n+1)-34*a(n),a(0)=1} ogf A009979 31.1426 -1+(1-35*x)*f(x) ogf A009979 41.5234 -1/(-1+35*x) ogf A009979 38.3293 -35/(-1+35*x) lgdogf A009979 49.8281 1/(1-35*x) ogf A009979 33.2187 1/35*ln(1+35*x) revegf A009979 49.8281 x/(1+35*x) revogf A009979 21.6644 {a(n+1)-35*a(n),a(0)=1} ogf A009980 31.4811 -1+(1-36*x)*f(x) ogf A009980 41.9748 -1/(-1+36*x) ogf A009980 38.7459 -36/(-1+36*x) lgdogf A009980 50.3697 1/(1-36*x) ogf A009980 33.5798 1/36*ln(1+36*x) revegf A009980 50.3697 x/(1+36*x) revogf A009980 21.8999 {a(n+1)-36*a(n),a(0)=1} ogf A009981 31.4811 -1+(1-37*x)*f(x) ogf A009981 41.9748 -1/(-1+37*x) ogf A009981 38.7459 -37/(-1+37*x) lgdogf A009981 50.3697 1/(1-37*x) ogf A009981 33.5798 1/37*ln(1+37*x) revegf A009981 50.3697 x/(1+37*x) revogf A009981 21.8999 {a(n+1)-37*a(n),a(0)=1} ogf A009982 31.8196 -1+(1-38*x)*f(x) ogf A009982 42.4261 -1/(-1+38*x) ogf A009982 39.1626 -38/(-1+38*x) lgdogf A009982 50.9113 1/(1-38*x) ogf A009982 33.9409 1/38*ln(1+38*x) revegf A009982 50.9113 x/(1+38*x) revogf A009982 22.1354 {a(n+1)-38*a(n),a(0)=1} ogf A009983 31.9888 -1+(1-39*x)*f(x) ogf A009983 42.6518 -1/(-1+39*x) ogf A009983 39.3709 -39/(-1+39*x) lgdogf A009983 51.1821 1/(1-39*x) ogf A009983 34.1214 1/39*ln(1+39*x) revegf A009983 51.1821 x/(1+39*x) revogf A009983 22.2531 {a(n+1)-39*a(n),a(0)=1} ogf A009984 32.3273 -1+(1-40*x)*f(x) ogf A009984 43.1031 -1/(-1+40*x) ogf A009984 39.7875 -40/(-1+40*x) lgdogf A009984 51.7238 1/(1-40*x) ogf A009984 34.4825 1/40*ln(1+40*x) revegf A009984 51.7238 x/(1+40*x) revogf A009984 22.4886 {a(n+1)-40*a(n),a(0)=1} ogf A009985 32.3273 -1+(1-41*x)*f(x) ogf A009985 43.1031 -1/(-1+41*x) ogf A009985 39.7875 -41/(-1+41*x) lgdogf A009985 51.7238 1/(1-41*x) ogf A009985 34.4825 1/41*ln(1+41*x) revegf A009985 51.7238 x/(1+41*x) revogf A009985 22.4886 {a(n+1)-41*a(n),a(0)=1} ogf A009986 32.4966 -1+(1-42*x)*f(x) ogf A009986 43.3288 -1/(-1+42*x) ogf A009986 39.9958 -42/(-1+42*x) lgdogf A009986 51.9946 1/(1-42*x) ogf A009986 34.663 1/42*ln(1+42*x) revegf A009986 51.9946 x/(1+42*x) revogf A009986 22.6063 {a(n+1)-42*a(n),a(0)=1} ogf A009987 32.6659 -1+(1-43*x)*f(x) ogf A009987 43.5545 -1/(-1+43*x) ogf A009987 40.2041 -43/(-1+43*x) lgdogf A009987 52.2654 1/(1-43*x) ogf A009987 34.8436 1/43*ln(1+43*x) revegf A009987 52.2654 x/(1+43*x) revogf A009987 22.7241 {a(n+1)-43*a(n),a(0)=1} ogf A009988 33.0044 -1+(1-44*x)*f(x) ogf A009988 44.0058 -1/(-1+44*x) ogf A009988 40.6208 -44/(-1+44*x) lgdogf A009988 52.807 1/(1-44*x) ogf A009988 35.2047 1/44*ln(1+44*x) revegf A009988 52.807 x/(1+44*x) revogf A009988 22.9596 {a(n+1)-44*a(n),a(0)=1} ogf A009989 33.0044 -1+(1-45*x)*f(x) ogf A009989 44.0058 -1/(-1+45*x) ogf A009989 40.6208 -45/(-1+45*x) lgdogf A009989 52.807 1/(1-45*x) ogf A009989 35.2047 1/45*ln(1+45*x) revegf A009989 52.807 x/(1+45*x) revogf A009989 22.9596 {a(n+1)-45*a(n),a(0)=1} ogf A009990 33.0044 -1+(1-46*x)*f(x) ogf A009990 44.0058 -1/(-1+46*x) ogf A009990 40.6208 -46/(-1+46*x) lgdogf A009990 52.807 1/(1-46*x) ogf A009990 35.2047 1/46*ln(1+46*x) revegf A009990 52.807 x/(1+46*x) revogf A009990 22.9596 {a(n+1)-46*a(n),a(0)=1} ogf A009991 28.6998 -1+(1-47*x)*f(x) ogf A009991 38.2664 -1/(-1+47*x) ogf A009991 35.3228 -47/(-1+47*x) lgdogf A009991 45.9196 1/(1-47*x) ogf A009991 30.6131 1/47*ln(1+47*x) revegf A009991 45.9196 x/(1+47*x) revogf A009991 19.9651 {a(n+1)-47*a(n),a(0)=1} ogf A009992 28.6998 -1+(1-48*x)*f(x) ogf A009992 38.2664 -1/(-1+48*x) ogf A009992 35.3228 -48/(-1+48*x) lgdogf A009992 45.9196 1/(1-48*x) ogf A009992 30.6131 1/48*ln(1+48*x) revegf A009992 45.9196 x/(1+48*x) revogf A009992 19.9651 {a(n+1)-48*a(n),a(0)=1} ogf A010000 28.5019 -(-1-x^3)/(-x^3+1-3*x+3*x^2) ogf A010000 33.2522 -(x+1)*(x^2-x+1)/(x-1)^3 ogf A010000 24.9391 -3*(1+x^2)/(x-1)/(x+1)/(x^2-x+1) lgdogf A010000 11.566 -7-7*x^3+(-13-21*x-27*x^3+21*x^2)*f(x)+(60*x^2-20*x^3+20-60*x)*f(x)^2 ogf A010000 88.6725 3+x^2-x^5 ogf_with_Euler_Transform A010000 7.32158 {5*a(n+3)*n-30*a(n+3)+5*a(n+3)*n^2+4*a(n+1)-5*a(n+1)*n+a(n+1)*n^2,a(0)=3,a(1)=0,a(2)=1,a(3)=0,a(4)=0,a(5)=-1} ogf_with_Euler_Transform A010000 12.8718 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=3,a(2)=6,a(3)=11} ogf A010001 21.6824 -(-1-4*x-4*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010001 21.1265 -(7+16*x+7*x^2)/(x-1)/(x+1)/(x^2+3*x+1) lgdogf A010001 31.6897 -(x+1)*(x^2+3*x+1)/(x-1)^3 ogf A010001 8.15774 -707-2828*x-707*x^3-2828*x^2+(1135-409*x-279*x^3+3833*x^2)*f(x)+(-1284*x^2-428+1284*x+428*x^3)*f(x)^2 ogf A010001 13.0783 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=7,a(2)=22,a(3)=47} ogf A010002 21.2114 -(-1-8*x-8*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010002 19.6593 -(11+32*x+11*x^2)/(x-1)/(x+1)/(x^2+7*x+1) lgdogf A010002 31.0012 -(x+1)*(x^2+7*x+1)/(x-1)^3 ogf A010002 7.46326 -3451-27608*x-3451*x^3-27608*x^2+(4247-3985*x-2655*x^3+16721*x^2)*f(x)+(-2388*x^2-796+2388*x+796*x^3)*f(x)^2 ogf A010002 12.5943 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=11,a(2)=38,a(3)=83} ogf A010003 19.9344 -(-1-10*x-10*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010003 19.4482 -(13+40*x+13*x^2)/(x-1)/(x+1)/(x^2+9*x+1) lgdogf A010003 30.6682 -(x+1)*(x^2+9*x+1)/(x-1)^3 ogf A010003 8.13647 -797-7970*x-797*x^3-7970*x^2+(937-991*x-657*x^3+3791*x^2)*f(x)+(-420*x^2-140+420*x+140*x^3)*f(x)^2 ogf A010003 12.2673 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=13,a(2)=46,a(3)=101} ogf A010004 20.3105 -(-1-12*x-12*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010004 30.0896 -(x+1)*(x^2+11*x+1)/(x-1)^3 ogf A010004 7.5224 -2737-32844*x-2737*x^3-32844*x^2+(3125-3555*x-2349*x^3+12867*x^2)*f(x)+(-1164*x^2-388+1164*x+388*x^3)*f(x)^2 ogf A010004 19.3433 -3*(5+16*x+5*x^2)/(x-1)/(x+1)/(x^2+11*x+1) lgdogf A010004 12.4988 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=15,a(2)=54,a(3)=119} ogf A010005 20.4985 -(-1-14*x-14*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010005 19.5224 -(17+56*x+17*x^2)/(x-1)/(x+1)/(x^2+13*x+1) lgdogf A010005 30.3682 -(x+1)*(x^2+13*x+1)/(x-1)^3 ogf A010005 7.06846 -11347-158858*x-11347*x^3-158858*x^2+(12695-15169*x-9999*x^3+52913*x^2)*f(x)+(-4044*x^2-1348+4044*x+1348*x^3)*f(x)^2 ogf A010005 12.6145 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=17,a(2)=62,a(3)=137} ogf A010006 19.9965 -(-1-15*x-15*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010006 29.6245 -(x+1)*(1+14*x+x^2)/(x-1)^3 ogf A010006 19.5088 -6*(x+3)*(3*x+1)/(x-1)/(x+1)/(x^2+14*x+1) lgdogf A010006 8.88735 -91-1365*x-91*x^3-1365*x^2+(101-123*x-81*x^3+423*x^2)*f(x)+(-30*x^2-10+30*x+10*x^3)*f(x)^2 ogf A010006 12.3056 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=18,a(2)=66,a(3)=146} ogf A010007 19.9965 -(-1-16*x-16*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010007 19.0443 -(19+64*x+19*x^2)/(x-1)/(x+1)/(x^2+15*x+1) lgdogf A010007 29.6245 -(x+1)*(x^2+15*x+1)/(x-1)^3 ogf A010007 6.83642 -14987-239792*x-14987*x^3-239792*x^2+(16519-20449*x-13455*x^3+69473*x^2)*f(x)+(-4596*x^2-1532+4596*x+1532*x^3)*f(x)^2 ogf A010007 12.3056 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=19,a(2)=70,a(3)=155} ogf A010008 20.09 -(-1-17*x-17*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010008 29.7629 -(x+1)*(x^2+16*x+1)/(x-1)^3 ogf A010008 19.1333 -4*(5+17*x+5*x^2)/(x-1)/(x+1)/(x^2+16*x+1) lgdogf A010008 8.19999 -607-10319*x-607*x^3-10319*x^2+(665-835*x-549*x^3+2807*x^2)*f(x)+(-174*x^2-58+174*x+58*x^3)*f(x)^2 ogf A010008 12.3631 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=20,a(2)=74,a(3)=164} ogf A010009 20.1834 -(-1-18*x-18*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010009 29.9014 -(x+1)*(x^2+17*x+1)/(x-1)^3 ogf A010009 19.2223 -3*(7+24*x+7*x^2)/(x-1)/(x+1)/(x^2+17*x+1) lgdogf A010009 7.33942 -6377-114786*x-6377*x^3-114786*x^2+(6949-8835*x-5805*x^3+29427*x^2)*f(x)+(-1716*x^2-572+1716*x+572*x^3)*f(x)^2 ogf A010009 12.4206 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=21,a(2)=78,a(3)=173} ogf A010010 20.1834 -(-1-19*x-19*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010010 29.9014 -(x+1)*(x^2+18*x+1)/(x-1)^3 ogf A010010 7.68892 -1337-25403*x-1337*x^3-25403*x^2+(1450-1864*x-1224*x^3+6158*x^2)*f(x)+(-339*x^2-113+339*x+113*x^3)*f(x)^2 ogf A010010 18.3486 -2*(11+38*x+11*x^2)/(x-1)/(x+1)/(x^2+18*x+1) lgdogf A010010 12.4206 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=22,a(2)=82,a(3)=182} ogf A010011 20.3703 -(-1-20*x-20*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010011 19.4003 -(23+80*x+23*x^2)/(x-1)/(x+1)/(x^2+19*x+1) lgdogf A010011 30.1782 -(x+1)*(x^2+19*x+1)/(x-1)^3 ogf A010011 6.90519 -23779-475580*x-23779*x^3-475580*x^2+(25679-33337*x-21879*x^3+109337*x^2)*f(x)+(-5700*x^2-1900+5700*x+1900*x^3)*f(x)^2 ogf A010011 12.5356 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=23,a(2)=86,a(3)=191} ogf A010012 20.3703 -(-1-21*x-21*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010012 30.1782 -(x+1)*(x^2+20*x+1)/(x-1)^3 ogf A010012 19.4003 -12*(2+7*x+2*x^2)/(x-1)/(x+1)/(x^2+20*x+1) lgdogf A010012 7.76011 2191+46011*x+2191*x^3+46011*x^2+(-2357+3087*x+2025*x^3-10059*x^2)*f(x)+(166-498*x+498*x^2-166*x^3)*f(x)^2 ogf A010012 12.5356 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=24,a(2)=90,a(3)=200} ogf A010013 20.4637 -(-1-22*x-22*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010013 19.4893 -(25+88*x+25*x^2)/(x-1)/(x+1)/(x^2+21*x+1) lgdogf A010013 30.3167 -(x+1)*(x^2+21*x+1)/(x-1)^3 ogf A010013 6.93686 -28931-636482*x-28931*x^3-636482*x^2+(31015-40945*x-26847*x^3+132641*x^2)*f(x)+(-6252*x^2-2084+6252*x+2084*x^3)*f(x)^2 ogf A010013 12.5931 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=25,a(2)=94,a(3)=209} ogf A010014 20.4637 -(-1-23*x-23*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010014 30.3167 -(x+1)*(x^2+22*x+1)/(x-1)^3 ogf A010014 7.79571 -1981-45563*x-1981*x^3-45563*x^2+(2117-2815*x-1845*x^3+9071*x^2)*f(x)+(-408*x^2-136+408*x+136*x^3)*f(x)^2 ogf A010014 18.6034 -2*(13+46*x+13*x^2)/(x-1)/(x+1)/(x^2+22*x+1) lgdogf A010014 12.5931 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=26,a(2)=98,a(3)=218} ogf A010015 19.9604 -(-1-24*x-24*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010015 29.571 -(x+1)*(x^2+23*x+1)/(x-1)^3 ogf A010015 19.0099 -3*(9+32*x+9*x^2)/(x-1)/(x+1)/(x^2+23*x+1) lgdogf A010015 9.28392 -61-1464*x-61*x^3-1464*x^2+(65-87*x-57*x^3+279*x^2)*f(x)+(-12*x^2-4+12*x+4*x^3)*f(x)^2 ogf A010015 12.0972 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=27,a(2)=102,a(3)=227} ogf A010016 19.9604 -(-1-25*x-25*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010016 29.571 -(x+1)*(x^2+24*x+1)/(x-1)^3 ogf A010016 19.0099 -4*(7+25*x+7*x^2)/(x-1)/(x+1)/(x^2+24*x+1) lgdogf A010016 7.19295 -9401-235025*x-9401*x^3-235025*x^2+(9991-13453*x-8811*x^3+42953*x^2)*f(x)+(-1770*x^2-590+1770*x+590*x^3)*f(x)^2 ogf A010016 12.0972 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=28,a(2)=106,a(3)=236} ogf A010017 19.9604 -(-1-26*x-26*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010017 18.5678 -(29+104*x+29*x^2)/(x-1)/(x+1)/(x^2+25*x+1) lgdogf A010017 29.571 -(x+1)*(x^2+25*x+1)/(x-1)^3 ogf A010017 6.65348 -40747-1059422*x-40747*x^3-1059422*x^2+(43199-58489*x-38295*x^3+185993*x^2)*f(x)+(-7356*x^2-2452+7356*x+2452*x^3)*f(x)^2 ogf A010017 12.0972 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=29,a(2)=110,a(3)=245} ogf A010018 20.1461 -(-1-27*x-27*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010018 29.8461 -(x+1)*(x^2+26*x+1)/(x-1)^3 ogf A010018 19.1868 -6*(5+18*x+5*x^2)/(x-1)/(x+1)/(x^2+26*x+1) lgdogf A010018 8.13985 -917-24759*x-917*x^3-24759*x^2+(970-1320*x-864*x^3+4182*x^2)*f(x)+(-159*x^2-53+159*x+53*x^3)*f(x)^2 ogf A010018 12.2098 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=30,a(2)=114,a(3)=254} ogf A010019 20.1461 -(-1-28*x-28*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010019 18.7406 -(31+112*x+31*x^2)/(x-1)/(x+1)/(x^2+27*x+1) lgdogf A010019 29.8461 -(x+1)*(x^2+27*x+1)/(x-1)^3 ogf A010019 6.71537 -47411-1327508*x-47411*x^3-1327508*x^2+(50047-68425*x-44775*x^3+216041*x^2)*f(x)+(-7908*x^2-2636+7908*x+2636*x^3)*f(x)^2 ogf A010019 12.2098 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=31,a(2)=118,a(3)=263} ogf A010020 20.239 -(-1-30*x-30*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010020 29.9836 -(x+1)*(x^2+29*x+1)/(x-1)^3 ogf A010020 7.03964 -18193-545790*x-18193*x^3-545790*x^2+(19133-26379*x-17253*x^3+82779*x^2)*f(x)+(-2820*x^2-940+2820*x+940*x^3)*f(x)^2 ogf A010020 18.3991 -3*(11+40*x+11*x^2)/(x-1)/(x+1)/(x^2+29*x+1) lgdogf A010020 12.266 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=33,a(2)=126,a(3)=281} ogf A010021 20.239 -(-1-31*x-31*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010021 29.9836 -(x+1)*(x^2+30*x+1)/(x-1)^3 ogf A010021 18.3991 -2*(17+62*x+17*x^2)/(x-1)/(x+1)/(x^2+30*x+1) lgdogf A010021 8.4329 -521-16151*x-521*x^3-16151*x^2+(547-757*x-495*x^3+2369*x^2)*f(x)+(-78*x^2-26+78*x+26*x^3)*f(x)^2 ogf A010021 12.266 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=34,a(2)=130,a(3)=290} ogf A010022 19.8277 -(-1-39*x-39*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010022 29.3744 -(x+1)*(x^2+38*x+1)/(x-1)^3 ogf A010022 7.70009 -1939-75621*x-1939*x^3-75621*x^2+(2015-2853*x-1863*x^3+8781*x^2)*f(x)+(-228*x^2-76+228*x+76*x^3)*f(x)^2 ogf A010022 18.8836 -6*(7+26*x+7*x^2)/(x-1)/(x+1)/(x^2+38*x+1) lgdogf A010022 12.0168 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=42,a(2)=162,a(3)=362} ogf A010023 19.8277 -(-1-41*x-41*x^2-x^3)/(-x^3+1-3*x+3*x^2) ogf A010023 29.3744 -(x+1)*(x^2+40*x+1)/(x-1)^3 ogf A010023 6.72126 -25753-1055873*x-25753*x^3-1055873*x^2+(26711-37981*x-24795*x^3+116537*x^2)*f(x)+(-2874*x^2-958+2874*x+958*x^3)*f(x)^2 ogf A010023 18.0252 -4*(11+41*x+11*x^2)/(x-1)/(x+1)/(x^2+40*x+1) lgdogf A010023 12.0168 {a(n+4)-3*a(n+3)+3*a(n+2)-a(n+1),a(0)=1,a(1)=44,a(2)=170,a(3)=380} ogf A010024 8.61246 -(-1-7*x-x^5-7*x^4-22*x^2-42*x^3)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A010024 13.9952 -(1+7*x+22*x^2+42*x^3+7*x^4+x^5)/(x-1)^5 ogf A010024 8.11318 -4*(3+18*x+3*x^4+28*x^3+48*x^2)/(x-1)/(x^5+7*x^4+42*x^3+22*x^2+7*x+1) lgdogf A010024 4.30623 {(594*n+267*n^2)*a(n)+(7107+2956*n-227*n^2)*a(n+1)+(1480-3552*n-247*n^2)*a(n+2)+(402*n-657+207*n^2)*a(n+3),a(0)=1,a(1)=12,a(2)=72} ogf A010025 14.5355 (1+7*x+22*x^2+42*x^3+7*x^4+x^5)/(x-1)^6 ogf A010025 7.8734 -(1+7*x+x^5+7*x^4+22*x^2+42*x^3)/(-15*x^2-1+6*x-15*x^4+20*x^3-x^6+6*x^5) ogf A010025 7.55846 -(13+79*x+19*x^4+x^5+154*x^3+214*x^2)/(x-1)/(x^5+7*x^4+42*x^3+22*x^2+7*x+1) lgdogf A010032 2.01412 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A010035 21.3165 (3*x+1)/(9*x-1)/(-1+3*x) ogf A010035 20.4638 -(1+3*x)/(-27*x^2-1+12*x) ogf A010035 11.6272 -1/6*(-1-12*x+(1+36*x+36*x^2)^(1/2))/(9*x-1) revogf A010035 11.8976 -3*(-5+18*x+27*x^2)/(3*x-1)/(3*x+1)/(9*x-1) lgdogf A010035 7.52346 -411-1233*x+(197-5574*x+11097*x^2)*f(x)+(5778*x^2+214-2568*x)*f(x)^2 ogf A010035 12.1808 {-a(n+2)+12*a(n+1)-27*a(n),a(0)=1,a(1)=15} ogf A010036 25.7587 -(1-x)/(-8*x^2-1+6*x) ogf A010036 14.6198 -(5-16*x+8*x^2)/(x-1)/(2*x-1)/(4*x-1) lgdogf A010036 24.5878 -(x-1)/(4*x-1)/(2*x-1) ogf A010036 13.1935 -1/2*(-1-6*x+(1+8*x+4*x^2)^(1/2))/(8*x+1) revogf A010036 9.83513 -11+11*x+(-3-52*x+88*x^2)*f(x)+(14-84*x+112*x^2)*f(x)^2 ogf A010036 7.21243 1/4*ln(8*x+1)-1/4*ln(2*(1+6*x)^(1/2)-1)+1/4*ln(2*(1+6*x)^(1/2)+1)-1/4*ln(3) revegf A010036 13.8701 {-a(n+2)+6*a(n+1)-8*a(n),a(0)=1,a(1)=5} ogf A010037 18.5726 (533360+1435391*x)/(x-1)^2 ogf A010037 8.77978 -(-266680-x+(71118222400+1968751*x)^(1/2))/(-1435391+x) revogf A010037 10.7308 -(2502111+1435391*x)/(1435391*x+533360)/(x-1) lgdogf A010037 15.0903 -(533360+1435391*x)/(-x^2-1+2*x) ogf A010037 3.52473 -2219019419877589360-5971877351352768991*x+(2060347322881-13972761712484*x+4160453389601*x^2)*f(x)+(3937502-7875004*x+3937502*x^2)*f(x)^2 ogf A010037 10.0602 {-a(n+2)+2*a(n+1)-a(n),a(0)=533360,a(1)=2502111} ogf A010049 25.4631 -(-1-3*x+3*x^2)/(x-1)/(x^2+x-1) lgdogf A010049 25.4631 -(-x+x^2)/(1-2*x+x^4-x^2+2*x^3) ogf A010049 43.8532 -(x-1)/(x^2+x-1)^2 ogf A010049 12.5295 -x+x^2+(1-x+x^4+2*x^3-2*x^2)*f(x)+(-x^4-1+2*x-2*x^3+x^2)*f(x)^2 ogf A010049 9.86696 {(n+3)*a(n+4)+(-5-2*n)*a(n+3)-3*a(n+2)+(n+3)*a(n+1),a(0)=0,a(1)=1,a(2)=1,a(3)=3} ogf A010050 10.2044 {(4*n^2+14*n+12)*a(n+1)-a(n+2),a(0)=1,a(1)=2} ogf A010054 108.075 -1/(-1-x) ogf_with_Euler_Transform A010054 46.318 {-a(n+1)-a(n),a(0)=1} ogf_with_Euler_Transform A010070 6.21416 (1+2*x+2*x^2+2*x^3+9*x^4+9*x^5+9*x^6+8*x^8+9*x^7+7*x^9+7*x^10)/(x+1)/(x^2+1)/(1+x^4)/(x-1)^2 ogf A010070 7.32952 -(-1-2*x-9*x^5-9*x^6-2*x^2-7*x^10-7*x^9-9*x^4-8*x^8-9*x^7-2*x^3)/(x^9+1-x-x^8) ogf A010076 9.12685 -(1+x^2+x^3+3*x^4+3*x^5+6*x^6+x^7+8*x^10)/(x-1)/(x^2+x+1)/(x^2-x+1)/(x^4-x^2+1) ogf A010076 11.266 -(x+3*x^5+3*x^6+x^4+x^8+8*x^11+6*x^7+x^3)/(-1+x+x^5-x^4-x^8+x^9) ogf A010079 11.8029 -(-1-14*x-71*x^2-124*x^3-63*x^4+2*x^5-25*x^6+8*x^7)/(x+1)^2/(x-1)^4 ogf A010079 9.6438 -(1+14*x-2*x^5+25*x^6+71*x^2+63*x^4-8*x^7+124*x^3)/(x^2-1+2*x+x^4-4*x^3-x^6+2*x^5) ogf A010079 6.93677 8*(2+22*x+61*x^4-x^6+34*x^5+98*x^3+73*x^2-2*x^7+x^8)/(x-1)/(x+1)/(8*x^7-25*x^6+2*x^5-63*x^4-124*x^3-71*x^2-14*x-1) lgdogf A010081 2.36875 {(6090-1261*n+87*n^2-2*n^3)*a(n+1)+(176*n+672-72*n^2+4*n^3)*a(n+2)+(-37*n-30-15*n^2-2*n^3)*a(n+3),a(0)=1,a(1)=0,a(2)=1240} ogf A010082 3.72357 {(56730-5581*n+183*n^2-2*n^3)*a(n+1)+(1328*n+3360-168*n^2+4*n^3)*a(n+2)+(-37*n-30-15*n^2-2*n^3)*a(n+3),a(0)=1,a(1)=0,a(2)=10416} ogf A010083 3.11088 {(488250-23437*n+375*n^2-2*n^3)*a(n+1)+(6704*n+14880-360*n^2+4*n^3)*a(n+2)+(-37*n-30-15*n^2-2*n^3)*a(n+3),a(0)=1,a(1)=0,a(2)=85344} ogf A010085 2.26428 (x^8-7*x^7+28*x^6-49*x^5+70*x^4-49*x^3+28*x^2-7*x+1)*(x+1)^7 ogf A010085 1.18136 {(-182+27*n-n^2)*a(n+1)+(11*n+26-n^2)*a(n+2)+(-9*n-36+n^2)*a(n+3)+(7*n+12+n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=35} ogf A010086 4.65045 {(870-59*n+n^2)*a(n+1)+(-27*n-58+n^2)*a(n+2)+(25*n+84-n^2)*a(n+3)+(-7*n-12-n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=155} ogf A010087 4.23415 {(3782-123*n+n^2)*a(n+1)+(-59*n-122+n^2)*a(n+2)+(57*n+180-n^2)*a(n+3)+(-7*n-12-n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=651} ogf A010088 3.682 {(15750-251*n+n^2)*a(n+1)+(-123*n-250+n^2)*a(n+2)+(121*n+372-n^2)*a(n+3)+(-7*n-12-n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=2667} ogf A010089 3.76118 {(-64262+507*n-n^2)*a(n+1)+(251*n+506-n^2)*a(n+2)+(-249*n-756+n^2)*a(n+3)+(7*n+12+n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=10795} ogf A010091 2.01994 {(5278-1147*n+83*n^2-2*n^3)*a(n+1)+(160*n+624-68*n^2+4*n^3)*a(n+2)+(-37*n-30-15*n^2-2*n^3)*a(n+3),a(0)=1,a(1)=0,a(2)=1085} ogf A010092 4.1698 {(53070-5339*n+179*n^2-2*n^3)*a(n+1)+(1280*n+3248-164*n^2+4*n^3)*a(n+2)+(-37*n-30-15*n^2-2*n^3)*a(n+3),a(0)=1,a(1)=0,a(2)=9765} ogf A010093 3.11088 {(472750-22939*n+371*n^2-2*n^3)*a(n+1)+(6592*n+14640-356*n^2+4*n^3)*a(n+2)+(-37*n-30-15*n^2-2*n^3)*a(n+3),a(0)=1,a(1)=0,a(2)=82677} ogf A010096 12.9435 (-2+2*x^3-3*x^2-15*x^14+14*x^15)/(x-1)/(x^15+x^3+x+1) lgdogf A010096 31.182 -(1+x+x^15+x^3)/(-1+x) ogf A010096 32.6668 -(1+x+x^3+x^15)/(x-1) ogf A010121 24.3968 -(-2-x-x^2-x^3-2*x^4)/(1-x^4) ogf A010121 8.73465 -(1+2*x+3*x^4+x^6+2*x^5+16*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(2*x^2+3*x+2)/(x^2-x+1) lgdogf A010121 16.0797 -(3*x+2+2*x^2)*(x^2-x+1)/(x-1)/(x+1)/(x^2+1) ogf A010121 9.43342 14+7*x+14*x^4+7*x^3+7*x^2+(-17-5*x-3*x^4-5*x^3-5*x^2)*f(x)+(5-5*x^4)*f(x)^2 ogf A010122 21.4396 -(-3-x^2-x^3-x^4-x-3*x^5)/(1-x^5) ogf A010122 6.73816 -(1+2*x+30*x^4+3*x^6+4*x^5+4*x^3+3*x^2+2*x^7+x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(3*x^4-2*x^3+3*x^2-2*x+3) lgdogf A010122 12.634 -(x+1)*(3*x^4-2*x^3+3*x^2-2*x+3)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010122 8.13226 21+7*x+7*x^4+7*x^3+21*x^5+7*x^2+(-16-3*x-3*x^4-3*x^3-2*x^5-3*x^2)*f(x)+(3-3*x^5)*f(x)^2 ogf A010123 8.73465 -(1+4*x+3*x^4+x^6+4*x^5+24*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(3*x^2+4*x+3)/(x^2-x+1) lgdogf A010123 16.0797 -(3*x^2+4*x+3)*(x^2-x+1)/(x-1)/(x+1)/(x^2+1) ogf A010123 22.8228 -(3+x+3*x^4+x^3+2*x^2)/(-1+x^4) ogf A010123 7.7748 -225-75*x-225*x^4-75*x^3-150*x^2+(267+64*x+117*x^4+64*x^3+128*x^2)*f(x)+(-64+64*x^4)*f(x)^2 ogf A010124 16.4536 -(-4-2*x-2*x^5-x^4-3*x^3-x^2-4*x^6)/(1-x^6) ogf A010124 5.3599 -(2+2*x+10*x^4+10*x^6+48*x^5+4*x^3+2*x^10+9*x^2+4*x^7+2*x^9+9*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(4*x^6+2*x^5+x^4+3*x^3+x^2+2*x+4) lgdogf A010124 10.7198 -(4+2*x+x^2+3*x^3+x^4+2*x^5+4*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010125 18.1412 -(-4-x-x^5-x^4-2*x^3-x^2-4*x^6)/(1-x^6) ogf A010125 5.7057 -(1+2*x+5*x^4+5*x^6+48*x^5+4*x^3+x^10+6*x^2+4*x^7+2*x^9+6*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^2+1)/(4*x^4+x^3-3*x^2+x+4) lgdogf A010125 11.4114 -(4*x^4+x^3-3*x^2+x+4)*(x^2+1)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010126 5.44236 -(1+4*x+5*x^4+5*x^6+48*x^5+8*x^3+x^10+12*x^2+8*x^7+4*x^9+12*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(4*x^6+x^5+2*x^4+4*x^3+2*x^2+x+4) lgdogf A010126 10.7198 -(4+x+2*x^2+4*x^3+2*x^4+x^5+4*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010126 16.4536 -(4+x+x^5+2*x^4+4*x^3+2*x^2+4*x^6)/(-1+x^6) ogf A010127 8.73465 -(1+6*x+3*x^4+x^6+6*x^5+32*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(4*x^2+5*x+4)/(x^2-x+1) lgdogf A010127 16.0797 -(4*x^2+5*x+4)*(x^2-x+1)/(x-1)/(x+1)/(x^2+1) ogf A010127 22.8228 -(4+x+4*x^4+x^3+3*x^2)/(-1+x^4) ogf A010127 7.21945 -468-117*x-468*x^4-117*x^3-351*x^2+(1217+275*x+983*x^4+275*x^3+825*x^2)*f(x)+(-275+275*x^4)*f(x)^2 ogf A010128 21.0221 -(-5-2*x-5*x^5-2*x^4-x^3-x^2)/(1-x^5) ogf A010128 7.26932 -(2+2*x+50*x^4+3*x^6+8*x^5+8*x^3+3*x^2+2*x^7+2*x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(5*x^4-3*x^3+4*x^2-3*x+5) lgdogf A010128 13.8896 -(x+1)*(5*x^4-3*x^3+4*x^2-3*x+5)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010129 14.0098 -(-5-x-3*x^5-5*x^8-x^7-5*x^4-3*x^3-x^2-x^6)/(1-x^8) ogf A010129 9.65541 -(x^2-x+1)*(5*x^6+6*x^5+2*x^4-x^3+2*x^2+6*x+5)/(x-1)/(x+1)/(x^2+1)/(1+x^4) ogf A010130 24.1153 -(-5-x-x^2-x^3-5*x^4)/(1-x^4) ogf A010130 9.0824 -(1+2*x+3*x^4+x^6+2*x^5+40*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(5*x^4+x^3+x^2+x+5) lgdogf A010130 17.4836 -(5+x+x^2+x^3+5*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010130 7.7705 -585-117*x-585*x^4-117*x^3-117*x^2+(227+22*x-7*x^4+22*x^3+22*x^2)*f(x)+(-22+22*x^4)*f(x)^2 ogf A010131 8.85247 -(1+4*x+3*x^4+x^6+4*x^5+40*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(5*x^4+x^3+2*x^2+x+5) lgdogf A010131 16.6511 -(5+x+2*x^2+x^3+5*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010131 22.5595 -(5+x+5*x^4+x^3+2*x^2)/(-1+x^4) ogf A010131 6.92421 -2625-525*x-2625*x^4-525*x^3-1050*x^2+(1165+128*x+115*x^4+128*x^3+256*x^2)*f(x)+(-128+128*x^4)*f(x)^2 ogf A010132 8.63389 -(1+8*x+3*x^4+x^6+8*x^5+40*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(5*x^2+6*x+5)/(x^2-x+1) lgdogf A010132 15.8942 -(5*x^2+6*x+5)*(x^2-x+1)/(x-1)/(x+1)/(x^2+1) ogf A010132 22.5595 -(5+x+5*x^4+x^3+4*x^2)/(-1+x^4) ogf A010132 8.96596 20+4*x+20*x^4+4*x^3+16*x^2+(31+7*x+39*x^4+7*x^3+28*x^2)*f(x)+(-7+7*x^4)*f(x)^2 ogf A010133 11.2829 -(1+2*x+x^4+2*x^3+18*x^2)/(x-1)/(x+1)/(x^2+x+1)/(3*x^2-2*x+3) lgdogf A010133 24.5806 -(6+2*x+6*x^3+2*x^2)/(x^3-1) ogf A010133 18.112 -2*(x+1)*(3*x^2-2*x+3)/(x-1)/(x^2+x+1) ogf A010133 9.17676 432+144*x+432*x^3+144*x^2+(-150-26*x-6*x^3-26*x^2)*f(x)+(-13*x^3+13)*f(x)^2 ogf A010133 15.2946 {-a(n+4)+a(n+1),a(0)=6,a(1)=2,a(2)=2,a(3)=12} ogf A010134 11.5703 -(-6-x-5*x^5-x^9-x^8-3*x^7-x^4-3*x^3-6*x^10-x^2-x^6)/(1-x^10) ogf A010134 7.12916 -(6+x+x^2+3*x^3+x^4+5*x^5+x^6+x^8+3*x^7+x^9+6*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010135 16.1655 -(-6-x-x^5-2*x^4-2*x^3-2*x^2-6*x^6)/(1-x^6) ogf A010135 5.60577 -(1+4*x+5*x^4+5*x^6+72*x^5+8*x^3+x^10+6*x^2+8*x^7+4*x^9+6*x^8)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1)/(x^2-x+1)/(6*x^4+x^3-4*x^2+x+6) lgdogf A010135 11.2115 -(x^2+1)*(6*x^4+x^3-4*x^2+x+6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010136 6.87677 -(6*x^8+x^7+3*x^6+x^5-5*x^4+x^3+3*x^2+x+6)*(1+x^4)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^2+1)/(x^4-x^2+1) ogf A010136 9.47879 -(6+x+2*x^5+x^9+x^8+2*x^7+x^4+x^3+3*x^10+3*x^2+6*x^6+x^11+6*x^12)/(x^12-1) ogf A010137 8.42584 -(1+10*x+3*x^4+x^6+10*x^5+48*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(6*x^2+7*x+6)/(x^2-x+1) lgdogf A010137 15.8942 -(6*x^2+7*x+6)*(x^2-x+1)/(x-1)/(x+1)/(x^2+1) ogf A010137 22.5595 -(6+x+6*x^4+x^3+5*x^2)/(-1+x^4) ogf A010137 6.72447 8550+1425*x+8550*x^4+1425*x^3+7125*x^2+(3573+833*x+6423*x^4+833*x^3+4165*x^2)*f(x)+(-833+833*x^4)*f(x)^2 ogf A010138 16.1655 -(7+4*x+4*x^5+x^4+2*x^3+x^2+7*x^6)/(-1+x^6) ogf A010138 10.5321 -(7+4*x+x^2+2*x^3+x^4+4*x^5+7*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010138 5.34705 -2*(2+x+10*x^4+10*x^6+42*x^5+2*x^3+2*x^10+3*x^2+2*x^7+x^9+3*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(7*x^6+4*x^5+x^4+2*x^3+x^2+4*x+7) lgdogf A010139 19.0203 -(-7-3*x-7*x^5-3*x^4-x^3-x^2)/(1-x^5) ogf A010139 6.45643 -(3+2*x+70*x^4+3*x^6+12*x^5+12*x^3+3*x^2+2*x^7+3*x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(7*x^4-4*x^3+5*x^2-4*x+7) lgdogf A010139 12.567 -(x+1)*(7*x^4-4*x^3+5*x^2-4*x+7)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010140 16.1655 -(7+2*x+2*x^5+x^4+6*x^3+x^2+7*x^6)/(-1+x^6) ogf A010140 10.5321 -(7+2*x+x^2+6*x^3+x^4+2*x^5+7*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010140 5.51679 -2*(1+x+5*x^4+5*x^6+42*x^5+2*x^3+x^10+9*x^2+2*x^7+x^9+9*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(7*x^6+2*x^5+x^4+6*x^3+x^2+2*x+7) lgdogf A010141 19.9813 -(-7-2*x-2*x^2-2*x^3-7*x^4)/(1-x^4) ogf A010141 15.2032 -(7+2*x+2*x^2+2*x^3+7*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010141 8.63389 -175-50*x-175*x^4-50*x^3-50*x^2+(53+8*x+3*x^4+8*x^3+8*x^2)*f(x)+(-4+4*x^4)*f(x)^2 ogf A010141 8.22759 -2*(1+2*x+3*x^4+x^6+2*x^5+28*x^3+3*x^2)/(x-1)/(x+1)/(7*x^4+2*x^3+2*x^2+2*x+7)/(x^2+1) lgdogf A010142 17.8235 -(-7-x-x^5-x^4-4*x^3-x^2-7*x^6)/(1-x^6) ogf A010142 5.51679 -(1+2*x+5*x^4+5*x^6+84*x^5+4*x^3+x^10+12*x^2+4*x^7+2*x^9+12*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(7*x^6+x^5+x^4+4*x^3+x^2+x+7) lgdogf A010142 11.2115 -(7+x+x^2+4*x^3+x^4+x^5+7*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010143 16.8581 -(-x-x^2-7-x^4-x^5-x^6-x^3-7*x^7)/(-x^7+1) ogf A010143 9.31633 -(x+1)*(7*x^6-6*x^5+7*x^4-6*x^3+7*x^2-6*x+7)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) ogf A010144 16.1655 -(-7-x-x^5-2*x^4-7*x^3-2*x^2-7*x^6)/(1-x^6) ogf A010144 5.34705 -(1+4*x+5*x^4+5*x^6+84*x^5+8*x^3+x^10+21*x^2+8*x^7+4*x^9+21*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(7*x^6+x^5+2*x^4+7*x^3+2*x^2+x+7) lgdogf A010144 10.5321 -(7+x+2*x^2+7*x^3+2*x^4+x^5+7*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010145 9.66832 -(-7-x-2*x^5-4*x^9-3*x^8-x^7-x^4-3*x^3-x^10-4*x^2-2*x^6-7*x^11)/(-x^11+1) ogf A010146 8.42584 -(1+12*x+3*x^4+x^6+12*x^5+56*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(x^2-x+1)/(7*x^2+8*x+7) lgdogf A010146 22.5595 -(7+x+7*x^4+x^3+6*x^2)/(-1+x^4) ogf A010146 15.8942 -(x^2-x+1)*(7*x^2+8*x+7)/(x-1)/(x+1)/(x^2+1) ogf A010146 6.53593 13167+1881*x+13167*x^4+1881*x^3+11286*x^2+(2599+640*x+6361*x^4+640*x^3+3840*x^2)*f(x)+(-640+640*x^4)*f(x)^2 ogf A010147 6.8523 -(8+5*x+2*x^2+x^3+x^4+7*x^5+x^6+2*x^8+x^7+5*x^9+8*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010147 10.8583 -(8+5*x+7*x^5+5*x^9+2*x^8+x^7+x^4+x^3+8*x^10+2*x^2+x^6)/(-1+x^10) ogf A010148 9.65541 -(8+3*x+3*x^2+x^3+4*x^4+x^5+3*x^6+8*x^8+3*x^7)/(x-1)/(x+1)/(x^2+1)/(1+x^4) ogf A010148 12.9909 -(8+3*x+x^5+8*x^8+3*x^7+4*x^4+x^3+3*x^2+3*x^6)/(-1+x^8) ogf A010149 16.1655 -(8+2*x+2*x^5+x^4+2*x^3+x^2+8*x^6)/(-1+x^6) ogf A010149 10.5321 -(8+2*x+x^2+2*x^3+x^4+2*x^5+8*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010149 5.51679 -2*(1+x+5*x^4+5*x^6+48*x^5+2*x^3+x^10+3*x^2+2*x^7+x^9+3*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(8*x^6+2*x^5+x^4+2*x^3+x^2+2*x+8) lgdogf A010150 12.9909 -(8+2*x+x^5+8*x^8+2*x^7+7*x^4+x^3+2*x^2+2*x^6)/(-1+x^8) ogf A010150 11.1641 -(x^2+x+1)*(8*x^6-6*x^5+7*x^3-6*x+8)/(x-1)/(x+1)/(x^2+1)/(1+x^4) ogf A010151 15.3922 -(-8-x-x^5-8*x^7-5*x^4-5*x^3-x^2-x^6)/(-x^7+1) ogf A010151 9.31633 -(x+1)*(8*x^6-7*x^5+8*x^4-3*x^3+8*x^2-7*x+8)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) ogf A010152 21.3258 -(-8-x^2-x^3-x^4-x-8*x^5)/(1-x^5) ogf A010152 6.70239 -(1+2*x+80*x^4+3*x^6+4*x^5+4*x^3+3*x^2+2*x^7+x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(8*x^4-7*x^3+8*x^2-7*x+8) lgdogf A010152 12.567 -(x+1)*(8*x^4-7*x^3+8*x^2-7*x+8)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010153 24.1153 -(-8-x-x^2-x^3-8*x^4)/(1-x^4) ogf A010153 9.0824 -(1+2*x+3*x^4+x^6+2*x^5+64*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(8*x^4+x^3+x^2+x+8) lgdogf A010153 17.4836 -(8+x+x^2+x^3+8*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010153 7.60158 -1064-133*x-1064*x^4-133*x^3-133*x^2+(269+17*x+3*x^4+17*x^3+17*x^2)*f(x)+(-17+17*x^4)*f(x)^2 ogf A010154 9.47879 -(8+x+5*x^5+x^9+x^8+5*x^7+x^4+x^3+2*x^10+2*x^2+4*x^6+x^11+8*x^12)/(x^12-1) ogf A010155 5.51679 -(1+6*x+5*x^4+5*x^6+96*x^5+12*x^3+x^10+6*x^2+12*x^7+6*x^9+6*x^8)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1)/(x^2-x+1)/(8*x^4+x^3-5*x^2+x+8) lgdogf A010155 16.1655 -(8+x+x^5+3*x^4+2*x^3+3*x^2+8*x^6)/(-1+x^6) ogf A010155 11.2115 -(x^2+1)*(8*x^4+x^3-5*x^2+x+8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010156 8.85247 -(1+8*x+3*x^4+x^6+8*x^5+64*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(8*x^4+x^3+4*x^2+x+8) lgdogf A010156 16.6511 -(8+x+4*x^2+x^3+8*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010156 22.5595 -(8+x+8*x^4+x^3+4*x^2)/(-1+x^4) ogf A010156 6.92421 -7128-891*x-7128*x^4-891*x^3-3564*x^2+(2171+160*x+389*x^4+160*x^3+640*x^2)*f(x)+(-160+160*x^4)*f(x)^2 ogf A010157 8.42584 -(1+14*x+3*x^4+x^6+14*x^5+64*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(x^2-x+1)/(8*x^2+9*x+8) lgdogf A010157 22.5595 -(8+x+8*x^4+x^3+7*x^2)/(-1+x^4) ogf A010157 15.8942 -(x^2-x+1)*(8*x^2+9*x+8)/(x-1)/(x+1)/(x^2+1) ogf A010157 6.92421 7000+875*x+7000*x^4+875*x^3+6125*x^2+(781+207*x+2531*x^4+207*x^3+1449*x^2)*f(x)+(-207+207*x^4)*f(x)^2 ogf A010158 19.0203 -(-9-4*x-9*x^5-4*x^4-x^3-x^2)/(1-x^5) ogf A010158 6.45643 -(4+2*x+90*x^4+3*x^6+16*x^5+16*x^3+3*x^2+2*x^7+4*x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(9*x^4-5*x^3+6*x^2-5*x+9) lgdogf A010158 12.567 -(x+1)*(9*x^4-5*x^3+6*x^2-5*x+9)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010159 11.5703 -(9+3*x+8*x^5+3*x^9+x^8+x^7+x^4+x^3+9*x^10+x^2+x^6)/(-1+x^10) ogf A010159 7.12916 -(9+3*x+x^2+x^3+x^4+8*x^5+x^6+x^8+x^7+3*x^9+9*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010160 5.30623 -(2+2*x+10*x^4+10*x^6+108*x^5+4*x^3+2*x^10+3*x^2+4*x^7+2*x^9+3*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(9*x^6+2*x^5+x^4+x^3+x^2+2*x+9) lgdogf A010160 16.954 -(9+2*x+2*x^5+x^4+x^3+x^2+9*x^6)/(-1+x^6) ogf A010160 10.8612 -(9+2*x+x^2+x^3+x^4+2*x^5+9*x^6)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1) ogf A010161 17.1647 -(-9-2*x-9*x^5-2*x^4-3*x^3-3*x^2)/(1-x^5) ogf A010161 6.51621 -(2+6*x+90*x^4+9*x^6+8*x^5+8*x^3+9*x^2+6*x^7+2*x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(9*x^4-7*x^3+10*x^2-7*x+9) lgdogf A010161 12.3465 -(x+1)*(9*x^4-7*x^3+10*x^2-7*x+9)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010162 14.5816 -(9+x+5*x^5+9*x^8+x^7+x^4+5*x^3+x^2+x^6)/(-1+x^8) ogf A010162 10.5074 -(9+x+x^2+5*x^3+x^4+5*x^5+x^6+9*x^8+x^7)/(x-1)/(x+1)/(x^2+1)/(1+x^4) ogf A010163 14.0098 -(9+x+2*x^5+9*x^8+x^7+4*x^4+2*x^3+x^2+x^6)/(-1+x^8) ogf A010163 10.2071 -(9+x+x^2+2*x^3+4*x^4+2*x^5+x^6+9*x^8+x^7)/(x-1)/(x+1)/(x^2+1)/(1+x^4) ogf A010164 11.5703 -(-9-x-6*x^5-x^9-x^8-x^7-4*x^4-x^3-9*x^10-x^2-4*x^6)/(1-x^10) ogf A010164 7.12916 -(9+x+x^2+x^3+4*x^4+6*x^5+4*x^6+x^8+x^7+x^9+9*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010166 8.85247 -(1+4*x+3*x^4+x^6+4*x^5+72*x^3+3*x^2)/(x-1)/(x+1)/(9*x^4+x^3+2*x^2+x+9)/(x^2+1) lgdogf A010166 16.6511 -(9+x+2*x^2+x^3+9*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010166 22.5595 -(9+x+9*x^4+x^3+2*x^2)/(-1+x^4) ogf A010166 5.97731 -196911-21879*x-196911*x^4-21879*x^3-43758*x^2+(44919+2560*x+1161*x^4+2560*x^3+5120*x^2)*f(x)+(-2560+2560*x^4)*f(x)^2 ogf A010167 8.85247 -(1+6*x+3*x^4+x^6+6*x^5+72*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(9*x^4+x^3+3*x^2+x+9) lgdogf A010167 16.6511 -(9+x+3*x^2+x^3+9*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010167 22.5595 -(9+x+9*x^4+x^3+3*x^2)/(-1+x^4) ogf A010167 5.92665 338238+37582*x+338238*x^4+37582*x^3+112746*x^2+(-80107-4725*x-4943*x^4-4725*x^3-14175*x^2)*f(x)+(4725-4725*x^4)*f(x)^2 ogf A010168 10.8583 -(-9-x-x^5-5*x^9-x^8-x^7-x^4-x^3-x^10-5*x^2-x^6-9*x^11)/(-x^11+1) ogf A010169 8.32554 -(1+16*x+3*x^4+x^6+16*x^5+72*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(9*x^2+10*x+9)/(x^2-x+1) lgdogf A010169 15.541 -(9*x^2+10*x+9)*(x^2-x+1)/(x-1)/(x+1)/(x^2+1) ogf A010169 22.5595 -(9+x+9*x^4+x^3+8*x^2)/(-1+x^4) ogf A010169 6.53593 16254+1806*x+16254*x^4+1806*x^3+14448*x^2+(1119+325*x+4731*x^4+325*x^3+2600*x^2)*f(x)+(-325+325*x^4)*f(x)^2 ogf A010170 18.4571 -(1+36*x+x^2)/(x-1)/(x+1)/(9*x^2+x+9) lgdogf A010170 32.5197 -(9+x+9*x^2)/(-1+x^2) ogf A010170 28.4547 -(9+x+9*x^2)/(x-1)/(x+1) ogf A010170 29.6919 -9-x-9*x^2+(1-x^2)*f(x) ogf A010170 17.9714 {-a(n+3)+a(n+1),a(0)=9,a(1)=1,a(2)=18} ogf A010171 9.28667 -(10+6*x+x^5+2*x^9+x^8+x^7+x^4+2*x^3+x^10+x^2+9*x^6+6*x^11+10*x^12)/(x^12-1) ogf A010172 12.1102 -(10+3*x+x^5+10*x^9+3*x^8+2*x^7+x^4+x^3+2*x^2+x^6)/(-1+x^9) ogf A010172 8.30814 -(x+1)*(10*x^8-7*x^7+9*x^6-8*x^5+9*x^4-8*x^3+9*x^2-7*x+10)/(x-1)/(1+x^2+x)/(x^6+x^3+1) ogf A010173 15.543 -(10+2*x+2*x^5+x^4+9*x^3+x^2+10*x^6)/(-1+x^6) ogf A010173 10.2858 -(10+2*x+x^2+9*x^3+x^4+2*x^5+10*x^6)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010174 9.8339 -(10+2*x+x^2+x^3+4*x^4+x^5+x^6+10*x^8+2*x^7)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A010174 13.3593 -(10+2*x+x^5+10*x^8+2*x^7+4*x^4+x^3+x^2+x^6)/(-1+x^8) ogf A010175 6.87677 -(-10-2*x-4*x^5-3*x^13-x^9-6*x^8-6*x^7-2*x^4-x^3-4*x^10-3*x^2-x^6-2*x^11-x^12-2*x^14-10*x^15)/(1-x^15) ogf A010176 5.42196 -(1+2*x+5*x^4+5*x^6+120*x^5+4*x^3+x^10+18*x^2+4*x^7+2*x^9+18*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(10*x^6+x^5+x^4+6*x^3+x^2+x+10) lgdogf A010176 10.9286 -(10+x+x^2+6*x^3+x^4+x^5+10*x^6)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010176 17.0594 -(10+x+x^5+x^4+6*x^3+x^2+10*x^6)/(-1+x^6) ogf A010177 17.0594 -(-10-x-x^5-x^4-2*x^3-x^2-10*x^6)/(1-x^6) ogf A010177 5.50735 -(1+2*x+5*x^4+5*x^6+120*x^5+4*x^3+x^10+6*x^2+4*x^7+2*x^9+6*x^8)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1)/(x^2-x+1)/(10*x^4+x^3-9*x^2+x+10) lgdogf A010177 10.9286 -(x^2+1)*(10*x^4+x^3-9*x^2+x+10)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010178 12.9909 -(-10-x-2*x^5-10*x^9-x^8-x^7-2*x^4-x^3-x^2-x^6)/(1-x^9) ogf A010178 9.40132 -(x+1)*(x^2-x+1)*(10*x^6+x^5+x^4-9*x^3+x^2+x+10)/(x-1)/(1+x^2+x)/(x^6+x^3+1) ogf A010179 5.16795 -(1+4*x+5*x^4+5*x^6+120*x^5+8*x^3+x^10+30*x^2+8*x^7+4*x^9+30*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(10*x^6+x^5+2*x^4+10*x^3+2*x^2+x+10) lgdogf A010179 10.0363 -(10+x+2*x^2+10*x^3+2*x^4+x^5+10*x^6)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010179 15.0545 -(10+x+x^5+2*x^4+10*x^3+2*x^2+10*x^6)/(-1+x^6) ogf A010180 11.6417 -(-10-x-x^5-x^9-2*x^8-x^7-x^4-x^3-10*x^10-2*x^2-x^6)/(1-x^10) ogf A010180 7.17317 -(10+x+2*x^2+x^3+x^4+x^5+x^6+2*x^8+x^7+x^9+10*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010181 6.76327 -(10+x+3*x^2+2*x^3+x^4+4*x^5+x^6+3*x^8+2*x^7+x^9+10*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010181 10.5992 -(10+x+4*x^5+x^9+3*x^8+2*x^7+x^4+2*x^3+10*x^10+3*x^2+x^6)/(-1+x^10) ogf A010182 5.42196 -(1+8*x+5*x^4+5*x^6+120*x^5+16*x^3+x^10+6*x^2+16*x^7+8*x^9+6*x^8)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1)/(x^2-x+1)/(10*x^4+x^3-6*x^2+x+10) lgdogf A010182 15.543 -(10+x+x^5+4*x^4+2*x^3+4*x^2+10*x^6)/(-1+x^6) ogf A010182 10.9286 -(x^2+1)*(10*x^4+x^3-6*x^2+x+10)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010183 9.83428 -(10+x+10*x^5+x^9+6*x^8+3*x^7+2*x^4+3*x^3+10*x^10+6*x^2+2*x^6)/(-1+x^10) ogf A010183 6.43699 -(10+x+6*x^2+3*x^3+2*x^4+10*x^5+2*x^6+6*x^8+3*x^7+x^9+10*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010184 8.00632 -(1+18*x+3*x^4+x^6+18*x^5+80*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(10*x^2+11*x+10)/(x^2-x+1) lgdogf A010184 14.6499 -(10*x^2+11*x+10)*(x^2-x+1)/(x-1)/(x+1)/(x^2+1) ogf A010184 20.865 -(10+x+10*x^4+x^3+9*x^2)/(-1+x^4) ogf A010184 6.81727 8370+837*x+8370*x^4+837*x^3+7533*x^2+(373+121*x+2047*x^4+121*x^3+1089*x^2)*f(x)+(-121+121*x^4)*f(x)^2 ogf A010186 18.1556 -(-11-5*x-11*x^5-5*x^4-x^3-x^2)/(1-x^5) ogf A010186 6.32204 -(5+2*x+110*x^4+3*x^6+20*x^5+20*x^3+3*x^2+2*x^7+5*x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(11*x^4-6*x^3+7*x^2-6*x+11) lgdogf A010186 12.2081 -(x+1)*(11*x^4-6*x^3+7*x^2-6*x+11)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010187 18.6093 -(-11-4*x-11*x^4-4*x^3-2*x^2)/(1-x^4) ogf A010187 14.3447 -(11+4*x+2*x^2+4*x^3+11*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010187 7.24783 -2728-992*x-2728*x^4-992*x^3-496*x^2+(523+100*x+27*x^4+100*x^3+50*x^2)*f(x)+(-25+25*x^4)*f(x)^2 ogf A010187 8.29571 -4*(1+x+3*x^4+x^6+x^5+22*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(11*x^4+4*x^3+2*x^2+4*x+11) lgdogf A010188 8.03946 -(-11-3*x-7*x^5-2*x^9-2*x^8-7*x^7-2*x^4-2*x^3-x^10-x^2-11*x^6-3*x^11-11*x^12)/(-x^12+1) ogf A010189 18.6093 -(11+3*x+11*x^4+3*x^3+5*x^2)/(-1+x^4) ogf A010189 14.3447 -(11+3*x+5*x^2+3*x^3+11*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010189 7.73645 -(3+10*x+9*x^4+3*x^6+10*x^5+88*x^3+9*x^2)/(x-1)/(x+1)/(x^2+1)/(11*x^4+3*x^3+5*x^2+3*x+11) lgdogf A010189 6.09331 -79618-21714*x-79618*x^4-21714*x^3-36190*x^2+(16775+2601*x+2299*x^4+2601*x^3+4335*x^2)*f(x)+(-867+867*x^4)*f(x)^2 ogf A010190 10.5992 -(11+2*x+6*x^5+2*x^9+x^8+3*x^7+x^4+3*x^3+11*x^10+x^2+x^6)/(-1+x^10) ogf A010190 6.76327 -(11+2*x+x^2+3*x^3+x^4+6*x^5+x^6+x^8+3*x^7+2*x^9+11*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010191 13.8501 -(-11-2*x-2*x^5-4*x^4-11*x^3-4*x^2-11*x^6)/(1-x^6) ogf A010191 9.48638 -(11+2*x+4*x^2+11*x^3+4*x^4+2*x^5+11*x^6)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010193 7.97248 -(-11-x-3*x^5-x^13-3*x^9-x^8-10*x^7-x^4-2*x^3-x^10-x^2-x^6-2*x^11-x^12-11*x^14)/(1-x^14) ogf A010194 15.0647 -(-11-x-x^2-x^3-x^5-x^6-x^7-x^4-11*x^8)/(1-x^8) ogf A010194 10.7279 -(11+x+x^2+x^3+x^5+x^6+x^7+x^4+11*x^8)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A010195 22.2111 -(-11-x-x^2-x^3-11*x^4)/(1-x^4) ogf A010195 8.71575 -(1+2*x+3*x^4+x^6+2*x^5+88*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(11*x^4+x^3+x^2+x+11) lgdogf A010195 16.3939 -(11+x+x^2+x^3+11*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010195 7.48417 -2750-250*x-2750*x^4-250*x^3-250*x^2+(503+23*x+3*x^4+23*x^3+23*x^2)*f(x)+(-23+23*x^4)*f(x)^2 ogf A010196 12.1102 -(-11-x-x^5-11*x^9-x^8-2*x^7-x^4-2*x^3-2*x^2-2*x^6)/(1-x^9) ogf A010196 7.6828 -(x+1)*(11*x^8-10*x^7+12*x^6-10*x^5+11*x^4-10*x^3+12*x^2-10*x+11)/(x-1)/(1+x^2+x)/(x^6+x^3+1) ogf A010197 8.50054 -(1+4*x+3*x^4+x^6+4*x^5+88*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(11*x^4+x^3+2*x^2+x+11) lgdogf A010197 20.865 -(11+x+11*x^4+x^3+2*x^2)/(-1+x^4) ogf A010197 15.6487 -(11+x+2*x^2+x^3+11*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010197 5.93572 -187187-17017*x-187187*x^4-17017*x^3-34034*x^2+(34617+1600*x+583*x^4+1600*x^3+3200*x^2)*f(x)+(-1600+1600*x^4)*f(x)^2 ogf A010199 8.50054 -(1+8*x+3*x^4+x^6+8*x^5+88*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(11*x^4+x^3+4*x^2+x+11) lgdogf A010199 20.865 -(11+x+11*x^4+x^3+4*x^2)/(-1+x^4) ogf A010199 15.6487 -(11+x+4*x^2+x^3+11*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010199 6.55756 -12166-1106*x-12166*x^4-1106*x^3-4424*x^2+(2393+117*x+181*x^4+117*x^3+468*x^2)*f(x)+(-117+117*x^4)*f(x)^2 ogf A010200 8.29571 -(1+12*x+3*x^4+x^6+12*x^5+88*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(11*x^4+x^3+6*x^2+x+11) lgdogf A010200 20.865 -(11+x+11*x^4+x^3+6*x^2)/(-1+x^4) ogf A010200 15.6487 -(11+x+6*x^2+x^3+11*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010200 5.73787 -268125-24375*x-268125*x^4-24375*x^3-146250*x^2+(63799+3584*x+15049*x^4+3584*x^3+21504*x^2)*f(x)+(-3584+3584*x^4)*f(x)^2 ogf A010201 7.98957 -(1+20*x+3*x^4+x^6+20*x^5+88*x^3+3*x^2)/(x-1)/(x+1)/(11*x^2+12*x+11)/(x^2-x+1)/(x^2+1) lgdogf A010201 14.6192 -(11*x^2+12*x+11)*(x^2-x+1)/(x-1)/(x+1)/(x^2+1) ogf A010201 20.2089 -(11+x+11*x^4+x^3+10*x^2)/(-1+x^4) ogf A010201 6.4821 23375+2125*x+23375*x^4+2125*x^3+21250*x^2+(691+256*x+4941*x^4+256*x^3+2560*x^2)*f(x)+(-256+256*x^4)*f(x)^2 ogf A010202 11.3413 -(-12-4*x-3*x^5-12*x^9-4*x^8-x^7-3*x^4-5*x^3-x^2-5*x^6)/(1-x^9) ogf A010202 8.30814 -(x+1)*(12*x^8-8*x^7+9*x^6-4*x^5+7*x^4-4*x^3+9*x^2-8*x+12)/(x-1)/(1+x^2+x)/(x^6+x^3+1) ogf A010204 12.4218 -(12+2*x+2*x^5+12*x^8+2*x^7+2*x^4+2*x^3+x^2+x^6)/(-1+x^8) ogf A010204 9.31633 -(12+2*x+x^2+2*x^3+2*x^4+2*x^5+x^6+12*x^8+2*x^7)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A010205 10.002 -(12+2*x+2*x^5+2*x^9+2*x^8+3*x^7+x^4+3*x^3+12*x^10+2*x^2+x^6)/(-1+x^10) ogf A010205 6.63686 -(x^2+1)*(12*x^8+2*x^7-10*x^6+x^5+11*x^4+x^3-10*x^2+2*x+12)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010207 12.7508 -(12+x+3*x^5+12*x^8+x^7+12*x^4+3*x^3+x^2+x^6)/(-1+x^8) ogf A010207 8.6068 -(x^2-x+1)*(12*x^6+13*x^5+2*x^4-8*x^3+2*x^2+13*x+12)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A010208 12.0363 -(12+x+3*x^5+x^9+x^8+x^7+x^4+x^3+12*x^10+x^2+x^6)/(-1+x^10) ogf A010208 7.32107 -(12+x+x^2+x^3+x^4+3*x^5+x^6+x^8+x^7+x^9+12*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010209 14.4498 -(-12-x-x^5-12*x^8-x^7-5*x^4-x^3-x^2-x^6)/(1-x^8) ogf A010209 10.4124 -(12+x+x^2+x^3+5*x^4+x^5+x^6+12*x^8+x^7)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A010210 6.76327 -(12+x+2*x^2+4*x^3+x^4+2*x^5+x^6+2*x^8+4*x^7+x^9+12*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010210 10.5992 -(12+x+2*x^5+x^9+2*x^8+4*x^7+x^4+4*x^3+12*x^10+2*x^2+x^6)/(-1+x^10) ogf A010211 10.4128 -(-12-x-12*x^5-x^9-2*x^8-x^7-2*x^4-x^3-12*x^10-2*x^2-2*x^6)/(1-x^10) ogf A010211 6.37899 -(1+x^2+x)*(12*x^8-11*x^7+x^6+11*x^5-10*x^4+11*x^3+x^2-11*x+12)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010213 5.33919 -(1+10*x+5*x^4+5*x^6+144*x^5+20*x^3+x^10+6*x^2+20*x^7+10*x^9+6*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^2+1)/(12*x^4+x^3-7*x^2+x+12) lgdogf A010213 15.543 -(12+x+x^5+5*x^4+2*x^3+5*x^2+12*x^6)/(-1+x^6) ogf A010213 10.9286 -(x^2+1)*(12*x^4+x^3-7*x^2+x+12)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010215 7.98957 -(1+22*x+3*x^4+x^6+22*x^5+96*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(12*x^2+13*x+12)/(x^2-x+1) lgdogf A010215 20.2089 -(12+x+12*x^4+x^3+11*x^2)/(-1+x^4) ogf A010215 14.6192 -(x^2-x+1)*(12*x^2+13*x+12)/(x-1)/(x+1)/(x^2+1) ogf A010215 5.72586 688644+57387*x+688644*x^4+57387*x^3+631257*x^2+(13593+5915*x+128367*x^4+5915*x^3+65065*x^2)*f(x)+(-5915+5915*x^4)*f(x)^2 ogf A010217 18.1556 -(-13-6*x-13*x^5-6*x^4-x^3-x^2)/(1-x^5) ogf A010217 6.32204 -(6+2*x+130*x^4+3*x^6+24*x^5+24*x^3+3*x^2+2*x^7+6*x^8)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(13*x^4-7*x^3+8*x^2-7*x+13) lgdogf A010217 12.2081 -(x+1)*(13*x^4-7*x^3+8*x^2-7*x+13)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010218 18.6093 -(13+5*x+13*x^4+5*x^3+4*x^2)/(-1+x^4) ogf A010218 14.3447 -(13+5*x+4*x^2+5*x^3+13*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010218 7.65049 -(5+8*x+15*x^4+5*x^6+8*x^5+104*x^3+15*x^2)/(x-1)/(x+1)/(x^2+1)/(13*x^4+5*x^3+4*x^2+5*x+13) lgdogf A010218 6.55756 -17550-6750*x-17550*x^4-6750*x^3-5400*x^2+(2923+605*x+223*x^4+605*x^3+484*x^2)*f(x)+(-121+121*x^4)*f(x)^2 ogf A010219 14.8816 -(-13-4*x-4*x^5-2*x^4-x^3-2*x^2-13*x^6)/(1-x^6) ogf A010219 9.99191 -(13+4*x+2*x^2+x^3+2*x^4+4*x^5+13*x^6)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010220 19.6727 -(-13-3*x-13*x^4-3*x^3-x^2)/(1-x^4) ogf A010220 14.9683 -(13+3*x+x^2+3*x^3+13*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010220 8.00632 -(3+2*x+9*x^4+3*x^6+2*x^5+104*x^3+9*x^2)/(x-1)/(x+1)/(x^2+1)/(13*x^4+3*x^3+x^2+3*x+13) lgdogf A010220 5.93572 -304304-70224*x-304304*x^4-70224*x^3-23408*x^2+(47783+5625*x+967*x^4+5625*x^3+1875*x^2)*f(x)+(-1875+1875*x^4)*f(x)^2 ogf A010221 11.6072 -(-13-3*x-2*x^5-13*x^8-3*x^7-8*x^4-2*x^3-3*x^2-3*x^6)/(1-x^8) ogf A010221 8.85051 -(13+3*x+3*x^2+2*x^3+8*x^4+2*x^5+3*x^6+13*x^8+3*x^7)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A010222 15.0545 -(13+2*x+2*x^5+x^4+12*x^3+x^2+13*x^6)/(-1+x^6) ogf A010222 10.0363 -(13+2*x+x^2+12*x^3+x^4+2*x^5+13*x^6)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010222 5.2863 -2*(1+x+5*x^4+5*x^6+78*x^5+2*x^3+x^10+18*x^2+2*x^7+x^9+18*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(13*x^6+2*x^5+x^4+12*x^3+x^2+2*x+13) lgdogf A010223 7.62585 -(13+2*x+3*x^5+2*x^13+3*x^9+5*x^8+13*x^7+x^4+x^3+x^10+x^2+5*x^6+x^11+x^12+13*x^14)/(-1+x^14) ogf A010225 5.42196 -(1+2*x+5*x^4+5*x^6+156*x^5+4*x^3+x^10+24*x^2+4*x^7+2*x^9+24*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(13*x^6+x^5+x^4+8*x^3+x^2+x+13) lgdogf A010225 10.9286 -(13+x+x^2+8*x^3+x^4+x^5+13*x^6)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010225 17.0594 -(13+x+x^5+x^4+8*x^3+x^2+13*x^6)/(-1+x^6) ogf A010226 9.28667 -(13+x+x^5+3*x^9+2*x^8+x^7+2*x^4+3*x^3+x^10+x^2+2*x^6+x^11+13*x^12)/(x^12-1) ogf A010227 20.2305 -(-13-x^2-x^3-x^4-x-13*x^5)/(1-x^5) ogf A010227 11.6077 -(x+1)*(13*x^4-12*x^3+13*x^2-12*x+13)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010227 6.37899 -(x^4+6*x^3+16*x^2+6*x+1)*(x^4-4*x^3+11*x^2-4*x+1)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(13*x^4-12*x^3+13*x^2-12*x+13) lgdogf A010228 11.2721 -(-13-x-4*x^5-x^9-x^8-x^7-3*x^4-x^3-13*x^10-x^2-3*x^6)/(1-x^10) ogf A010228 7.03113 -(13+x+x^2+x^3+3*x^4+4*x^5+3*x^6+x^8+x^7+x^9+13*x^10)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010229 15.0545 -(-13-x-x^5-2*x^4-13*x^3-2*x^2-13*x^6)/(1-x^6) ogf A010229 5.16795 -(1+4*x+5*x^4+5*x^6+156*x^5+8*x^3+x^10+39*x^2+8*x^7+4*x^9+39*x^8)/(x-1)/(x+1)/(x^2+x+1)/(x^2-x+1)/(13*x^6+x^5+2*x^4+13*x^3+2*x^2+x+13) lgdogf A010229 10.0363 -(13+x+2*x^2+13*x^3+2*x^4+x^5+13*x^6)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010230 12.4218 -(-13-x-2*x^5-13*x^8-x^7-6*x^4-2*x^3-2*x^2-2*x^6)/(1-x^8) ogf A010230 9.31633 -(13+x+2*x^2+2*x^3+6*x^4+2*x^5+2*x^6+13*x^8+x^7)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A010231 8.39688 -(1+4*x+3*x^4+x^6+4*x^5+104*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(13*x^4+x^3+2*x^2+x+13) lgdogf A010231 20.865 -(13+x+13*x^4+x^3+2*x^2)/(-1+x^4) ogf A010231 15.6487 -(13+x+2*x^2+x^3+13*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010231 6.62061 -21125-1625*x-21125*x^4-1625*x^3-3250*x^2+(3289+128*x+39*x^4+128*x^3+256*x^2)*f(x)+(-128+128*x^4)*f(x)^2 ogf A010232 8.06242 -(-13-x-x^5-x^13-x^9-2*x^8-2*x^7-x^4-x^3-x^10-3*x^2-2*x^6-x^11-3*x^12-13*x^14)/(1-x^14) ogf A010234 8.19695 -(1+10*x+3*x^4+x^6+10*x^5+104*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(13*x^4+x^3+5*x^2+x+13) lgdogf A010234 20.865 -(13+x+13*x^4+x^3+5*x^2)/(-1+x^4) ogf A010234 15.6487 -(13+x+5*x^2+x^3+13*x^4)/(x-1)/(x+1)/(x^2+1) ogf A010234 5.88499 -215644-16588*x-215644*x^4-16588*x^3-82940*x^2+(36335+1519*x+3159*x^4+1519*x^3+7595*x^2)*f(x)+(-1519+1519*x^4)*f(x)^2 ogf A010235 7.9708 -(13+x+x^5+13*x^13+2*x^9+x^8+3*x^7+2*x^4+3*x^3+3*x^10+8*x^2+3*x^6+8*x^11+x^12)/(-1+x^13) ogf A010236 7.89773 -(1+24*x+3*x^4+x^6+24*x^5+104*x^3+3*x^2)/(x-1)/(x+1)/(x^2+1)/(x^2-x+1)/(13*x^2+14*x+13) lgdogf A010236 14.6192 -(13*x^2+14*x+13)*(x^2-x+1)/(x-1)/(x+1)/(x^2+1) ogf A010236 20.2089 -(13+x+13*x^4+x^3+12*x^2)/(-1+x^4) ogf A010236 6.02722 134550+10350*x+134550*x^4+10350*x^3+124200*x^2+(1753+931*x+22453*x^4+931*x^3+11172*x^2)*f(x)+(-931+931*x^4)*f(x)^2 ogf A010368 8.0086 (1+8*x+252*x^2+952*x^3+1670*x^4+952*x^5+252*x^6+x^8+8*x^7)/(x-1)^8 ogf A010368 4.67759 -(1+8*x+952*x^5+8*x^7+252*x^2+252*x^6+1670*x^4+952*x^3+x^8)/(-28*x^2-1+8*x-x^8-70*x^4+56*x^3-28*x^6+56*x^5+8*x^7) ogf A010368 4.67759 -16*(x+1)*(1+6*x+x^2)*(x^4+28*x^3+70*x^2+28*x+1)/(x-1)/(x^8+8*x^7+252*x^6+952*x^5+1670*x^4+952*x^3+252*x^2+8*x+1) lgdogf A010368 6.95484 {(n+2*n^2)*a(n)+(-4*n^2-8*n-132)*a(n+1)+(2*n^2+7*n+6)*a(n+2),a(0)=1,a(1)=16} ogf A010370 20.2185 hypergeom([-1/2,1/2],[1],16*x) ogf A010370 10.1092 {(-12-16*n^2-32*n)*a(n+1)+(n^2+4*n+4)*a(n+2),a(0)=1,a(1)=-4} ogf A010379 1.02196 -x^2+(2*x-4*x^2)*f(x)+(-1+4*x-4*x^2)*f(x)^2 ogf A010387 2.58973 (x^2+3*x+1)/(x+1)/(x-1)^2 ogf A010387 1.13585 {a(n+4)-a(n+3)-a(n+2)+a(n+1),a(0)=0,a(1)=1,a(2)=4,a(3)=6} ogf A010389 2.3979 (2*x+1)*(x^4-x^3+1)/(x-1)^2 ogf A010410 5.21061 (1+x+2*x^2+3*x^3)/(1+x^2+x)/(x-1)^2 ogf A010410 2.68193 -(2+6*x+3*x^5+7*x^4+8*x^3+16*x^2)/(-1+x)/(1+x^2+x)/(3*x^3+2*x^2+x+1) lgdogf A010410 4.92896 x+3*x^4+2*x^3+x^2+(-1+x-x^4+x^3)*f(x) ogf A010410 2.89478 {(n+1)*a(n)-a(n+3)*n+a(n+1)+a(n+2),a(0)=0,a(1)=1,a(2)=2,a(3)=4} ogf A010442 3.78174 (2*x+1)*(1+x^2+x)*(x^7+x^4+1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x-1)^2 ogf A010461 3.25092 (1+2*x+3*x^2+4*x^3-4*x^6+x^8+x^7+x^9+x^10)/(x^2+1)/(x-1)^2 ogf A010551 4.73074 {(-12-16*n-7*n^2-n^3)*a(n+1)+(-100-82*n-22*n^2-2*n^3)*a(n+2)-8*a(n+3)+(8*n+32)*a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=2} ogf A010555 132.956 1/(1-x) ogf A010671 1.27007 -(-1+x^2+x^4+x+4*x^5+x^3)/(1-2*x-4*x^5+6*x^6) ogf A010673 48.6339 (-1+(1+x^2)^(1/2))/x revogf A010673 60.7924 -2*x/(x-1)/(x+1) lgdogf A010673 69.477 -2/(x-1)/(x+1) ogf A010673 57.2163 2*x+(-1+x^2)*f(x) ogf A010673 88.4252 2*x/(1-x^2) ogf A010673 69.477 arcsinh(1/2*x) revegf A010673 36.0251 {a(n+2)-a(n),a(0)=0,a(1)=2} ogf A010674 41.618 -2*x/(-1+x)/(x+1) lgdogf A010674 50.5362 -3/(x-1)/(x+1) ogf A010674 27.2118 1/2/x*(-3+(9+4*x^2)^(1/2)) revogf A010674 41.618 3*x+(-1+x^2)*f(x) ogf A010674 64.3188 3*x/(1-x^2) ogf A010674 50.5362 arcsinh(1/3*x) revegf A010674 26.2039 {a(n+2)-a(n),a(0)=0,a(1)=3} ogf A010675 35.3753 (-2+(x^2+4)^(1/2))/x revogf A010675 41.618 -2*x/(-1+x)/(x+1) lgdogf A010675 50.5362 -4/(x-1)/(x+1) ogf A010675 41.618 4*x+(-1+x^2)*f(x) ogf A010675 64.3188 4*x/(1-x^2) ogf A010675 50.5362 arcsinh(1/4*x) revegf A010675 26.2039 {a(n+2)-a(n),a(0)=0,a(1)=4} ogf A010676 41.618 -2*x/(-1+x)/(x+1) lgdogf A010676 50.5362 -5/(x-1)/(x+1) ogf A010676 26.2039 1/2/x*(-5+(25+4*x^2)^(1/2)) revogf A010676 41.618 5*x+(-1+x^2)*f(x) ogf A010676 64.3188 5*x/(1-x^2) ogf A010676 50.5362 arcsinh(1/5*x) revegf A010676 26.2039 {a(n+2)-a(n),a(0)=0,a(1)=5} ogf A010677 35.3753 (-3+(9+x^2)^(1/2))/x revogf A010677 41.618 -2*x/(-1+x)/(x+1) lgdogf A010677 50.5362 -6/(x-1)/(x+1) ogf A010677 41.618 6*x+(-1+x^2)*f(x) ogf A010677 64.3188 6*x/(1-x^2) ogf A010677 50.5362 arcsinh(1/6*x) revegf A010677 26.2039 {a(n+2)-a(n),a(0)=0,a(1)=6} ogf A010678 41.618 -2*x/(-1+x)/(x+1) lgdogf A010678 50.5362 -7/(x-1)/(x+1) ogf A010678 26.2039 1/2/x*(-7+(49+4*x^2)^(1/2)) revogf A010678 41.618 7*x+(-1+x^2)*f(x) ogf A010678 64.3188 7*x/(1-x^2) ogf A010678 50.5362 arcsinh(1/7*x) revegf A010678 26.2039 {a(n+2)-a(n),a(0)=0,a(1)=7} ogf A010679 33.6908 (-4+(16+x^2)^(1/2))/x revogf A010679 41.618 -2*x/(-1+x)/(x+1) lgdogf A010679 50.5362 -8/(x-1)/(x+1) ogf A010679 41.618 8*x+(-1+x^2)*f(x) ogf A010679 64.3188 8*x/(1-x^2) ogf A010679 50.5362 arcsinh(1/8*x) revegf A010679 26.2039 {a(n+2)-a(n),a(0)=0,a(1)=8} ogf A010680 41.618 -2*x/(-1+x)/(x+1) lgdogf A010680 50.5362 -9/(x-1)/(x+1) ogf A010680 26.2039 1/2/x*(-9+(81+4*x^2)^(1/2)) revogf A010680 41.618 9*x+(-1+x^2)*f(x) ogf A010680 64.3188 9*x/(1-x^2) ogf A010680 50.5362 arcsinh(1/9*x) revegf A010680 26.2039 {a(n+2)-a(n),a(0)=0,a(1)=9} ogf A010681 32.7192 (-5+(25+x^2)^(1/2))/x revogf A010681 45.8068 -10/(x-1)/(x+1) ogf A010681 42.9439 -2*x/(x-1)/(x+1) lgdogf A010681 38.1724 10*x+(-1+x^2)*f(x) ogf A010681 57.2585 10*x/(1-x^2) ogf A010681 45.8068 arcsinh(1/10*x) revegf A010681 29.874 {-a(n+2),a(0)=0,a(1)=1} ogf_with_Euler_Transform A010681 24.5394 {a(n+2)-a(n),a(0)=0,a(1)=10} ogf A010683 12.6452 -(x-1+(x^2+1-6*x)^(1/2))/(x^2+1-6*x)^(1/2)/x lgdogf A010683 9.93549 -1/2*(2*(4*x^2+1)^(1/2)*x+(4*x^2+1)^(1/2)-1-2*x-4*x^2)/x revogf A010683 9.59288 -1/8*((x^2-6*x+1)^(1/2)*x+(x^2-6*x+1)^(1/2)-1-x^2+2*x)/x^2 ogf A010683 17.3871 1+(-1+2*x-x^2)*f(x)+4*x^2*f(x)^2 ogf A010683 5.29893 {(-2*n-n^2)*a(n)+(21+26*n+7*n^2)*a(n+1)+(-66-44*n-7*n^2)*a(n+2)+(8*n+15+n^2)*a(n+3),a(0)=1,a(1)=2,a(2)=7} ogf A010684 41.618 -(-1-3*x)/(1-x^2) ogf A010684 35.3753 -(3*x+1)/(x-1)/(x+1) ogf A010684 20.2145 -(3+2*x+3*x^2)/(-1+x)/(1+3*x)/(x+1) lgdogf A010684 15.0533 -7-21*x+(-3-30*x-7*x^2)*f(x)+(10-10*x^2)*f(x)^2 ogf A010684 20.2145 1/2/(3+x)*(-1+(1+12*x+4*x^2)^(1/2)) revogf A010684 26.2039 {a(n+2)-a(n),a(0)=1,a(1)=3} ogf A010685 41.618 -(-1-4*x)/(1-x^2) ogf A010685 35.3753 -(1+4*x)/(x-1)/(x+1) ogf A010685 14.4389 -14-56*x+(-3-68*x-14*x^2)*f(x)+(17-17*x^2)*f(x)^2 ogf A010685 20.2145 -2*(2+x+2*x^2)/(-1+x)/(4*x+1)/(x+1) lgdogf A010685 20.2145 1/2/(4+x)*(-1+(1+16*x+4*x^2)^(1/2)) revogf A010685 26.2039 {a(n+2)-a(n),a(0)=1,a(1)=4} ogf A010686 41.618 -(-1-5*x)/(1-x^2) ogf A010686 35.3753 -(1+5*x)/(x-1)/(x+1) ogf A010686 20.2145 -(5+2*x+5*x^2)/(-1+x)/(5*x+1)/(x+1) lgdogf A010686 13.8727 -23-115*x+(-3-130*x-23*x^2)*f(x)+(26-26*x^2)*f(x)^2 ogf A010686 20.2145 1/2/(5+x)*(-1+(1+20*x+4*x^2)^(1/2)) revogf A010686 26.2039 {a(n+2)-a(n),a(0)=1,a(1)=5} ogf A010687 44.8055 -(-1-6*x)/(1-x^2) ogf A010687 38.0847 -(1+6*x)/(x-1)/(x+1) ogf A010687 21.7627 -2*(3+x+3*x^2)/(-1+x)/(6*x+1)/(x+1) lgdogf A010687 14.9352 -34-204*x+(-3-222*x-34*x^2)*f(x)+(37-37*x^2)*f(x)^2 ogf A010687 21.7627 1/2/(6+x)*(-1+(1+24*x+4*x^2)^(1/2)) revogf A010687 28.2109 {a(n+2)-a(n),a(0)=1,a(1)=6} ogf A010688 41.618 -(-1-7*x)/(1-x^2) ogf A010688 35.3753 -(1+7*x)/(x-1)/(x+1) ogf A010688 20.2145 -(7+2*x+7*x^2)/(-1+x)/(7*x+1)/(x+1) lgdogf A010688 20.2145 1/2/(7+x)*(-1+(1+28*x+4*x^2)^(1/2)) revogf A010688 14.4389 47+329*x+(-45+14*x+47*x^2)*f(x)+(-2+2*x^2)*f(x)^2 ogf A010688 26.2039 {a(n+2)-a(n),a(0)=1,a(1)=7} ogf A010689 57.2163 -(-1-8*x)/(1-x^2) ogf A010689 48.6339 -(1+8*x)/(x-1)/(x+1) ogf A010689 28.6082 -2*(4+x+4*x^2)/(x-1)/(8*x+1)/(x+1) lgdogf A010689 27.7908 1/2/(8+x)*(-1+(1+32*x+4*x^2)^(1/2)) revogf A010689 21.1452 31+248*x+(-30+8*x+31*x^2)*f(x)+(-1+x^2)*f(x)^2 ogf A010689 36.0251 {a(n+2)-a(n),a(0)=1,a(1)=8} ogf A010690 41.618 -(-1-9*x)/(1-x^2) ogf A010690 35.3753 -(1+9*x)/(x-1)/(x+1) ogf A010690 20.2145 -(9+2*x+9*x^2)/(-1+x)/(9*x+1)/(x+1) lgdogf A010690 20.2145 1/2/(9+x)*(-1+(1+36*x+4*x^2)^(1/2)) revogf A010690 14.4389 79+711*x+(-77+18*x+79*x^2)*f(x)+(-2+2*x^2)*f(x)^2 ogf A010690 26.2039 {a(n+2)-a(n),a(0)=1,a(1)=9} ogf A010691 38.1724 -(-1-10*x)/(1-x^2) ogf A010691 32.7192 -(1+10*x)/(x-1)/(x+1) ogf A010691 19.6315 -2*(5+x+5*x^2)/(x-1)/(10*x+1)/(x+1) lgdogf A010691 12.7241 -98-980*x+(-3-1010*x-98*x^2)*f(x)+(101-101*x^2)*f(x)^2 ogf A010691 19.6315 -ln(11)+ln(10+x+(1+x^2+20*x)^(1/2)) revegf A010691 19.0862 1/2/(10+x)*(-1+(1+40*x+4*x^2)^(1/2)) revogf A010691 24.5394 {a(n+2)-a(n),a(0)=1,a(1)=10} ogf A010692 103.17 -1/(x-1) lgdogf A010692 58.9544 -10+(1-x)*f(x) ogf A010692 91.7068 -10/(x-1) ogf A010692 51.5851 -ln(10)+ln(10+x) revegf A010692 103.17 10/(1-x) ogf A010692 103.17 x/(10+x) revogf A010692 51.5851 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010692 39.3029 {a(n+1)-a(n),a(0)=10} ogf A010693 33.531 (-1+(1+3*x+x^2)^(1/2))/(3+x) revogf A010693 55.2276 -(-2-3*x)/(1-x^2) ogf A010693 46.9434 -(2+3*x)/(x-1)/(x+1) ogf A010693 27.6138 -(3+4*x+3*x^2)/(x-1)/(3*x+2)/(x+1) lgdogf A010693 22.8992 2+3*x+(7+12*x+x^2)*f(x)+(-4+4*x^2)*f(x)^2 ogf A010693 34.7729 {a(n+2)-a(n),a(0)=2,a(1)=3} ogf A010694 25.2681 (-1+(1+4*x+x^2)^(1/2))/(4+x) revogf A010694 41.618 -(-2-4*x)/(1-x^2) ogf A010694 32.1594 -2*(2*x+1)/(x-1)/(x+1) ogf A010694 21.4396 -2*(x^2+x+1)/(-1+x)/(2*x+1)/(x+1) lgdogf A010694 37.2372 -2-4*x+(1-x^2)*f(x) ogf A010694 26.2039 {a(n+2)-a(n),a(0)=2,a(1)=4} ogf A010695 25.2681 (-1+(1+5*x+x^2)^(1/2))/(5+x) revogf A010695 41.618 -(-2-5*x)/(1-x^2) ogf A010695 35.3753 -(2+5*x)/(x-1)/(x+1) ogf A010695 20.2145 -(5+4*x+5*x^2)/(-1+x)/(5*x+2)/(x+1) lgdogf A010695 15.0533 34+85*x+(-9+20*x+17*x^2)*f(x)+(-4+4*x^2)*f(x)^2 ogf A010695 26.2039 {a(n+2)-a(n),a(0)=2,a(1)=5} ogf A010696 25.2681 (-1+(1+6*x+x^2)^(1/2))/(6+x) revogf A010696 41.618 -(-2-6*x)/(1-x^2) ogf A010696 20.2145 -(3+2*x+3*x^2)/(-1+x)/(1+3*x)/(x+1) lgdogf A010696 15.3806 -14-42*x+(-3-30*x-7*x^2)*f(x)+(5-5*x^2)*f(x)^2 ogf A010696 32.1594 -2*(3*x+1)/(x-1)/(x+1) ogf A010696 26.2039 {a(n+2)-a(n),a(0)=2,a(1)=6} ogf A010697 25.2681 (-1+(1+7*x+x^2)^(1/2))/(7+x) revogf A010697 41.618 -(-2-7*x)/(1-x^2) ogf A010697 35.3753 -(2+7*x)/(x-1)/(x+1) ogf A010697 20.2145 -(7+4*x+7*x^2)/(-1+x)/(7*x+2)/(x+1) lgdogf A010697 14.4389 82+287*x+(-33+28*x+41*x^2)*f(x)+(-4+4*x^2)*f(x)^2 ogf A010697 26.2039 {a(n+2)-a(n),a(0)=2,a(1)=7} ogf A010698 25.2681 (-1+(1+8*x+x^2)^(1/2))/(8+x) revogf A010698 41.618 -(-2-8*x)/(1-x^2) ogf A010698 32.1594 -2*(1+4*x)/(x-1)/(x+1) ogf A010698 20.2145 -2*(2+x+2*x^2)/(-1+x)/(4*x+1)/(x+1) lgdogf A010698 37.2372 2+8*x+(-1+x^2)*f(x) ogf A010698 26.2039 {a(n+2)-a(n),a(0)=2,a(1)=8} ogf A010699 25.2681 (-1+(1+9*x+x^2)^(1/2))/(9+x) revogf A010699 41.618 -(-2-9*x)/(1-x^2) ogf A010699 35.3753 -(2+9*x)/(x-1)/(x+1) ogf A010699 20.2145 -(9+4*x+9*x^2)/(-1+x)/(9*x+2)/(x+1) lgdogf A010699 14.1501 146+657*x+(-65+36*x+73*x^2)*f(x)+(-4+4*x^2)*f(x)^2 ogf A010699 26.2039 {a(n+2)-a(n),a(0)=2,a(1)=9} ogf A010700 22.9034 (-1+(1+10*x+x^2)^(1/2))/(10+x) revogf A010700 38.1724 -(-2-10*x)/(1-x^2) ogf A010700 20.2089 -(5+2*x+5*x^2)/(x-1)/(5*x+1)/(x+1) lgdogf A010700 31.2319 -2*(1+5*x)/(x-1)/(x+1) ogf A010700 19.6315 -ln(12)+ln(10+x+(4+x^2+20*x)^(1/2)) revegf A010700 14.6192 46+230*x+(-21+10*x+23*x^2)*f(x)+(-1+x^2)*f(x)^2 ogf A010700 24.5394 {a(n+2)-a(n),a(0)=2,a(1)=10} ogf A010701 78.6118 -1/(-1+x) lgdogf A010701 54.4236 -3+(1-x)*f(x) ogf A010701 88.4383 -3/(x-1) ogf A010701 50.5362 -ln(3)+ln(3+x) revegf A010701 101.072 3/(1-x) ogf A010701 101.072 x/(3+x) revogf A010701 44.2192 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010701 35.3753 {a(n+1)-a(n),a(0)=3} ogf A010702 41.618 -(-3-4*x)/(1-x^2) ogf A010702 35.3753 -(3+4*x)/(x-1)/(x+1) ogf A010702 19.1218 -2*(2+3*x+2*x^2)/(-1+x)/(4*x+3)/(x+1) lgdogf A010702 13.3492 -93-124*x+(-194-300*x-31*x^2)*f(x)+(75-75*x^2)*f(x)^2 ogf A010702 20.2145 1/2/(4+x)*(-3+(9+16*x+4*x^2)^(1/2)) revogf A010702 26.2039 {a(n+2)-a(n),a(0)=3,a(1)=4} ogf A010703 41.618 -(-3-5*x)/(1-x^2) ogf A010703 35.3753 -(3+5*x)/(x-1)/(x+1) ogf A010703 20.2145 -(5+6*x+5*x^2)/(-1+x)/(5*x+3)/(x+1) lgdogf A010703 18.6186 1/2/(5+x)*(-3+((2*x+9)*(2*x+1))^(1/2)) revogf A010703 15.3806 21+35*x+(11+30*x+7*x^2)*f(x)+(-6+6*x^2)*f(x)^2 ogf A010703 26.2039 {a(n+2)-a(n),a(0)=3,a(1)=5} ogf A010704 41.618 -(-3-6*x)/(1-x^2) ogf A010704 21.4396 -2*(x^2+x+1)/(-1+x)/(2*x+1)/(x+1) lgdogf A010704 32.1594 -3*(2*x+1)/(x-1)/(x+1) ogf A010704 14.7397 -99-198*x+(18-30*x-33*x^2)*f(x)+(5-5*x^2)*f(x)^2 ogf A010704 20.2145 1/2/(6+x)*(-3+(9+24*x+4*x^2)^(1/2)) revogf A010704 26.2039 {a(n+2)-a(n),a(0)=3,a(1)=6} ogf A010705 41.618 -(-3-7*x)/(1-x^2) ogf A010705 35.3753 -(3+7*x)/(x-1)/(x+1) ogf A010705 20.2145 -(7+6*x+7*x^2)/(-1+x)/(7*x+3)/(x+1) lgdogf A010705 20.2145 1/2/(7+x)*(-3+(9+28*x+4*x^2)^(1/2)) revogf A010705 14.4389 93+217*x+(-13+42*x+31*x^2)*f(x)+(-6+6*x^2)*f(x)^2 ogf A010705 26.2039 {a(n+2)-a(n),a(0)=3,a(1)=7} ogf A010706 41.618 -(-3-8*x)/(1-x^2) ogf A010706 35.3753 -(3+8*x)/(x-1)/(x+1) ogf A010706 19.1218 -2*(4+3*x+4*x^2)/(-1+x)/(8*x+3)/(x+1) lgdogf A010706 20.2145 1/2/(8+x)*(-3+(9+32*x+4*x^2)^(1/2)) revogf A010706 14.4389 69+184*x+(-14+24*x+23*x^2)*f(x)+(-3+3*x^2)*f(x)^2 ogf A010706 26.2039 {a(n+2)-a(n),a(0)=3,a(1)=8} ogf A010707 41.618 -(-3-9*x)/(1-x^2) ogf A010707 20.2145 -(3+2*x+3*x^2)/(-1+x)/(1+3*x)/(x+1) lgdogf A010707 32.1594 -3*(3*x+1)/(x-1)/(x+1) ogf A010707 20.2145 1/2/(9+x)*(-3+(9+36*x+4*x^2)^(1/2)) revogf A010707 37.2372 3+9*x+(-1+x^2)*f(x) ogf A010707 26.2039 {a(n+2)-a(n),a(0)=3,a(1)=9} ogf A010708 38.1724 -(-3-10*x)/(1-x^2) ogf A010708 32.7192 -(3+10*x)/(x-1)/(x+1) ogf A010708 18.5703 -2*(5+3*x+5*x^2)/(x-1)/(10*x+3)/(x+1) lgdogf A010708 19.0862 1/2/(10+x)*(-3+(9+40*x+4*x^2)^(1/2)) revogf A010708 13.7421 123+410*x+(-32+30*x+41*x^2)*f(x)+(-3+3*x^2)*f(x)^2 ogf A010708 24.5394 {a(n+2)-a(n),a(0)=3,a(1)=10} ogf A010709 121.585 -1/(x-1) lgdogf A010709 60.7924 -2*ln(2)+ln(4+x) revegf A010709 74.8214 -4+(1-x)*f(x) ogf A010709 121.585 -4/(x-1) ogf A010709 138.954 4/(1-x) ogf A010709 138.954 x/(4+x) revogf A010709 60.7924 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010709 48.6339 {a(n+1)-a(n),a(0)=4} ogf A010710 23.5835 (-2+((4+x)*(x+1))^(1/2))/(5+x) revogf A010710 41.618 -(-4-5*x)/(1-x^2) ogf A010710 35.3753 -(4+5*x)/(x-1)/(x+1) ogf A010710 20.2145 -(5+8*x+5*x^2)/(-1+x)/(5*x+4)/(x+1) lgdogf A010710 15.0533 -28-35*x+(39+40*x-7*x^2)*f(x)+(-8+8*x^2)*f(x)^2 ogf A010710 26.2039 {a(n+2)-a(n),a(0)=4,a(1)=5} ogf A010711 25.2681 (-2+(4+6*x+x^2)^(1/2))/(6+x) revogf A010711 41.618 -(-4-6*x)/(1-x^2) ogf A010711 20.2145 -(3+4*x+3*x^2)/(-1+x)/(3*x+2)/(x+1) lgdogf A010711 32.1594 -2*(2+3*x)/(x-1)/(x+1) ogf A010711 17.2563 4+6*x+(7+12*x+x^2)*f(x)+(-2+2*x^2)*f(x)^2 ogf A010711 26.2039 {a(n+2)-a(n),a(0)=4,a(1)=6} ogf A010712 25.2681 (-2+(4+7*x+x^2)^(1/2))/(7+x) revogf A010712 41.618 -(-4-7*x)/(1-x^2) ogf A010712 35.3753 -(4+7*x)/(x-1)/(x+1) ogf A010712 20.2145 -(7+8*x+7*x^2)/(-1+x)/(7*x+4)/(x+1) lgdogf A010712 14.7397 68+119*x+(15+56*x+17*x^2)*f(x)+(-8+8*x^2)*f(x)^2 ogf A010712 26.2039 {a(n+2)-a(n),a(0)=4,a(1)=7} ogf A010713 25.2681 (-2+(4+8*x+x^2)^(1/2))/(8+x) revogf A010713 41.618 -(-4-8*x)/(1-x^2) ogf A010713 21.4396 -2*(x^2+x+1)/(-1+x)/(2*x+1)/(x+1) lgdogf A010713 32.1594 -4*(2*x+1)/(x-1)/(x+1) ogf A010713 37.2372 4+8*x+(-1+x^2)*f(x) ogf A010713 26.2039 {a(n+2)-a(n),a(0)=4,a(1)=8} ogf A010714 25.2681 (-2+(4+9*x+x^2)^(1/2))/(9+x) revogf A010714 41.618 -(-4-9*x)/(1-x^2) ogf A010714 35.3753 -(4+9*x)/(x-1)/(x+1) ogf A010714 20.2145 -(9+8*x+9*x^2)/(-1+x)/(9*x+4)/(x+1) lgdogf A010714 14.1501 196+441*x+(-17+72*x+49*x^2)*f(x)+(-8+8*x^2)*f(x)^2 ogf A010714 26.2039 {a(n+2)-a(n),a(0)=4,a(1)=9} ogf A010715 22.9034 (-2+(4+10*x+x^2)^(1/2))/(10+x) revogf A010715 38.1724 -(-4-10*x)/(1-x^2) ogf A010715 20.2089 -(5+4*x+5*x^2)/(x-1)/(5*x+2)/(x+1) lgdogf A010715 31.2319 -2*(2+5*x)/(x-1)/(x+1) ogf A010715 12.2697 -2036-5090*x+(393-290*x-509*x^2)*f(x)+(29-29*x^2)*f(x)^2 ogf A010715 19.0862 -ln(14)+ln(10+x+(16+x^2+20*x)^(1/2)) revegf A010715 24.5394 {a(n+2)-a(n),a(0)=4,a(1)=10} ogf A010716 78.6118 -1/(-1+x) lgdogf A010716 54.4236 -5+(1-x)*f(x) ogf A010716 88.4383 -5/(x-1) ogf A010716 50.5362 -ln(5)+ln(5+x) revegf A010716 101.072 5/(1-x) ogf A010716 101.072 x/(5+x) revogf A010716 44.2192 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010716 35.3753 {a(n+1)-a(n),a(0)=5} ogf A010717 41.618 -(-5-6*x)/(1-x^2) ogf A010717 35.3753 -(5+6*x)/(x-1)/(x+1) ogf A010717 19.1218 -2*(3+5*x+3*x^2)/(6*x+5)/(-1+x)/(x+1) lgdogf A010717 15.0533 -35-42*x+(32+30*x-7*x^2)*f(x)+(-5+5*x^2)*f(x)^2 ogf A010717 19.653 1/2/(6+x)*(-5+(25+24*x+4*x^2)^(1/2)) revogf A010717 26.2039 {a(n+2)-a(n),a(0)=5,a(1)=6} ogf A010718 41.618 -(-5-7*x)/(1-x^2) ogf A010718 35.3753 -(5+7*x)/(x-1)/(x+1) ogf A010718 19.653 -(7+10*x+7*x^2)/(7*x+5)/(-1+x)/(x+1) lgdogf A010718 15.7224 -5-7*x+(51+70*x-x^2)*f(x)+(-10+10*x^2)*f(x)^2 ogf A010718 19.653 1/2/(7+x)*(-5+(25+28*x+4*x^2)^(1/2)) revogf A010718 26.2039 {a(n+2)-a(n),a(0)=5,a(1)=7} ogf A010719 41.618 -(-5-8*x)/(1-x^2) ogf A010719 35.3753 -(5+8*x)/(x-1)/(x+1) ogf A010719 19.1218 -2*(4+5*x+4*x^2)/(8*x+5)/(-1+x)/(x+1) lgdogf A010719 19.653 1/2/(8+x)*(-5+(25+32*x+4*x^2)^(1/2)) revogf A010719 15.3806 35+56*x+(18+40*x+7*x^2)*f(x)+(-5+5*x^2)*f(x)^2 ogf A010719 26.2039 {a(n+2)-a(n),a(0)=5,a(1)=8} ogf A010720 41.618 -(-5-9*x)/(1-x^2) ogf A010720 35.3753 -(5+9*x)/(x-1)/(x+1) ogf A010720 19.653 -(9+10*x+9*x^2)/(9*x+5)/(-1+x)/(x+1) lgdogf A010720 19.653 1/2/(9+x)*(-5+(25+36*x+4*x^2)^(1/2)) revogf A010720 13.8727 155+279*x+(19+90*x+31*x^2)*f(x)+(-10+10*x^2)*f(x)^2 ogf A010720 26.2039 {a(n+2)-a(n),a(0)=5,a(1)=9} ogf A010721 38.1724 -(-5-10*x)/(1-x^2) ogf A010721 21.472 -2*(x^2+x+1)/(x-1)/(2*x+1)/(x+1) lgdogf A010721 31.2319 -5*(2*x+1)/(x-1)/(x+1) ogf A010721 15.2689 -55-110*x+(6-10*x-11*x^2)*f(x)+(1-x^2)*f(x)^2 ogf A010721 19.0862 -ln(15)+ln(10+x+(25+x^2+20*x)^(1/2)) revegf A010721 18.5703 1/2/(10+x)*(-5+(25+40*x+4*x^2)^(1/2)) revogf A010721 24.5394 {a(n+2)-a(n),a(0)=5,a(1)=10} ogf A010722 78.6118 -1/(-1+x) lgdogf A010722 54.4236 -6+(1-x)*f(x) ogf A010722 88.4383 -6/(x-1) ogf A010722 50.5362 -ln(6)+ln(6+x) revegf A010722 101.072 6/(1-x) ogf A010722 101.072 x/(6+x) revogf A010722 44.2192 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010722 35.3753 {a(n+1)-a(n),a(0)=6} ogf A010723 25.2681 (-3+(9+7*x+x^2)^(1/2))/(7+x) revogf A010723 41.618 -(-6-7*x)/(1-x^2) ogf A010723 35.3753 -(6+7*x)/(x-1)/(x+1) ogf A010723 19.653 -(7+12*x+7*x^2)/(-1+x)/(7*x+6)/(x+1) lgdogf A010723 13.6059 -138-161*x+(95+84*x-23*x^2)*f(x)+(-12+12*x^2)*f(x)^2 ogf A010723 26.2039 {a(n+2)-a(n),a(0)=6,a(1)=7} ogf A010724 25.2681 (-3+(9+8*x+x^2)^(1/2))/(8+x) revogf A010724 41.618 -(-6-8*x)/(1-x^2) ogf A010724 19.1218 -2*(2+3*x+2*x^2)/(-1+x)/(4*x+3)/(x+1) lgdogf A010724 32.1594 -2*(3+4*x)/(x-1)/(x+1) ogf A010724 37.2372 6+8*x+(-1+x^2)*f(x) ogf A010724 26.2039 {a(n+2)-a(n),a(0)=6,a(1)=8} ogf A010725 25.2681 (-3+(9+9*x+x^2)^(1/2))/(9+x) revogf A010725 41.618 -(-6-9*x)/(1-x^2) ogf A010725 20.2145 -(3+4*x+3*x^2)/(-1+x)/(3*x+2)/(x+1) lgdogf A010725 32.1594 -3*(2+3*x)/(x-1)/(x+1) ogf A010725 37.2372 6+9*x+(-1+x^2)*f(x) ogf A010725 26.2039 {a(n+2)-a(n),a(0)=6,a(1)=9} ogf A010726 22.1646 (-3+((9+x)*(x+1))^(1/2))/(10+x) revogf A010726 38.1724 -(-6-10*x)/(1-x^2) ogf A010726 20.2089 -(5+6*x+5*x^2)/(x-1)/(5*x+3)/(x+1) lgdogf A010726 31.2319 -2*(3+5*x)/(x-1)/(x+1) ogf A010726 18.5703 -ln(16)+ln(10+x+((x+18)*(x+2))^(1/2)) revegf A010726 14.937 42+70*x+(11+30*x+7*x^2)*f(x)+(-3+3*x^2)*f(x)^2 ogf A010726 24.5394 {a(n+2)-a(n),a(0)=6,a(1)=10} ogf A010727 78.6118 -1/(-1+x) lgdogf A010727 54.4236 -7+(1-x)*f(x) ogf A010727 88.4383 -7/(x-1) ogf A010727 50.5362 -ln(7)+ln(7+x) revegf A010727 101.072 7/(1-x) ogf A010727 101.072 x/(7+x) revogf A010727 44.2192 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010727 35.3753 {a(n+1)-a(n),a(0)=7} ogf A010728 41.618 -(-7-8*x)/(1-x^2) ogf A010728 35.3753 -(7+8*x)/(x-1)/(x+1) ogf A010728 14.1501 -119-136*x+(66+56*x-17*x^2)*f(x)+(-7+7*x^2)*f(x)^2 ogf A010728 19.1218 -2*(4+7*x+4*x^2)/(-1+x)/(8*x+7)/(x+1) lgdogf A010728 19.653 1/2/(8+x)*(-7+(49+32*x+4*x^2)^(1/2)) revogf A010728 26.2039 {a(n+2)-a(n),a(0)=7,a(1)=8} ogf A010729 41.618 -(-7-9*x)/(1-x^2) ogf A010729 35.3753 -(7+9*x)/(x-1)/(x+1) ogf A010729 19.653 -(9+14*x+9*x^2)/(-1+x)/(9*x+7)/(x+1) lgdogf A010729 13.102 -119-153*x+(115+126*x-17*x^2)*f(x)+(-14+14*x^2)*f(x)^2 ogf A010729 19.653 1/2/(9+x)*(-7+(49+36*x+4*x^2)^(1/2)) revogf A010729 26.2039 {a(n+2)-a(n),a(0)=7,a(1)=9} ogf A010730 38.1724 -(-7-10*x)/(1-x^2) ogf A010730 32.7192 -(7+10*x)/(x-1)/(x+1) ogf A010730 18.5703 -2*(5+7*x+5*x^2)/(x-1)/(10*x+7)/(x+1) lgdogf A010730 18.5703 1/2/(10+x)*(-7+(49+40*x+4*x^2)^(1/2)) revogf A010730 15.9791 7+10*x+(48+70*x+x^2)*f(x)+(-7+7*x^2)*f(x)^2 ogf A010730 24.5394 {a(n+2)-a(n),a(0)=7,a(1)=10} ogf A010731 78.6118 -1/(-1+x) lgdogf A010731 44.2192 -3*ln(2)+ln(8+x) revegf A010731 54.4236 -8+(1-x)*f(x) ogf A010731 88.4383 -8/(x-1) ogf A010731 101.072 8/(1-x) ogf A010731 101.072 x/(8+x) revogf A010731 44.2192 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010731 35.3753 {a(n+1)-a(n),a(0)=8} ogf A010732 24.3968 (-4+(16+9*x+x^2)^(1/2))/(9+x) revogf A010732 41.618 -(-8-9*x)/(1-x^2) ogf A010732 35.3753 -(8+9*x)/(x-1)/(x+1) ogf A010732 19.653 -(9+16*x+9*x^2)/(-1+x)/(9*x+8)/(x+1) lgdogf A010732 13.102 -376-423*x+(175+144*x-47*x^2)*f(x)+(-16+16*x^2)*f(x)^2 ogf A010732 26.2039 {a(n+2)-a(n),a(0)=8,a(1)=9} ogf A010733 22.1646 (-4+((8+x)*(x+2))^(1/2))/(10+x) revogf A010733 38.1724 -(-8-10*x)/(1-x^2) ogf A010733 20.2089 -(5+8*x+5*x^2)/(x-1)/(5*x+4)/(x+1) lgdogf A010733 31.2319 -2*(4+5*x)/(x-1)/(x+1) ogf A010733 14.6192 -56-70*x+(39+40*x-7*x^2)*f(x)+(-4+4*x^2)*f(x)^2 ogf A010733 18.5703 -ln(18)+ln(10+x+((x+16)*(4+x))^(1/2)) revegf A010733 24.5394 {a(n+2)-a(n),a(0)=8,a(1)=10} ogf A010734 78.6118 -1/(-1+x) lgdogf A010734 44.2192 -2*ln(3)+ln(9+x) revegf A010734 54.4236 -9+(1-x)*f(x) ogf A010734 88.4383 -9/(x-1) ogf A010734 101.072 9/(1-x) ogf A010734 101.072 x/(9+x) revogf A010734 44.2192 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010734 35.3753 {a(n+1)-a(n),a(0)=9} ogf A010735 38.1724 -(-9-10*x)/(1-x^2) ogf A010735 32.7192 -(9+10*x)/(x-1)/(x+1) ogf A010735 18.5703 -2*(5+9*x+5*x^2)/(x-1)/(10*x+9)/(x+1) lgdogf A010735 13.4726 -279-310*x+(112+90*x-31*x^2)*f(x)+(-9+9*x^2)*f(x)^2 ogf A010735 18.5703 1/2/(10+x)*(-9+(81+40*x+4*x^2)^(1/2)) revogf A010735 24.5394 {a(n+2)-a(n),a(0)=9,a(1)=10} ogf A010736 15.2112 -1+(1-3*x+x^3-3*x^2)*f(x)-8*x^3*f(x)^2 ogf A010736 8.62723 -1/16*((x^2-6*x+1)^(1/2)*x^2+(x^2-6*x+1)^(1/2)-1+3*x+3*x^2-x^3)/x^3 ogf A010736 12.0422 -3/2*(x-1+(1-6*x+x^2)^(1/2))/(1-6*x+x^2)^(1/2)/x lgdogf A010736 5.45306 {(3*n+n^2)*a(n)+(-32-33*n-7*n^2)*a(n+1)+(86+51*n+7*n^2)*a(n+2)+(-9*n-18-n^2)*a(n+3),a(0)=1,a(1)=3,a(2)=12} ogf A010737 17.2539 -(-4-2*x+5*x^2)/(-2*x^2+1-x+2*x^3) ogf A010737 18.9236 -(-4-2*x+5*x^2)/(x-1)/(2*x^2-1) ogf A010737 10.1144 -(6+6*x+10*x^4-8*x^3-15*x^2)/(x-1)/(5*x^2-2*x-4)/(2*x^2-1) lgdogf A010737 8.26243 -68-34*x+85*x^2+(25-13*x+34*x^3-44*x^2)*f(x)+(4*x^2-2+2*x-4*x^3)*f(x)^2 ogf A010737 11.2814 {a(n+3)-a(n+2)-2*a(n+1)+2*a(n),a(0)=4,a(1)=6,a(2)=9} ogf A010761 24.0034 (1+2*x+2*x^2)/(x+1)/(1+x^2+x)/(x-1)^2 ogf A010761 26.9129 -(-x-2*x^3-2*x^2)/(1-x^2-x^3+x^5) ogf A010761 12.5088 -(2+8*x+6*x^5+17*x^3+14*x^4+13*x^2)/(x-1)/(x+1)/(x^2+x+1)/(2*x^2+2*x+1) lgdogf A010762 10.8644 -(-x^7-x^8-x^4-2*x^3-x^9-3*x^5-2*x^6-x^2)/(1-x^2-x^11-x^3-x^6+x^9+x^5+x^8) ogf A010762 10.8644 -(1+2*x+x^2+3*x^3+2*x^4+x^5+x^6+x^7)/(x^2-x+1)/(x+1)^2/(1+x^2+x)^2/(x-1)^3 ogf A010763 12.055 2*x+x^2+(-1+4*x-4*x^3+x^2)*f(x)+(6*x^2-x-9*x^3+4*x^4)*f(x)^2 ogf A010763 5.56383 {(-20-18*n-4*n^2)*a(n+1)+(244+143*n+21*n^2)*a(n+2)+(-284-157*n-21*n^2)*a(n+3)+(60+4*n^2+32*n)*a(n+4),a(0)=0,a(1)=2,a(2)=9,a(3)=34} ogf A010764 7.9998 (1+x-13*x^7-4*x^8+4*x^9+7*x^5-11*x^6+8*x^3+13*x^4+2*x^2+4*x^10)/(x-1)/(x+1)/(x^2+x+1)/(2*x^7-2*x^5-x^4+x^3+x^2-x-1) lgdogf A010764 16.7269 -(-1-x+x^2+x^3-x^4-2*x^5+2*x^7)/(x+1)/(1+x^2+x)/(x-1)^2 ogf A010764 17.6919 -(-x^7-2*x^8-x^4-x^3+2*x^10+x^5+x^6)/(1-x^2-x^3+x^5) ogf A010784 14.9167 (1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x-1)^2 ogf A010784 21.7832 -(x+x^8+x^2+x^9+x^11+x^3+x^5+x^10+x^6+x^7+x^4)/(-1+x+x^10-x^11) ogf A010784 137.234 2+x^9-x^10 ogf_with_Euler_Transform A010785 8.57823 (9*x^8+8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1)/(x-1)/(10*x^9-1)/(1+x^2+x)/(x^6+x^3+1) ogf A010785 10.4845 -(-x-8*x^8-2*x^2-9*x^9-3*x^3-5*x^5-6*x^6-7*x^7-4*x^4)/(1-11*x^9+10*x^18) ogf A010790 15.3408 {(n^2+5*n+6)*a(n+1)-a(n+2),a(0)=1,a(1)=2} ogf A010791 11.2946 {(n^2+6*n+8)*a(n+1)-a(n+2),a(0)=1,a(1)=3} ogf A010792 9.61372 {(n^2+7*n+10)*a(n+1)-a(n+2),a(0)=1,a(1)=4} ogf A010793 9.92789 {(n^2+8*n+12)*a(n+1)-a(n+2),a(0)=1,a(1)=5} ogf A010794 14.5231 {(n^2+9*n+14)*a(n+1)-a(n+2),a(0)=1,a(1)=6} ogf A010795 10.3107 {(n^2+10*n+16)*a(n+1)-a(n+2),a(0)=1,a(1)=7} ogf A010796 9.86506 {(n^2+7*n+12)*a(n+1)-a(n+2),a(0)=1,a(1)=6} ogf A010797 7.98038 {(-n^3-12*n^2-47*n-60)*a(n+1)+a(n+2),a(0)=1,a(1)=24} ogf A010797 7.15483 {(60+47*n+12*n^2+n^3)*a(n+1)+(-n-2)*a(n+2),a(0)=1,a(1)=24} egf A010815 109.349 1/(-1+x) ogf_with_Euler_Transform A010815 124.97 1/(x-1) ogf_with_Euler_Transform A010815 39.7633 {-a(n+1)+a(n),a(0)=-1} ogf_with_Euler_Transform A010816 122.345 3/(-1+x) ogf_with_Euler_Transform A010816 139.823 3/(x-1) ogf_with_Euler_Transform A010816 44.4891 {-a(n+1)+a(n),a(0)=-3} ogf_with_Euler_Transform A010817 87.7331 9/(-1+x) ogf_with_Euler_Transform A010817 100.266 9/(x-1) ogf_with_Euler_Transform A010817 31.9029 {-a(n+1)+a(n),a(0)=-9} ogf_with_Euler_Transform A010818 86.7825 10/(-1+x) ogf_with_Euler_Transform A010818 97.6303 10/(x-1) ogf_with_Euler_Transform A010818 33.9584 {-a(n+1)+a(n),a(0)=-10} ogf_with_Euler_Transform A010819 88.7131 11/(-1+x) ogf_with_Euler_Transform A010819 99.8022 11/(x-1) ogf_with_Euler_Transform A010819 34.7138 {-a(n+1)+a(n),a(0)=-11} ogf_with_Euler_Transform A010820 72.0945 13/(-1+x) ogf_with_Euler_Transform A010820 81.1063 13/(x-1) ogf_with_Euler_Transform A010820 28.2109 {-a(n+1)+a(n),a(0)=-13} ogf_with_Euler_Transform A010821 72.2184 14/(-1+x) ogf_with_Euler_Transform A010821 81.2457 14/(x-1) ogf_with_Euler_Transform A010821 28.2594 {-a(n+1)+a(n),a(0)=-14} ogf_with_Euler_Transform A010822 72.7805 15/(-1+x) ogf_with_Euler_Transform A010822 81.8781 15/(x-1) ogf_with_Euler_Transform A010822 28.4793 {-a(n+1)+a(n),a(0)=-15} ogf_with_Euler_Transform A010823 68.7798 17/(-1+x) ogf_with_Euler_Transform A010823 77.3773 17/(x-1) ogf_with_Euler_Transform A010823 26.9138 {-a(n+1)+a(n),a(0)=-17} ogf_with_Euler_Transform A010824 67.7201 18/(-1+x) ogf_with_Euler_Transform A010824 76.1852 18/(x-1) ogf_with_Euler_Transform A010824 26.4992 {-a(n+1)+a(n),a(0)=-18} ogf_with_Euler_Transform A010825 67.7547 19/(-1+x) ogf_with_Euler_Transform A010825 76.2241 19/(x-1) ogf_with_Euler_Transform A010825 26.5127 {-a(n+1)+a(n),a(0)=-19} ogf_with_Euler_Transform A010826 68.4952 20/(-1+x) ogf_with_Euler_Transform A010826 77.0571 20/(x-1) ogf_with_Euler_Transform A010826 26.8025 {-a(n+1)+a(n),a(0)=-20} ogf_with_Euler_Transform A010827 67.7478 21/(-1+x) ogf_with_Euler_Transform A010827 76.2163 21/(x-1) ogf_with_Euler_Transform A010827 26.51 {-a(n+1)+a(n),a(0)=-21} ogf_with_Euler_Transform A010828 68.4802 22/(-1+x) ogf_with_Euler_Transform A010828 77.0403 22/(x-1) ogf_with_Euler_Transform A010828 26.7966 {-a(n+1)+a(n),a(0)=-22} ogf_with_Euler_Transform A010829 67.3341 23/(-1+x) ogf_with_Euler_Transform A010829 75.7508 23/(x-1) ogf_with_Euler_Transform A010829 26.3481 {-a(n+1)+a(n),a(0)=-23} ogf_with_Euler_Transform A010830 69.8681 25/(-1+x) ogf_with_Euler_Transform A010830 78.6017 25/(x-1) ogf_with_Euler_Transform A010830 27.3397 {-a(n+1)+a(n),a(0)=-25} ogf_with_Euler_Transform A010831 63.6623 26/(-1+x) ogf_with_Euler_Transform A010831 71.6201 26/(x-1) ogf_with_Euler_Transform A010831 24.9113 {-a(n+1)+a(n),a(0)=-26} ogf_with_Euler_Transform A010832 63.2079 27/(-1+x) ogf_with_Euler_Transform A010832 71.1089 27/(x-1) ogf_with_Euler_Transform A010832 24.7335 {-a(n+1)+a(n),a(0)=-27} ogf_with_Euler_Transform A010833 64.2672 28/(-1+x) ogf_with_Euler_Transform A010833 72.3006 28/(x-1) ogf_with_Euler_Transform A010833 25.148 {-a(n+1)+a(n),a(0)=-28} ogf_with_Euler_Transform A010834 65.6797 29/(-1+x) ogf_with_Euler_Transform A010834 73.8897 29/(x-1) ogf_with_Euler_Transform A010834 25.7008 {-a(n+1)+a(n),a(0)=-29} ogf_with_Euler_Transform A010835 107.438 30/(-1+x) ogf_with_Euler_Transform A010835 120.868 30/(x-1) ogf_with_Euler_Transform A010835 42.0409 {-a(n+1)+a(n),a(0)=-30} ogf_with_Euler_Transform A010836 64.1034 31/(-1+x) ogf_with_Euler_Transform A010836 72.1163 31/(x-1) ogf_with_Euler_Transform A010836 25.0839 {-a(n+1)+a(n),a(0)=-31} ogf_with_Euler_Transform A010837 64.4517 32/(-1+x) ogf_with_Euler_Transform A010837 72.5082 32/(x-1) ogf_with_Euler_Transform A010837 25.2202 {-a(n+1)+a(n),a(0)=-32} ogf_with_Euler_Transform A010838 63.9349 44/(-1+x) ogf_with_Euler_Transform A010838 71.9268 44/(x-1) ogf_with_Euler_Transform A010838 25.018 {-a(n+1)+a(n),a(0)=-44} ogf_with_Euler_Transform A010839 64.2418 48/(-1+x) ogf_with_Euler_Transform A010839 72.272 48/(x-1) ogf_with_Euler_Transform A010839 25.1381 {-a(n+1)+a(n),a(0)=-48} ogf_with_Euler_Transform A010840 61.9052 40/(-1+x) ogf_with_Euler_Transform A010840 69.6434 40/(x-1) ogf_with_Euler_Transform A010840 24.2238 {-a(n+1)+a(n),a(0)=-40} ogf_with_Euler_Transform A010841 58.7709 64/(-1+x) ogf_with_Euler_Transform A010841 66.1172 64/(x-1) ogf_with_Euler_Transform A010841 22.9973 {-a(n+1)+a(n),a(0)=-64} ogf_with_Euler_Transform A010842 38.9445 (-3+2*x)/(x-1) lgdegf A010842 32.0719 -3+2*x+(1-x)*f(x) lgdegf A010842 36.3482 -exp(2*x)/(x-1) egf A010842 9.24107 {(-2*n-4)*a(n+1)+(n+5)*a(n+2)-a(n+3),a(0)=1,a(1)=3,a(2)=10} ogf A010843 43.0538 -(3*x-2)/(x-1) lgdegf A010843 37.672 -exp(-3*x)/(x-1) egf A010843 37.672 2-3*x+(1-x)*f(x) lgdegf A010843 10.9591 {(-3*n-6)*a(n+1)-a(n+2)*n+a(n+3),a(0)=1,a(1)=-2,a(2)=5} ogf A010844 32.5167 (-3+2*x)/(2*x-1) lgdegf A010844 27.3825 -3+2*x+(1-2*x)*f(x) lgdegf A010844 34.6844 -exp(x)/(2*x-1) egf A010844 8.52896 {(-2*n-4)*a(n+1)+(2*n+7)*a(n+2)-a(n+3),a(0)=1,a(1)=3,a(2)=13} ogf A010845 30.332 (-4+3*x)/(-1+3*x) lgdegf A010845 27.1392 -4+3*x+(1-3*x)*f(x) lgdegf A010845 34.3763 -exp(x)/(3*x-1) egf A010845 8.31684 {(3*n+6)*a(n+1)+(-3*n-10)*a(n+2)+a(n+3),a(0)=1,a(1)=4,a(2)=25} ogf A010849 13.1884 -1+(1-4*x+x^4-4*x^3-2*x^2)*f(x)-16*x^4*f(x)^2 ogf A010849 13.1884 -1+(1-4*x-4*x^3+x^4-2*x^2)*f(x)-16*x^4*f(x)^2 ogf A010849 5.1162 -1/32*(-(x^2-6*x+1)^(1/2)*x^2+(x^2-6*x+1)^(1/2)-(x^2-6*x+1)^(1/2)*x+(x^2-6*x+1)^(1/2)*x^3-1+4*x+2*x^2+4*x^3-x^4)/x^4 ogf A010849 12.9017 -2*(x-1+(x^2+1-6*x)^(1/2))/x/(x^2+1-6*x)^(1/2) lgdogf A010849 5.49518 {(-4*n-n^2)*a(n)+(45+40*n+7*n^2)*a(n+1)+(-108-58*n-7*n^2)*a(n+2)+(10*n+21+n^2)*a(n+3),a(0)=1,a(1)=4,a(2)=18} ogf A010850 89.9813 -1/(-1+x) lgdogf A010850 57.8451 -11+(1-x)*f(x) ogf A010850 89.9813 -11/(x-1) ogf A010850 50.6145 -ln(11)+ln(11+x) revegf A010850 101.229 11/(1-x) ogf A010850 101.229 x/(11+x) revogf A010850 50.6145 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010850 38.5634 {a(n+1)-a(n),a(0)=11} ogf A010851 71.3584 -1/(-1+x) lgdogf A010851 45.8733 -12+(1-x)*f(x) ogf A010851 71.3584 -12/(x-1) ogf A010851 40.1391 -ln(12)+ln(12+x) revegf A010851 80.2782 12/(1-x) ogf A010851 80.2782 x/(12+x) revogf A010851 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010851 30.5822 {a(n+1)-a(n),a(0)=12} ogf A010852 71.3584 -1/(-1+x) lgdogf A010852 45.8733 -13+(1-x)*f(x) ogf A010852 71.3584 -13/(x-1) ogf A010852 40.1391 -ln(13)+ln(13+x) revegf A010852 80.2782 13/(1-x) ogf A010852 80.2782 x/(13+x) revogf A010852 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010852 30.5822 {a(n+1)-a(n),a(0)=13} ogf A010853 71.3584 -1/(-1+x) lgdogf A010853 45.8733 -14+(1-x)*f(x) ogf A010853 71.3584 -14/(x-1) ogf A010853 40.1391 -ln(14)+ln(14+x) revegf A010853 80.2782 14/(1-x) ogf A010853 80.2782 x/(14+x) revogf A010853 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010853 30.5822 {a(n+1)-a(n),a(0)=14} ogf A010854 71.3584 -1/(-1+x) lgdogf A010854 45.8733 -15+(1-x)*f(x) ogf A010854 71.3584 -15/(x-1) ogf A010854 40.1391 -ln(15)+ln(15+x) revegf A010854 80.2782 15/(1-x) ogf A010854 80.2782 x/(15+x) revogf A010854 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010854 30.5822 {a(n+1)-a(n),a(0)=15} ogf A010855 71.3584 -1/(-1+x) lgdogf A010855 45.8733 -16+(1-x)*f(x) ogf A010855 71.3584 -16/(x-1) ogf A010855 37.778 -4*ln(2)+ln(x+16) revegf A010855 80.2782 16/(1-x) ogf A010855 80.2782 x/(16+x) revogf A010855 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010855 30.5822 {a(n+1)-a(n),a(0)=16} ogf A010856 71.3584 -1/(-1+x) lgdogf A010856 45.8733 -17+(1-x)*f(x) ogf A010856 71.3584 -17/(x-1) ogf A010856 40.1391 -ln(17)+ln(17+x) revegf A010856 80.2782 17/(1-x) ogf A010856 80.2782 x/(17+x) revogf A010856 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010856 30.5822 {a(n+1)-a(n),a(0)=17} ogf A010857 71.3584 -1/(-1+x) lgdogf A010857 45.8733 -18+(1-x)*f(x) ogf A010857 71.3584 -18/(x-1) ogf A010857 40.1391 -ln(18)+ln(x+18) revegf A010857 80.2782 18/(1-x) ogf A010857 80.2782 x/(18+x) revogf A010857 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010857 30.5822 {a(n+1)-a(n),a(0)=18} ogf A010858 71.3584 -1/(-1+x) lgdogf A010858 45.8733 -19+(1-x)*f(x) ogf A010858 71.3584 -19/(x-1) ogf A010858 40.1391 -ln(19)+ln(19+x) revegf A010858 80.2782 19/(1-x) ogf A010858 80.2782 x/(19+x) revogf A010858 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010858 30.5822 {a(n+1)-a(n),a(0)=19} ogf A010859 71.3584 -1/(-1+x) lgdogf A010859 45.8733 -20+(1-x)*f(x) ogf A010859 71.3584 -20/(x-1) ogf A010859 40.1391 -ln(20)+ln(20+x) revegf A010859 80.2782 20/(1-x) ogf A010859 80.2782 x/(20+x) revogf A010859 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010859 30.5822 {a(n+1)-a(n),a(0)=20} ogf A010860 71.3584 -1/(-1+x) lgdogf A010860 45.8733 -21+(1-x)*f(x) ogf A010860 71.3584 -21/(x-1) ogf A010860 40.1391 -ln(21)+ln(21+x) revegf A010860 80.2782 21/(1-x) ogf A010860 80.2782 x/(21+x) revogf A010860 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010860 30.5822 {a(n+1)-a(n),a(0)=21} ogf A010861 71.3584 -1/(-1+x) lgdogf A010861 45.8733 -22+(1-x)*f(x) ogf A010861 71.3584 -22/(x-1) ogf A010861 40.1391 -ln(22)+ln(22+x) revegf A010861 80.2782 22/(1-x) ogf A010861 80.2782 x/(22+x) revogf A010861 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010861 30.5822 {a(n+1)-a(n),a(0)=22} ogf A010862 71.3584 -1/(-1+x) lgdogf A010862 45.8733 -23+(1-x)*f(x) ogf A010862 71.3584 -23/(x-1) ogf A010862 40.1391 -ln(23)+ln(23+x) revegf A010862 80.2782 23/(1-x) ogf A010862 80.2782 x/(23+x) revogf A010862 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010862 30.5822 {a(n+1)-a(n),a(0)=23} ogf A010863 71.3584 -1/(-1+x) lgdogf A010863 45.8733 -24+(1-x)*f(x) ogf A010863 71.3584 -24/(x-1) ogf A010863 40.1391 -ln(24)+ln(24+x) revegf A010863 80.2782 24/(1-x) ogf A010863 80.2782 x/(24+x) revogf A010863 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010863 30.5822 {a(n+1)-a(n),a(0)=24} ogf A010864 71.3584 -1/(-1+x) lgdogf A010864 37.778 -2*ln(5)+ln(25+x) revegf A010864 45.8733 -25+(1-x)*f(x) ogf A010864 71.3584 -25/(x-1) ogf A010864 80.2782 25/(1-x) ogf A010864 80.2782 x/(25+x) revogf A010864 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010864 30.5822 {a(n+1)-a(n),a(0)=25} ogf A010865 71.3584 -1/(-1+x) lgdogf A010865 45.8733 -26+(1-x)*f(x) ogf A010865 71.3584 -26/(x-1) ogf A010865 40.1391 -ln(26)+ln(26+x) revegf A010865 80.2782 26/(1-x) ogf A010865 80.2782 x/(26+x) revogf A010865 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010865 30.5822 {a(n+1)-a(n),a(0)=26} ogf A010866 71.3584 -1/(-1+x) lgdogf A010866 45.8733 -27+(1-x)*f(x) ogf A010866 71.3584 -27/(x-1) ogf A010866 37.778 -3*ln(3)+ln(27+x) revegf A010866 80.2782 27/(1-x) ogf A010866 80.2782 x/(27+x) revogf A010866 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010866 30.5822 {a(n+1)-a(n),a(0)=27} ogf A010867 71.3584 -1/(-1+x) lgdogf A010867 45.8733 -28+(1-x)*f(x) ogf A010867 71.3584 -28/(x-1) ogf A010867 40.1391 -ln(28)+ln(28+x) revegf A010867 80.2782 28/(1-x) ogf A010867 80.2782 x/(28+x) revogf A010867 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010867 30.5822 {a(n+1)-a(n),a(0)=28} ogf A010868 71.3584 -1/(-1+x) lgdogf A010868 45.8733 -29+(1-x)*f(x) ogf A010868 71.3584 -29/(x-1) ogf A010868 40.1391 -ln(29)+ln(29+x) revegf A010868 80.2782 29/(1-x) ogf A010868 80.2782 x/(29+x) revogf A010868 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010868 30.5822 {a(n+1)-a(n),a(0)=29} ogf A010869 71.3584 -1/(-1+x) lgdogf A010869 45.8733 -30+(1-x)*f(x) ogf A010869 71.3584 -30/(x-1) ogf A010869 40.1391 -ln(30)+ln(30+x) revegf A010869 80.2782 30/(1-x) ogf A010869 80.2782 x/(30+x) revogf A010869 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010869 30.5822 {a(n+1)-a(n),a(0)=30} ogf A010870 71.3584 -1/(-1+x) lgdogf A010870 45.8733 -31+(1-x)*f(x) ogf A010870 71.3584 -31/(x-1) ogf A010870 40.1391 -ln(31)+ln(31+x) revegf A010870 80.2782 31/(1-x) ogf A010870 80.2782 x/(31+x) revogf A010870 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010870 30.5822 {a(n+1)-a(n),a(0)=31} ogf A010871 71.3584 -1/(-1+x) lgdogf A010871 45.8733 -32+(1-x)*f(x) ogf A010871 71.3584 -32/(x-1) ogf A010871 37.778 -5*ln(2)+ln(32+x) revegf A010871 80.2782 32/(1-x) ogf A010871 80.2782 x/(32+x) revogf A010871 40.1391 {-a(n+1),a(0)=1} ogf_with_Euler_Transform A010871 30.5822 {a(n+1)-a(n),a(0)=32} ogf A010872 40.5282 -(2*x+1)/(x-1)/(1+x^2+x) ogf A010872 24.3169 -(2+4*x^3+3*x^2)/(x-1)/(2*x+1)/(x^2+x+1) lgdogf A010872 51.1936 -(x+2*x^2)/(-1+x^3) ogf A010872 46.318 -x-2*x^2+(1-x^3)*f(x) ogf A010872 27.7908 {-a(n+3)+a(n),a(0)=0,a(1)=1,a(2)=2} ogf A010873 20.809 -(1+2*x+3*x^2)/(x-1)/(x+1)/(x^2+1) ogf A010873 28.3003 -(x+2*x^2+3*x^3)/(-1+x^4) ogf A010873 11.2303 -2*(1+3*x+3*x^5+3*x^4+2*x^3)/(-1+x)/(x+1)/(x^2+1)/(3*x^2+2*x+1) lgdogf A010873 9.1884 -95*x-285*x^3-190*x^2+(95-34*x-95*x^4-102*x^3-68*x^2)*f(x)+(34-34*x^4)*f(x)^2 ogf A010874 22.8228 -(-x-2*x^2-3*x^3-4*x^4)/(1-x^5) ogf A010874 16.0797 -(1+2*x+3*x^2+4*x^3)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010874 8.4227 -(2+6*x+9*x^6+8*x^5+8*x^7+5*x^4+12*x^2)/(-1+x)/(4*x^3+3*x^2+2*x+1)/(x^4+x^3+x^2+x+1) lgdogf A010875 12.1984 -(1+2*x+3*x^2+4*x^3+5*x^4)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010875 19.1218 -(x+2*x^2+3*x^3+4*x^4+5*x^5)/(-1+x^6) ogf A010875 6.31702 -2*(1+3*x+6*x^8+5*x^6+3*x^5+6*x^7+10*x^3+5*x^9+6*x^2)/(-1+x)/(x+1)/(x^2+x+1)/(x^2-x+1)/(5*x^4+4*x^3+3*x^2+2*x+1) lgdogf A010876 16.4536 -(-x-2*x^2-3*x^3-4*x^4-5*x^5-6*x^6)/(1-x^7) ogf A010876 11.0548 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) ogf A010877 10.7198 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A010877 14.4389 -(x+2*x^2+3*x^3+4*x^4+5*x^5+6*x^6+7*x^7)/(-1+x^8) ogf A010878 17.685 -(-x-2*x^2-3*x^3-4*x^4-5*x^5-6*x^6-7*x^7-8*x^8)/(1-x^9) ogf A010878 13.5094 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7)/(x-1)/(1+x^2+x)/(x^6+x^3+1) ogf A010879 7.21945 -(9*x^8+8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010879 11.4114 -(x+2*x^2+3*x^3+4*x^4+5*x^5+6*x^6+7*x^7+8*x^8+9*x^9)/(-1+x^10) ogf A010880 10.0827 -(-x-2*x^2-3*x^3-4*x^4-5*x^5-6*x^6-7*x^7-8*x^8-9*x^9-10*x^10)/(1-x^11) ogf A010880 6.65837 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7+9*x^8+10*x^9)/(x-1)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A010881 8.91174 -(x+2*x^2+3*x^3+4*x^4+5*x^5+6*x^6+7*x^7+8*x^8+9*x^9+10*x^10+11*x^11)/(-1+x^12) ogf A010882 42.2903 -(-1-2*x-3*x^2)/(1-x^3) ogf A010882 32.4226 -(1+2*x+3*x^2)/(x-1)/(1+x^2+x) ogf A010882 17.3692 -(2+6*x+3*x^4+4*x^3+3*x^2)/(x-1)/(x^2+x+1)/(3*x^2+2*x+1) lgdogf A010882 18.3524 2+4*x+6*x^2+(-3-2*x+2*x^3-3*x^2)*f(x)+(-x^3+1)*f(x)^2 ogf A010882 28.6082 {a(n+3)-a(n),a(0)=1,a(1)=2,a(2)=3} ogf A010883 24.3968 -(-1-2*x-3*x^2-4*x^3)/(1-x^4) ogf A010883 17.6877 -(1+2*x+3*x^2+4*x^3)/(x-1)/(x+1)/(x^2+1) ogf A010883 8.73465 -2*(1+3*x+2*x^6+3*x^5+3*x^4+2*x^3+6*x^2)/(-1+x)/(x+1)/(x^2+1)/(4*x^3+3*x^2+2*x+1) lgdogf A010883 8.32361 100+200*x+400*x^3+300*x^2+(-51+98*x+100*x^4+196*x^3+147*x^2)*f(x)+(-49+49*x^4)*f(x)^2 ogf A010884 20.2145 -(-1-2*x-3*x^2-4*x^3-5*x^4)/(1-x^5) ogf A010884 14.1501 -(1+2*x+3*x^2+4*x^3+5*x^4)/(x-1)/(x^4+x^3+x^2+x+1) ogf A010884 6.86899 -(2+6*x+5*x^8+9*x^6+8*x^5+8*x^7+5*x^4+20*x^3+12*x^2)/(-1+x)/(x^4+x^3+x^2+x+1)/(5*x^4+4*x^3+3*x^2+2*x+1) lgdogf A010885 17.2563 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5)/(-1+x^6) ogf A010885 11.0548 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5)/(x-1)/(1+x^2+x)/(x+1)/(x^2-x+1) ogf A010885 5.3599 -2*(1+3*x+6*x^8+5*x^6+3*x^5+6*x^7+15*x^4+10*x^3+5*x^9+3*x^10+6*x^2)/(-1+x)/(x+1)/(x^2+x+1)/(x^2-x+1)/(6*x^5+5*x^4+4*x^3+3*x^2+2*x+1) lgdogf A010886 15.0533 -(-1-2*x-3*x^2-4*x^3-5*x^4-6*x^5-7*x^6)/(1-x^7) ogf A010886 10.1072 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) ogf A010887 13.3492 -(-1-2*x-3*x^2-4*x^3-5*x^4-6*x^5-7*x^6-8*x^7)/(1-x^8) ogf A010887 9.82648 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7)/(x-1)/(x+1)/(x^2+1)/(x^4+1) ogf A010888 12.4702 -(9*x^8+8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1)/(x-1)/(1+x^2+x)/(x^6+x^3+1) ogf A010888 15.9455 -(x+2*x^2+3*x^3+4*x^4+5*x^5+6*x^6+7*x^7+8*x^8+9*x^9)/(-1+x^9) ogf A010889 14.5342 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7+9*x^8+10*x^9)/(-1+x^10) ogf A010889 9.27419 -(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+7*x^6+8*x^7+9*x^8+10*x^9)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A010890 2.58496 (1-x+x^3)/(x^4+1) ogf A010891 51.8545 -(-1-x)/(1-x^5) ogf A010891 15.2513 -1+(x^2+x+2+x^3+x^4)*f(x)+(-x^2-x^3-1-x-x^4)*f(x)^2 ogf A010891 129.636 -1+x^4 ogf_with_Euler_Transform A010891 37.0389 -1/(-1-x-x^2-x^3-x^4) ogf A010891 40.9378 1/(x^4+x^3+x^2+x+1) ogf A010891 11.6092 {-a(n+4)-a(n+3)-a(n+2)-a(n+1)-a(n),a(0)=-1,a(1)=-1,a(2)=-1,a(3)=-1} lgdogf A010891 17.6777 {a(n+5),a(0)=-1,a(1)=0,a(2)=0,a(3)=0,a(4)=1} ogf_with_Euler_Transform A010892 73.0745 -(-1-x)/(1-x^3) ogf A010892 60.8954 -(2*x-1)/(x^2-x+1) lgdogf A010892 28.1056 -2+(2*x^2+3-2*x)*f(x)+(-x^2-1+x)*f(x)^2 ogf A010892 99.6471 1-x-x^2+x^5 ogf_with_Euler_Transform A010892 99.6471 1/(x^2-x+1) ogf A010892 31.3177 {-a(n+2)+a(n+1)-a(n),a(0)=1,a(1)=1} ogf A010900 11.0996 -(4+x+x^3-x^4+x^5-x^2)/(x^2-1+3*x+x^4-x^3+x^6-x^5) ogf A010900 11.0996 -(4+x-x^2+x^3-x^4+x^5)/(x^2-1+3*x+x^4-x^3+x^6-x^5) ogf A010901 26.6038 -(-4+x-2*x^2)/(x^2+1-2*x-x^3) ogf A010901 26.6038 -(4-x+2*x^2)/(-x^2-1+2*x+x^3) ogf A010901 14.2872 -(7-4*x+2*x^4-2*x^3+9*x^2)/(2*x^2-x+4)/(x^3-x^2+2*x-1) lgdogf A010901 14.2872 8-2*x+4*x^2+(2+3*x+2*x^3)*f(x)+(-x^2-1+2*x+x^3)*f(x)^2 ogf A010901 15.1277 {a(n+3)-2*a(n+2)+a(n+1)-a(n),a(0)=4,a(1)=7,a(2)=12} ogf A010903 23.0325 -(-3+2*x)/(3*x^2+1-5*x) ogf A010903 13.9407 -(13-18*x+6*x^2)/(2*x-3)/(3*x^2-5*x+1) lgdogf A010903 23.0325 -(3-2*x)/(-3*x^2-1+5*x) ogf A010903 12.0397 -1/2*(-3-5*x+((1+x)*(13*x+9))^(1/2))/(2+3*x) revogf A010903 9.13356 -84+56*x+(-113-46*x+84*x^2)*f(x)+(47-235*x+141*x^2)*f(x)^2 ogf A010903 13.2437 {-a(n+2)+5*a(n+1)-3*a(n),a(0)=3,a(1)=13} ogf A010904 18.7118 -(-4+2*x-x^2)/(2*x^2+1-4*x-x^3) ogf A010904 18.7118 -(4-2*x+x^2)/(-2*x^2-1+4*x+x^3) ogf A010904 7.9461 -36+18*x-9*x^2+(-31-16*x-9*x^3+8*x^2)*f(x)+(10-40*x+20*x^2-10*x^3)*f(x)^2 ogf A010904 10.742 {a(n+3)-4*a(n+2)+2*a(n+1)-a(n),a(0)=4,a(1)=14,a(2)=49} ogf A010905 14.8704 -(-2-2*x+((3*x+4)*(1+x))^(1/2))/(1+x) revogf A010905 28.9582 -(4-x)/(-x^2-1+4*x) ogf A010905 18.3402 -(x-3)*(x-5)/(x-4)/(x^2-4*x+1) lgdogf A010905 30.567 -(x-4)/(x^2+1-4*x) ogf A010905 9.65272 -68+17*x+(-191-16*x+17*x^2)*f(x)+(52-208*x+52*x^2)*f(x)^2 ogf A010905 14.4791 {-a(n+2)+4*a(n+1)-a(n),a(0)=4,a(1)=15} ogf A010907 11.5744 -(-4-3*x-x^3-2*x^2)/(-3*x^2+1-4*x-x^4-2*x^3) ogf A010907 6.13583 -(19+28*x+x^6+4*x^5+10*x^4+20*x^3+28*x^2)/(x^3+2*x^2+3*x+4)/(x^4+2*x^3+3*x^2+4*x-1) lgdogf A010907 12.1256 -(x^3+2*x^2+3*x+4)/(3*x^2-1+4*x+x^4+2*x^3) ogf A010907 6.06279 -4-3*x-x^3-2*x^2+(25+14*x-x^4+4*x^3+9*x^2)*f(x)+(-6+24*x+18*x^2+12*x^3+6*x^4)*f(x)^2 ogf A010908 13.6728 -(-2-3*x+((1+x)*(5*x+4))^(1/2))/(3+4*x) revogf A010908 24.2382 -(3*x-4)/(4*x^2+1-6*x) ogf A010908 23.1843 -(4-3*x)/(-4*x^2-1+6*x) ogf A010908 14.0326 -(6*x-7)*(2*x-3)/(3*x-4)/(4*x^2-6*x+1) lgdogf A010908 8.60064 -260+195*x+(-311-108*x+260*x^2)*f(x)+(94-564*x+376*x^2)*f(x)^2 ogf A010908 13.331 {-a(n+2)+6*a(n+1)-4*a(n),a(0)=4,a(1)=21} ogf A010909 22.0237 -(-4-x-2*x^2)/(-x^2+1-6*x-3*x^3) ogf A010909 11.945 -(25+12*x+6*x^4+6*x^3+25*x^2)/(3*x^3+x^2+6*x-1)/(2*x^2+x+4) lgdogf A010909 23.4919 -(4+x+2*x^2)/(x^2-1+6*x+3*x^3) ogf A010909 8.80946 92+23*x+46*x^2+(-343+58*x+69*x^3-137*x^2)*f(x)+(-80*x^2+80-480*x-240*x^3)*f(x)^2 ogf A010909 12.8138 {a(n+3)-6*a(n+2)-a(n+1)-3*a(n),a(0)=4,a(1)=25,a(2)=156} ogf A010910 18.3917 (-2-3*x+((7*x+4)*(2*x+1))^(1/2))/(3+5*x) revogf A010910 30.6528 -(-4-3*x)/(-5*x^2+1-6*x) ogf A010910 18.8633 -(27+40*x+15*x^2)/(3*x+4)/(5*x^2+6*x-1) lgdogf A010910 33.4394 -(4+3*x)/(5*x^2-1+6*x) ogf A010910 11.318 -316-237*x+(887+132*x-395*x^2)*f(x)+(-202+1212*x+1010*x^2)*f(x)^2 ogf A010910 18.8633 {a(n+2)-6*a(n+1)-5*a(n),a(0)=4,a(1)=27} ogf A010911 18.225 -(-3-2*x-x^2)/(-2*x^2+1-3*x-x^3) ogf A010911 10.2316 -(11+14*x+10*x^2+4*x^3+x^4)/(x^2+2*x+3)/(x^3+2*x^2+3*x-1) lgdogf A010911 19.44 -(3+2*x+x^2)/(2*x^2-1+3*x+x^3) ogf A010911 7.8811 12+8*x+4*x^2+(-103-54*x+4*x^3-25*x^2)*f(x)+(-66*x^2+33-99*x-33*x^3)*f(x)^2 ogf A010911 10.6037 {-a(n+3)+3*a(n+2)+2*a(n+1)+a(n),a(0)=3,a(1)=11,a(2)=40} ogf A010912 23.8084 -(-3+2*x-x^2)/(2*x^2+1-3*x-x^3) ogf A010912 23.8084 -(3-2*x+x^2)/(-2*x^2-1+3*x+x^3) ogf A010912 13.1796 -(7-10*x+x^4-4*x^3+10*x^2)/(x^2-2*x+3)/(x^3-2*x^2+3*x-1) lgdogf A010912 10.2508 36-24*x+12*x^2+(63-14*x+12*x^3+x^2)*f(x)+(-25+75*x-50*x^2+25*x^3)*f(x)^2 ogf A010912 13.9257 {a(n+3)-3*a(n+2)+2*a(n+1)-a(n),a(0)=3,a(1)=7,a(2)=16} ogf A010913 15.0619 -(17-12*x+2*x^2)/(x-3)/(2*x^2-6*x+1) lgdogf A010913 25.8203 -(3-x)/(-2*x^2-1+6*x) ogf A010913 27.1114 -(x-3)/(2*x^2+1-6*x) ogf A010913 11.7875 -1/2*(-3-6*x+((14*x+9)*(2*x+1))^(1/2))/(2*x+1) revogf A010913 9.34874 -57+19*x+(-251-24*x+38*x^2)*f(x)+(90-540*x+180*x^2)*f(x)^2 ogf A010913 13.5557 {-a(n+2)+6*a(n+1)-2*a(n),a(0)=3,a(1)=17} ogf A010914 32.4393 -(-5+3*x)/(2*x^2+1-4*x) ogf A010914 19.6343 -(17-20*x+6*x^2)/(3*x-5)/(2*x^2-4*x+1) lgdogf A010914 17.3513 -1/2*(-5-4*x+(25+28*x+8*x^2)^(1/2))/(3+2*x) revogf A010914 12.8639 245-147*x+(191+52*x-98*x^2)*f(x)+(-48+192*x-96*x^2)*f(x)^2 ogf A010914 19.1309 {a(n+2)-4*a(n+1)+2*a(n),a(0)=5,a(1)=17} ogf A010915 5.63531 -(16-10*x+6*x^6-2*x^5+6*x^7+9*x^4+14*x^3+2*x^8+8*x^2)/(2*x^4+3*x^3+x^2-2*x+6)/(x^5+x^4-x^2+3*x-1) lgdogf A010915 12.1472 -(6-2*x+3*x^3+2*x^4+x^2)/(-x^2-1+3*x+x^4+x^5) ogf A010915 12.1472 -(6-2*x+x^2+3*x^3+2*x^4)/(-x^2-1+3*x+x^4+x^5) ogf A010918 11.471 -(-8-7*x+7*x^2+7*x^3)/(-7*x^2+1-6*x+6*x^4+5*x^3) ogf A010918 5.98489 -(55+98*x+42*x^6-50*x^2-178*x^3-42*x^4+84*x^5)/(7*x^3+7*x^2-7*x-8)/(6*x^4+5*x^3-7*x^2-6*x+1) lgdogf A010918 11.9698 -(8+7*x-7*x^3-7*x^2)/(7*x^2-1+6*x-6*x^4-5*x^3) ogf A010918 4.04861 -48344-42301*x+42301*x^3+42301*x^2+(38355-7985*x+36258*x^4+1942*x^3-70574*x^2)*f(x)+(-4039+24234*x+28273*x^2-20195*x^3-24234*x^4)*f(x)^2 ogf A010919 15.4162 -(-4-x+x^2+x^4)/(-x^2+1-3*x+x^5+x^3) ogf A010919 16.323 -(4+x-x^4-x^2)/(x^2-1+3*x-x^5-x^3) ogf A010920 23.0325 -(-3+2*x)/(3*x^2+1-5*x) ogf A010920 13.9407 -(13-18*x+6*x^2)/(2*x-3)/(3*x^2-5*x+1) lgdogf A010920 23.0325 -(3-2*x)/(-3*x^2-1+5*x) ogf A010920 12.0397 -1/2*(-3-5*x+((1+x)*(13*x+9))^(1/2))/(2+3*x) revogf A010920 9.13356 -84+56*x+(-113-46*x+84*x^2)*f(x)+(47-235*x+141*x^2)*f(x)^2 ogf A010920 13.2437 {-a(n+2)+5*a(n+1)-3*a(n),a(0)=3,a(1)=13} ogf A010922 5.21305 -(14-5*x-9*x^2-x^3-x^4-2*x^5-3*x^6+x^8+5*x^11+9*x^12+9*x^7-12*x^9-6*x^10)/(x-1)/(x^12+x^11-x^9+x^7-x^2-x+1) ogf A010924 13.7653 (-4-3*x+((15*x+16)*(1+x))^(1/2))/(7+6*x) revogf A010924 22.9421 -(-8-7*x)/(-6*x^2+1-6*x) ogf A010924 14.1182 -(55+96*x+42*x^2)/(7*x+8)/(6*x^2+6*x-1) lgdogf A010924 25.0277 -(8+7*x)/(6*x^2-1+6*x) ogf A010924 7.97986 -3064-2681*x+(3791+684*x-2298*x^2)*f(x)+(-426+2556*x+2556*x^2)*f(x)^2 ogf A010924 14.1182 {a(n+2)-6*a(n+1)-6*a(n),a(0)=8,a(1)=55} ogf A010925 25.2681 -(-5-x+x^4+x^2)/(-x^2+1-4*x+x^5+x^3) ogf A010926 10.4908 (x+1)^10 ogf A010926 11.9895 10-10*x ogf_with_Euler_Transform A010926 10.4908 10/(x+1) lgdogf A010926 1.95178 {(-n-2)*a(n+2)+(9-n)*a(n+1),a(0)=1,a(1)=10} ogf A010927 12.1139 (x+1)^11 ogf A010927 13.8445 11-11*x ogf_with_Euler_Transform A010927 12.1139 11/(x+1) lgdogf A010927 2.20253 {(-n-2)*a(n+2)+(10-n)*a(n+1),a(0)=1,a(1)=11} ogf A010927 3.87646 {a(n+2),a(0)=11,a(1)=-11} ogf_with_Euler_Transform A010928 13.7866 (x+1)^12 ogf A010928 7.87806 -12+(x+1)*f(x) lgdogf A010928 15.7561 12-12*x ogf_with_Euler_Transform A010928 13.7866 12/(x+1) lgdogf A010928 2.50666 {(-n-2)*a(n+2)+(11-n)*a(n+1),a(0)=1,a(1)=12} ogf A010928 4.41171 {a(n+2),a(0)=12,a(1)=-12} ogf_with_Euler_Transform A010929 16.824 (x+1)^13 ogf A010929 9.61372 -13+(x+1)*f(x) lgdogf A010929 19.2274 13-13*x ogf_with_Euler_Transform A010929 16.824 13/(x+1) lgdogf A010929 3.05891 {(-n-2)*a(n+2)+(12-n)*a(n+1),a(0)=1,a(1)=13} ogf A010929 5.38368 {a(n+2),a(0)=13,a(1)=-13} ogf_with_Euler_Transform A010930 19.6334 (x+1)^14 ogf A010930 11.2191 -14+(x+1)*f(x) lgdogf A010930 22.4381 14-14*x ogf_with_Euler_Transform A010930 19.6334 14/(x+1) lgdogf A010930 3.5697 {(-n-2)*a(n+2)+(13-n)*a(n+1),a(0)=1,a(1)=14} ogf A010930 6.28268 {a(n+2),a(0)=14,a(1)=-14} ogf_with_Euler_Transform A010931 22.5273 (x+1)^15 ogf A010931 12.8727 -15+(1+x)*f(x) lgdogf A010931 25.7455 15-15*x ogf_with_Euler_Transform A010931 22.5273 15/(x+1) lgdogf A010931 4.09587 {(-n-2)*a(n+2)+(14-n)*a(n+1),a(0)=1,a(1)=15} ogf A010931 7.20873 {a(n+2),a(0)=15,a(1)=-15} ogf_with_Euler_Transform A010932 25.853 (x+1)^16 ogf A010932 14.7732 -16+(1+x)*f(x) lgdogf A010932 29.5463 16-16*x ogf_with_Euler_Transform A010932 25.853 16/(x+1) lgdogf A010932 4.70055 {(-n-2)*a(n+2)+(15-n)*a(n+1),a(0)=1,a(1)=16} ogf A010932 8.27297 {a(n+2),a(0)=16,a(1)=-16} ogf_with_Euler_Transform A010933 29.265 (x+1)^17 ogf A010933 16.7229 -17+(1+x)*f(x) lgdogf A010933 33.4457 17-17*x ogf_with_Euler_Transform A010933 29.265 17/(x+1) lgdogf A010933 5.32091 {(-n-2)*a(n+2)+(16-n)*a(n+1),a(0)=1,a(1)=17} ogf A010933 9.3648 {a(n+2),a(0)=17,a(1)=-17} ogf_with_Euler_Transform A010934 32.0208 (x+1)^18 ogf A010934 18.2976 -18+(1+x)*f(x) lgdogf A010934 36.5952 18-18*x ogf_with_Euler_Transform A010934 32.0208 18/(x+1) lgdogf A010934 5.82196 {(-n-2)*a(n+2)+(17-n)*a(n+1),a(0)=1,a(1)=18} ogf A010934 10.2467 {a(n+2),a(0)=18,a(1)=-18} ogf_with_Euler_Transform A010935 35.5743 (x+1)^19 ogf A010935 20.3282 -19+(1+x)*f(x) lgdogf A010935 40.6563 19-19*x ogf_with_Euler_Transform A010935 35.5743 19/(x+1) lgdogf A010935 6.46805 {(-n-2)*a(n+2)+(18-n)*a(n+1),a(0)=1,a(1)=19} ogf A010935 11.3838 {a(n+2),a(0)=19,a(1)=-19} ogf_with_Euler_Transform A010936 41.101 (x+1)^20 ogf A010936 23.4863 -20+(1+x)*f(x) lgdogf A010936 46.9726 20-20*x ogf_with_Euler_Transform A010936 41.101 20/(x+1) lgdogf A010936 7.47291 {(-n-2)*a(n+2)+(19-n)*a(n+1),a(0)=1,a(1)=20} ogf A010936 13.1523 {a(n+2),a(0)=20,a(1)=-20} ogf_with_Euler_Transform A010937 45.2065 (x+1)^21 ogf A010937 25.8323 -21+(1+x)*f(x) lgdogf A010937 51.6645 21-21*x ogf_with_Euler_Transform A010937 45.2065 21/(x+1) lgdogf A010937 8.21936 {(-n-2)*a(n+2)+(20-n)*a(n+1),a(0)=1,a(1)=21} ogf A010937 14.4661 {a(n+2),a(0)=21,a(1)=-21} ogf_with_Euler_Transform A010938 48.6001 (x+1)^22 ogf A010938 27.7715 -22+(1+x)*f(x) lgdogf A010938 55.543 22-22*x ogf_with_Euler_Transform A010938 48.6001 22/(x+1) lgdogf A010938 8.83638 {(-n-2)*a(n+2)+(21-n)*a(n+1),a(0)=1,a(1)=22} ogf A010938 15.552 {a(n+2),a(0)=22,a(1)=-22} ogf_with_Euler_Transform A010939 54.4241 (x+1)^23 ogf A010939 31.0995 -23+(1+x)*f(x) lgdogf A010939 62.199 23-23*x ogf_with_Euler_Transform A010939 54.4241 23/(x+1) lgdogf A010939 9.89529 {(-n-2)*a(n+2)+(22-n)*a(n+1),a(0)=1,a(1)=23} ogf A010939 17.4157 {a(n+2),a(0)=23,a(1)=-23} ogf_with_Euler_Transform A010940 59.9516 (x+1)^24 ogf A010940 34.2581 -24+(1+x)*f(x) lgdogf A010940 68.5162 24-24*x ogf_with_Euler_Transform A010940 59.9516 24/(x+1) lgdogf A010940 10.9003 {(-n-2)*a(n+2)+(23-n)*a(n+1),a(0)=1,a(1)=24} ogf A010940 19.1845 {a(n+2),a(0)=24,a(1)=-24} ogf_with_Euler_Transform A010941 64.7547 (x+1)^25 ogf A010941 37.0027 -25+(1+x)*f(x) lgdogf A010941 74.0054 25-25*x ogf_with_Euler_Transform A010941 64.7547 25/(x+1) lgdogf A010941 11.7736 {(-n-2)*a(n+2)+(24-n)*a(n+1),a(0)=1,a(1)=25} ogf A010941 20.7215 {a(n+2),a(0)=25,a(1)=-25} ogf_with_Euler_Transform A010942 69.2126 (x+1)^26 ogf A010942 39.5501 -26+(1+x)*f(x) lgdogf A010942 79.1002 26-26*x ogf_with_Euler_Transform A010942 69.2126 26/(x+1) lgdogf A010942 12.5841 {(-n-2)*a(n+2)+(25-n)*a(n+1),a(0)=1,a(1)=26} ogf A010942 22.148 {a(n+2),a(0)=26,a(1)=-26} ogf_with_Euler_Transform A010943 75.391 (x+1)^27 ogf A010943 43.0806 -27+(1+x)*f(x) lgdogf A010943 86.1612 27-27*x ogf_with_Euler_Transform A010943 75.391 27/(1+x) lgdogf A010943 13.7075 {(-n-2)*a(n+2)+(26-n)*a(n+1),a(0)=1,a(1)=27} ogf A010943 24.1251 {a(n+2),a(0)=27,a(1)=-27} ogf_with_Euler_Transform A010944 81.657 (x+1)^28 ogf A010944 46.6612 -28+(1+x)*f(x) lgdogf A010944 93.3223 28-28*x ogf_with_Euler_Transform A010944 81.657 28/(x+1) lgdogf A010944 14.8467 {(-n-2)*a(n+2)+(27-n)*a(n+1),a(0)=1,a(1)=28} ogf A010944 26.1302 {a(n+2),a(0)=28,a(1)=-28} ogf_with_Euler_Transform A010945 88.006 (x+1)^29 ogf A010945 50.2892 -29+(1+x)*f(x) lgdogf A010945 100.578 29-29*x ogf_with_Euler_Transform A010945 88.006 29/(x+1) lgdogf A010945 16.0011 {(-n-2)*a(n+2)+(28-n)*a(n+1),a(0)=1,a(1)=29} ogf A010945 28.1619 {a(n+2),a(0)=29,a(1)=-29} ogf_with_Euler_Transform A010946 94.864 (x+1)^30 ogf A010946 54.208 -30+(1+x)*f(x) lgdogf A010946 108.416 30-30*x ogf_with_Euler_Transform A010946 94.864 30/(x+1) lgdogf A010946 17.248 {(-n-2)*a(n+2)+(29-n)*a(n+1),a(0)=1,a(1)=30} ogf A010946 30.3565 {a(n+2),a(0)=30,a(1)=-30} ogf_with_Euler_Transform A010947 96.9342 (x+1)^31 ogf A010947 55.391 -31+(1+x)*f(x) lgdogf A010947 110.782 31-31*x ogf_with_Euler_Transform A010947 96.9342 31/(x+1) lgdogf A010947 17.6244 {(-n-2)*a(n+2)+(30-n)*a(n+1),a(0)=1,a(1)=31} ogf A010947 31.0189 {a(n+2),a(0)=31,a(1)=-31} ogf_with_Euler_Transform A010948 94.5512 (x+1)^32 ogf A010948 54.0292 -32+(1+x)*f(x) lgdogf A010948 108.058 32-32*x ogf_with_Euler_Transform A010948 94.5512 32/(x+1) lgdogf A010948 17.1911 {(-n-2)*a(n+2)+(31-n)*a(n+1),a(0)=1,a(1)=32} ogf A010948 30.2564 {a(n+2),a(0)=32,a(1)=-32} ogf_with_Euler_Transform A010949 89.5978 (x+1)^33 ogf A010949 51.1987 -33+(1+x)*f(x) lgdogf A010949 102.397 33-33*x ogf_with_Euler_Transform A010949 89.5978 33/(1+x) lgdogf A010949 16.2905 {(-n-2)*a(n+2)+(32-n)*a(n+1),a(0)=1,a(1)=33} ogf A010949 28.6713 {a(n+2),a(0)=33,a(1)=-33} ogf_with_Euler_Transform A010950 92.0413 (x+1)^34 ogf A010950 52.595 -34+(1+x)*f(x) lgdogf A010950 105.19 34-34*x ogf_with_Euler_Transform A010950 16.7348 {(-n-2)*a(n+2)+(33-n)*a(n+1),a(0)=1,a(1)=34} ogf A010950 29.4532 {a(n+2),a(0)=34,a(1)=-34} ogf_with_Euler_Transform A010951 88.5192 (x+1)^35 ogf A010951 50.5824 -35+(1+x)*f(x) lgdogf A010951 101.165 35-35*x ogf_with_Euler_Transform A010951 88.5192 35/(x+1) lgdogf A010951 16.0944 {(-n-2)*a(n+2)+(34-n)*a(n+1),a(0)=1,a(1)=35} ogf A010951 28.3261 {a(n+2),a(0)=35,a(1)=-35} ogf_with_Euler_Transform A010952 89.7263 (x+1)^36 ogf A010952 51.2722 -36+(1+x)*f(x) lgdogf A010952 102.544 36-36*x ogf_with_Euler_Transform A010952 89.7263 36/(x+1) lgdogf A010952 16.3139 {(-n-2)*a(n+2)+(35-n)*a(n+1),a(0)=1,a(1)=36} ogf A010952 28.7124 {a(n+2),a(0)=36,a(1)=-36} ogf_with_Euler_Transform A010953 87.3964 (x+1)^37 ogf A010953 49.9408 -37+(1+x)*f(x) lgdogf A010953 99.8816 37-37*x ogf_with_Euler_Transform A010953 87.3964 37/(x+1) lgdogf A010953 15.8902 {(-n-2)*a(n+2)+(36-n)*a(n+1),a(0)=1,a(1)=37} ogf A010953 27.9668 {a(n+2),a(0)=37,a(1)=-37} ogf_with_Euler_Transform A010954 88.9854 (x+1)^38 ogf A010954 50.8488 -38+(1+x)*f(x) lgdogf A010954 101.698 38-38*x ogf_with_Euler_Transform A010954 88.9854 38/(x+1) lgdogf A010954 16.1792 {(-n-2)*a(n+2)+(37-n)*a(n+1),a(0)=1,a(1)=38} ogf A010954 28.4753 {a(n+2),a(0)=38,a(1)=-38} ogf_with_Euler_Transform A010955 89.3827 (x+1)^39 ogf A010955 51.0758 -39+(1+x)*f(x) lgdogf A010955 102.152 39-39*x ogf_with_Euler_Transform A010955 16.2514 {(-n-2)*a(n+2)+(38-n)*a(n+1),a(0)=1,a(1)=39} ogf A010955 28.6024 {a(n+2),a(0)=39,a(1)=-39} ogf_with_Euler_Transform A010956 85.834 (x+1)^40 ogf A010956 49.048 -40+(1+x)*f(x) lgdogf A010956 98.096 40-40*x ogf_with_Euler_Transform A010956 85.834 40/(1+x) lgdogf A010956 15.6062 {(-n-2)*a(n+2)+(39-n)*a(n+1),a(0)=1,a(1)=40} ogf A010956 27.4669 {a(n+2),a(0)=40,a(1)=-40} ogf_with_Euler_Transform A010957 87.7937 (x+1)^41 ogf A010957 50.1678 -41+(1+x)*f(x) lgdogf A010957 100.336 41-41*x ogf_with_Euler_Transform A010957 87.7937 41/(x+1) lgdogf A010957 15.9625 {(-n-2)*a(n+2)+(40-n)*a(n+1),a(0)=1,a(1)=41} ogf A010957 28.094 {a(n+2),a(0)=41,a(1)=-41} ogf_with_Euler_Transform A010958 88.5776 (x+1)^42 ogf A010958 50.6158 -42+(1+x)*f(x) lgdogf A010958 101.232 42-42*x ogf_with_Euler_Transform A010958 88.5776 42/(x+1) lgdogf A010958 16.105 {(-n-2)*a(n+2)+(41-n)*a(n+1),a(0)=1,a(1)=42} ogf A010958 28.3448 {a(n+2),a(0)=42,a(1)=-42} ogf_with_Euler_Transform A010959 89.7534 (x+1)^43 ogf A010959 51.2877 -43+(1+x)*f(x) lgdogf A010959 102.575 43-43*x ogf_with_Euler_Transform A010959 89.7534 43/(x+1) lgdogf A010959 16.3188 {(-n-2)*a(n+2)+(42-n)*a(n+1),a(0)=1,a(1)=43} ogf A010959 28.7211 {a(n+2),a(0)=43,a(1)=-43} ogf_with_Euler_Transform A010960 85.0036 (x+1)^44 ogf A010960 48.5735 -44+(1+x)*f(x) lgdogf A010960 97.147 44-44*x ogf_with_Euler_Transform A010960 85.0036 44/(x+1) lgdogf A010960 15.4552 {(-n-2)*a(n+2)+(43-n)*a(n+1),a(0)=1,a(1)=44} ogf A010960 27.2012 {a(n+2),a(0)=44,a(1)=-44} ogf_with_Euler_Transform A010961 85.7764 (x+1)^45 ogf A010961 49.0151 -45+(1+x)*f(x) lgdogf A010961 98.0301 45-45*x ogf_with_Euler_Transform A010961 85.7764 45/(1+x) lgdogf A010961 15.5957 {(-n-2)*a(n+2)+(44-n)*a(n+1),a(0)=1,a(1)=45} ogf A010961 27.4484 {a(n+2),a(0)=45,a(1)=-45} ogf_with_Euler_Transform A010962 86.9355 (x+1)^46 ogf A010962 49.6774 -46+(1+x)*f(x) lgdogf A010962 99.3549 46-46*x ogf_with_Euler_Transform A010962 86.9355 46/(1+x) lgdogf A010962 15.8065 {(-n-2)*a(n+2)+(45-n)*a(n+1),a(0)=1,a(1)=46} ogf A010962 27.8194 {a(n+2),a(0)=46,a(1)=-46} ogf_with_Euler_Transform A010963 81.0603 (x+1)^47 ogf A010963 46.3202 -47+(1+x)*f(x) lgdogf A010963 92.6404 47-47*x ogf_with_Euler_Transform A010963 81.0603 47/(x+1) lgdogf A010963 14.7382 {(-n-2)*a(n+2)+(46-n)*a(n+1),a(0)=1,a(1)=47} ogf A010963 25.9393 {a(n+2),a(0)=47,a(1)=-47} ogf_with_Euler_Transform A010964 82.202 (x+1)^48 ogf A010964 46.9726 -48+(1+x)*f(x) lgdogf A010964 93.9452 48-48*x ogf_with_Euler_Transform A010964 82.202 48/(x+1) lgdogf A010964 14.9458 {(-n-2)*a(n+2)+(47-n)*a(n+1),a(0)=1,a(1)=48} ogf A010964 26.3047 {a(n+2),a(0)=48,a(1)=-48} ogf_with_Euler_Transform A010965 63.6981 -1/(-1+x)^13 ogf A010965 69.4888 -1/(x-1)^13 ogf A010965 54.5984 -13+(1-x)*f(x) lgdogf A010965 84.9308 -13/(x-1) lgdogf A010965 17.3722 {(-n-2)*a(n+2)+(14+n)*a(n+1),a(0)=1,a(1)=13} ogf A010965 44.9634 {-a(n+1),a(0)=13} ogf_with_Euler_Transform A010966 53.5532 -14+(1-x)*f(x) lgdogf A010966 83.305 -14/(x-1) lgdogf A010966 68.1586 1/(-1+x)^14 ogf A010966 74.9745 1/(x-1)^14 ogf A010966 17.0397 {(-n-2)*a(n+2)+(15+n)*a(n+1),a(0)=1,a(1)=14} ogf A010966 44.1026 {-a(n+1),a(0)=14} ogf_with_Euler_Transform A010967 64.4225 -1/(-1+x)^15 ogf A010967 70.2791 -1/(x-1)^15 ogf A010967 55.2193 -15+(1-x)*f(x) lgdogf A010967 17.5698 {(-n-2)*a(n+2)+(16+n)*a(n+1),a(0)=1,a(1)=15} ogf A010967 45.4747 {-a(n+1),a(0)=15} ogf_with_Euler_Transform A010968 53.4397 -16+(1-x)*f(x) lgdogf A010968 83.1284 -16/(x-1) lgdogf A010968 68.0142 1/(-1+x)^16 ogf A010968 74.8156 1/(x-1)^16 ogf A010968 17.0035 {(-n-2)*a(n+2)+(17+n)*a(n+1),a(0)=1,a(1)=16} ogf A010968 44.0092 {-a(n+1),a(0)=16} ogf_with_Euler_Transform A010969 64.2689 -1/(-1+x)^17 ogf A010969 70.1115 -1/(x-1)^17 ogf A010969 55.0876 -17+(1-x)*f(x) lgdogf A010969 85.6918 -17/(x-1) lgdogf A010969 17.5279 {(-n-2)*a(n+2)+(18+n)*a(n+1),a(0)=1,a(1)=17} ogf A010969 45.3663 {-a(n+1),a(0)=17} ogf_with_Euler_Transform A010970 53.0605 -18+(1-x)*f(x) lgdogf A010970 82.5385 -18/(x-1) lgdogf A010970 67.5315 1/(-1+x)^18 ogf A010970 74.2847 1/(x-1)^18 ogf A010970 16.8829 {(-n-2)*a(n+2)+(19+n)*a(n+1),a(0)=1,a(1)=18} ogf A010970 43.6969 {-a(n+1),a(0)=18} ogf_with_Euler_Transform A010971 63.2614 -1/(-1+x)^19 ogf A010971 69.0125 -1/(x-1)^19 ogf A010971 54.2241 -19+(1-x)*f(x) lgdogf A010971 84.3486 -19/(x-1) lgdogf A010971 17.2531 {(-n-2)*a(n+2)+(20+n)*a(n+1),a(0)=1,a(1)=19} ogf A010971 44.6551 {-a(n+1),a(0)=19} ogf_with_Euler_Transform A010972 51.2722 -20+(1-x)*f(x) lgdogf A010972 79.7567 -20/(x-1) lgdogf A010972 65.2555 1/(-1+x)^20 ogf A010972 71.781 1/(x-1)^20 ogf A010972 16.3139 {(-n-2)*a(n+2)+(21+n)*a(n+1),a(0)=1,a(1)=20} ogf A010972 42.2241 {-a(n+1),a(0)=20} ogf_with_Euler_Transform A010973 61.427 -1/(-1+x)^21 ogf A010973 67.0112 -1/(x-1)^21 ogf A010973 52.6517 -21+(1-x)*f(x) lgdogf A010973 81.9026 -21/(x-1) lgdogf A010973 16.7528 {(-n-2)*a(n+2)+(22+n)*a(n+1),a(0)=1,a(1)=21} ogf A010973 43.3602 {-a(n+1),a(0)=21} ogf_with_Euler_Transform A010974 54.0312 -22+(1-x)*f(x) lgdogf A010974 84.0485 -22/(x-1) lgdogf A010974 68.767 1/(-1+x)^22 ogf A010974 75.6437 1/(x-1)^22 ogf A010974 17.1917 {(-n-2)*a(n+2)+(23+n)*a(n+1),a(0)=1,a(1)=22} ogf A010974 44.4963 {-a(n+1),a(0)=22} ogf_with_Euler_Transform A010975 59.3236 -1/(-1+x)^23 ogf A010975 64.7167 -1/(x-1)^23 ogf A010975 50.8488 -23+(1-x)*f(x) lgdogf A010975 79.0981 -23/(x-1) lgdogf A010975 16.1792 {(-n-2)*a(n+2)+(24+n)*a(n+1),a(0)=1,a(1)=23} ogf A010975 41.8755 {-a(n+1),a(0)=23} ogf_with_Euler_Transform A010976 51.0758 -24+(1-x)*f(x) lgdogf A010976 79.4513 -24/(x-1) lgdogf A010976 65.0056 1/(-1+x)^24 ogf A010976 71.5061 1/(x-1)^24 ogf A010976 16.2514 {(-n-2)*a(n+2)+(25+n)*a(n+1),a(0)=1,a(1)=24} ogf A010976 42.0624 {-a(n+1),a(0)=24} ogf_with_Euler_Transform A010977 61.4423 -1/(-1+x)^25 ogf A010977 67.028 -1/(x-1)^25 ogf A010977 52.6648 -25+(1-x)*f(x) lgdogf A010977 73.7308 -25/(-1+x) lgdogf A010977 16.757 {(-n-2)*a(n+2)+(26+n)*a(n+1),a(0)=1,a(1)=25} ogf A010977 43.371 {-a(n+1),a(0)=25} ogf_with_Euler_Transform A010978 53.5728 -26+(1-x)*f(x) lgdogf A010978 83.3355 -26/(x-1) lgdogf A010978 68.1836 1/(-1+x)^26 ogf A010978 75.002 1/(x-1)^26 ogf A010978 17.0459 {(-n-2)*a(n+2)+(27+n)*a(n+1),a(0)=1,a(1)=26} ogf A010978 44.1188 {-a(n+1),a(0)=26} ogf_with_Euler_Transform A010979 58.2679 -1/(-1+x)^27 ogf A010979 63.5649 -1/(x-1)^27 ogf A010979 49.9439 -27+(1-x)*f(x) lgdogf A010979 77.6905 -27/(x-1) lgdogf A010979 15.8912 {(-n-2)*a(n+2)+(28+n)*a(n+1),a(0)=1,a(1)=27} ogf A010979 41.1303 {-a(n+1),a(0)=27} ogf_with_Euler_Transform A010980 50.6158 -28+(1-x)*f(x) lgdogf A010980 78.7356 -28/(x-1) lgdogf A010980 64.4201 1/(-1+x)^28 ogf A010980 70.8621 1/(x-1)^28 ogf A010980 16.105 {(-n-2)*a(n+2)+(29+n)*a(n+1),a(0)=1,a(1)=28} ogf A010980 41.6836 {-a(n+1),a(0)=28} ogf_with_Euler_Transform A010981 60.0969 -1/(-1+x)^29 ogf A010981 65.5602 -1/(x-1)^29 ogf A010981 51.5116 -29+(1-x)*f(x) lgdogf A010981 80.1292 -29/(x-1) lgdogf A010981 16.3901 {(-n-2)*a(n+2)+(30+n)*a(n+1),a(0)=1,a(1)=29} ogf A010981 42.4213 {-a(n+1),a(0)=29} ogf_with_Euler_Transform A010982 51.9595 -30+(1-x)*f(x) lgdogf A010982 80.826 -30/(x-1) lgdogf A010982 66.1303 1/(-1+x)^30 ogf A010982 72.7434 1/(x-1)^30 ogf A010982 16.5326 {(-n-2)*a(n+2)+(31+n)*a(n+1),a(0)=1,a(1)=30} ogf A010982 42.7902 {-a(n+1),a(0)=30} ogf_with_Euler_Transform A010983 61.6646 -1/(-1+x)^31 ogf A010983 67.2705 -1/(x-1)^31 ogf A010983 52.8554 -31+(1-x)*f(x) lgdogf A010983 82.2195 -31/(x-1) lgdogf A010983 16.8176 {(-n-2)*a(n+2)+(32+n)*a(n+1),a(0)=1,a(1)=31} ogf A010983 43.528 {-a(n+1),a(0)=31} ogf_with_Euler_Transform A010984 49.2359 -32+(1-x)*f(x) lgdogf A010984 62.6638 1/(-1+x)^32 ogf A010984 68.9302 1/(x-1)^32 ogf A010984 15.666 {(-n-2)*a(n+2)+(33+n)*a(n+1),a(0)=1,a(1)=32} ogf A010984 40.5472 {-a(n+1),a(0)=32} ogf_with_Euler_Transform A010985 57.6994 -1/(-1+x)^33 ogf A010985 62.9448 -1/(x-1)^33 ogf A010985 49.4566 -33+(1-x)*f(x) lgdogf A010985 15.7362 {(-n-2)*a(n+2)+(34+n)*a(n+1),a(0)=1,a(1)=33} ogf A010985 40.729 {-a(n+1),a(0)=33} ogf_with_Euler_Transform A010986 49.8982 -34+(1-x)*f(x) lgdogf A010986 77.6194 -34/(x-1) lgdogf A010986 63.5068 1/(-1+x)^34 ogf A010986 69.8575 1/(x-1)^34 ogf A010986 15.8767 {(-n-2)*a(n+2)+(35+n)*a(n+1),a(0)=1,a(1)=34} ogf A010986 41.0926 {-a(n+1),a(0)=34} ogf_with_Euler_Transform A010987 59.2449 -1/(-1+x)^35 ogf A010987 64.6308 -1/(x-1)^35 ogf A010987 50.7814 -35+(1-x)*f(x) lgdogf A010987 78.9932 -35/(x-1) lgdogf A010987 16.1577 {(-n-2)*a(n+2)+(36+n)*a(n+1),a(0)=1,a(1)=35} ogf A010987 41.82 {-a(n+1),a(0)=35} ogf_with_Euler_Transform A010988 51.0022 -36+(1-x)*f(x) lgdogf A010988 79.3367 -36/(x-1) lgdogf A010988 64.9118 1/(-1+x)^36 ogf A010988 71.403 1/(x-1)^36 ogf A010988 16.228 {(-n-2)*a(n+2)+(37+n)*a(n+1),a(0)=1,a(1)=36} ogf A010988 42.0018 {-a(n+1),a(0)=36} ogf_with_Euler_Transform A010989 59.7601 -1/(-1+x)^37 ogf A010989 65.1928 -1/(x-1)^37 ogf A010989 51.2229 -37+(1-x)*f(x) lgdogf A010989 79.6801 -37/(x-1) lgdogf A010989 16.2982 {(-n-2)*a(n+2)+(38+n)*a(n+1),a(0)=1,a(1)=37} ogf A010989 42.1836 {-a(n+1),a(0)=37} ogf_with_Euler_Transform A010990 52.3269 -38+(1-x)*f(x) lgdogf A010990 81.3974 -38/(x-1) lgdogf A010990 66.5979 1/(-1+x)^38 ogf A010990 73.2576 1/(x-1)^38 ogf A010990 16.6495 {(-n-2)*a(n+2)+(39+n)*a(n+1),a(0)=1,a(1)=38} ogf A010990 43.0927 {-a(n+1),a(0)=38} ogf_with_Euler_Transform A010991 61.5632 -1/(-1+x)^39 ogf A010991 67.1599 -1/(x-1)^39 ogf A010991 52.7685 -39+(1-x)*f(x) lgdogf A010991 82.0843 -39/(x-1) lgdogf A010991 16.79 {(-n-2)*a(n+2)+(40+n)*a(n+1),a(0)=1,a(1)=39} ogf A010991 43.4564 {-a(n+1),a(0)=39} ogf_with_Euler_Transform A010992 48.4949 -40+(1-x)*f(x) lgdogf A010992 75.4364 -40/(x-1) lgdogf A010992 61.7207 1/(-1+x)^40 ogf A010992 67.8928 1/(x-1)^40 ogf A010992 15.4302 {(-n-2)*a(n+2)+(41+n)*a(n+1),a(0)=1,a(1)=40} ogf A010992 39.9369 {-a(n+1),a(0)=40} ogf_with_Euler_Transform A010993 57.5922 -1/(-1+x)^41 ogf A010993 62.8278 -1/(x-1)^41 ogf A010993 49.3647 -41+(1-x)*f(x) lgdogf A010993 15.707 {(-n-2)*a(n+2)+(42+n)*a(n+1),a(0)=1,a(1)=41} ogf A010993 40.6533 {-a(n+1),a(0)=41} ogf_with_Euler_Transform A010994 49.7996 -42+(1-x)*f(x) lgdogf A010994 77.4661 -42/(x-1) lgdogf A010994 63.3814 1/(-1+x)^42 ogf A010994 69.7195 1/(x-1)^42 ogf A010994 15.8453 {(-n-2)*a(n+2)+(43+n)*a(n+1),a(0)=1,a(1)=42} ogf A010994 41.0115 {-a(n+1),a(0)=42} ogf_with_Euler_Transform A010995 58.0996 -1/(-1+x)^43 ogf A010995 63.3814 -1/(x-1)^43 ogf A010995 49.7996 -43+(1-x)*f(x) lgdogf A010995 77.4661 -43/(x-1) lgdogf A010995 15.8453 {(-n-2)*a(n+2)+(44+n)*a(n+1),a(0)=1,a(1)=43} ogf A010995 41.0115 {-a(n+1),a(0)=43} ogf_with_Euler_Transform A010996 50.452 -44+(1-x)*f(x) lgdogf A010996 78.481 -44/(x-1) lgdogf A010996 64.2117 1/(-1+x)^44 ogf A010996 70.6329 1/(x-1)^44 ogf A010996 16.0529 {(-n-2)*a(n+2)+(45+n)*a(n+1),a(0)=1,a(1)=44} ogf A010996 41.5487 {-a(n+1),a(0)=44} ogf_with_Euler_Transform A010997 59.8756 -1/(-1+x)^45 ogf A010997 65.3188 -1/(x-1)^45 ogf A010997 51.3219 -45+(1-x)*f(x) lgdogf A010997 79.8341 -45/(x-1) lgdogf A010997 16.3297 {(-n-2)*a(n+2)+(46+n)*a(n+1),a(0)=1,a(1)=45} ogf A010997 42.2651 {-a(n+1),a(0)=45} ogf_with_Euler_Transform A010998 51.3219 -46+(1-x)*f(x) lgdogf A010998 79.8341 -46/(x-1) lgdogf A010998 65.3188 1/(-1+x)^46 ogf A010998 71.8507 1/(x-1)^46 ogf A010998 16.3297 {(-n-2)*a(n+2)+(47+n)*a(n+1),a(0)=1,a(1)=46} ogf A010998 42.2651 {-a(n+1),a(0)=46} ogf_with_Euler_Transform A010999 60.6367 -1/(-1+x)^47 ogf A010999 66.1491 -1/(x-1)^47 ogf A010999 51.9743 -47+(1-x)*f(x) lgdogf A010999 80.8489 -47/(x-1) lgdogf A010999 16.5373 {(-n-2)*a(n+2)+(48+n)*a(n+1),a(0)=1,a(1)=47} ogf A010999 42.8024 {-a(n+1),a(0)=47} ogf_with_Euler_Transform A011000 52.1918 -48+(1-x)*f(x) lgdogf A011000 81.1872 -48/(x-1) lgdogf A011000 66.4259 1/(-1+x)^48 ogf A011000 73.0685 1/(x-1)^48 ogf A011000 16.6065 {(-n-2)*a(n+2)+(49+n)*a(n+1),a(0)=1,a(1)=48} ogf A011000 42.9815 {-a(n+1),a(0)=48} ogf_with_Euler_Transform A011001 55.6706 -1/(-1+x)^49 ogf A011001 60.7316 -1/(x-1)^49 ogf A011001 47.7177 -49+(1-x)*f(x) lgdogf A011001 74.2275 -49/(x-1) lgdogf A011001 15.1829 {(-n-2)*a(n+2)+(50+n)*a(n+1),a(0)=1,a(1)=49} ogf A011001 39.2969 {-a(n+1),a(0)=49} ogf_with_Euler_Transform A011195 11.1193 -(-4*x-15*x^2-5*x^3)/(1-5*x+10*x^2-x^5-10*x^3+5*x^4) ogf A011195 25.1393 -(4+15*x+5*x^2)/(x-1)^5 ogf A011195 15.2159 -5*(7+14*x+3*x^2)/(x-1)/(5*x^2+15*x+4) lgdogf A011195 5.72479 {(12+4*n)*a(n+4)+(-13+11*n)*a(n+3)+(-80-10*n)*a(n+2)+(-15-5*n)*a(n+1),a(0)=0,a(1)=4,a(2)=35,a(3)=140} ogf A011197 8.00122 -(-20*x-195*x^2-230*x^3-35*x^4)/(1-6*x+x^6+15*x^2-20*x^3+15*x^4-6*x^5) ogf A011197 10.3719 -(63+287*x+21*x^3+205*x^2)/(x-1)/(7*x^3+46*x^2+39*x+4) lgdogf A011197 18.0673 5*(4+39*x+46*x^2+7*x^3)/(x-1)^6 ogf A011197 4.30835 {(-172662-122675*n-21707*n^2)*a(n+1)+(443360+177804*n+39742*n^2)*a(n+2)+(-74838-73489*n-18035*n^2)*a(n+3),a(0)=0,a(1)=20,a(2)=315} ogf A011199 25.531 (1+20*x+15*x^2)/(x-1)^4 ogf A011199 14.3223 -(1+20*x+15*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A011199 15.0567 -6*(4+15*x+5*x^2)/(x-1)/(15*x^2+20*x+1) lgdogf A011199 5.87212 {(n+4)*a(n+4)+(33+19*n)*a(n+3)+(-100-5*n)*a(n+2)+(-45-15*n)*a(n+1),a(0)=1,a(1)=24,a(2)=105,a(3)=280} ogf A011245 9.71908 -(-1-115*x-105*x^3-355*x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A011245 16.8655 -(1+115*x+355*x^2+105*x^3)/(x-1)^5 ogf A011245 10.0601 -30*(4+39*x+7*x^3+46*x^2)/(x-1)/(105*x^3+355*x^2+115*x+1) lgdogf A011245 4.34413 {(-515067-368606*n-65639*n^2)*a(n+1)+(478320+258368*n+82294*n^2)*a(n+2)+(-85698*n-107199-16655*n^2)*a(n+3),a(0)=1,a(1)=120,a(2)=945} ogf A011270 16.6293 1+(-1-2*x)*f(x)+(3*x+x^2)*f(x)^2-x^2*f(x)^3 ogf A011270 34.0505 x*(1-3*x+x^2)/(x-1)^2 revogf A011272 6.49778 1/2*(2*(5*x^2+2*x+1)^(1/2)*x+(5*x^2+2*x+1)^(1/2)-1-3*x-4*x^2)/x^2/(1+x) revogf A011272 10.7289 x+(-1+3*x)*f(x)+(4*x+x^2)*f(x)^2+x^2*f(x)^3 ogf A011272 3.5217 {(25*n^2+155*n+210)*a(n+1)+(35*n^2+232*n+372)*a(n+2)+(15*n^2+123*n+258)*a(n+3)+(5*n^2+46*n+96)*a(n+4),a(0)=0,a(1)=1,a(2)=-3,a(3)=5} revogf A011365 16.3316 -x^2-x*f(x)+(1-x)*f(x)^2-f(x)^3 ogf A011367 15.9761 (-1+x^2+x^3)/(-1+2*x+5*x^2+4*x^3+x^4) ogf A011367 15.9761 -(-1+x^3+x^2)/(1-2*x-5*x^2-4*x^3-x^4) ogf A011367 8.6929 -(x^2+x+1)*(x^4+x^3-3*x^2-6*x-2)/(x^3+x^2-1)/(x^4+4*x^3+5*x^2+2*x-1) lgdogf A011367 7.03711 -3+3*x^3+3*x^2+(11-6*x-3*x^4-20*x^3-23*x^2)*f(x)+(40*x^2+8*x^4-8+16*x+32*x^3)*f(x)^2 ogf A011369 12.1927 -(-1-x-2*x^2+7*x^3-x^4+2*x^6)/(x-1)/(x^2+x-1)/(x^4-x^3+2*x^2+x+1) ogf A011377 16.762 -(-3-x+8*x^2)/(x-1)/(2*x-1)/(x+1) lgdogf A011377 23.0477 -1/(x+1)/(2*x-1)/(x-1)^2 ogf A011377 6.21511 -320+(633-960*x-640*x^4+960*x^3+320*x^2)*f(x)+(-313*x^2-939*x^3-313+939*x+626*x^4)*f(x)^2 ogf A011377 22.1258 1/(1-3*x+x^2+3*x^3-2*x^4) ogf A011377 6.21511 {(-n-4)*a(n+4)+(9+2*n)*a(n+3)+(n+3)*a(n+2)+(-10-2*n)*a(n+1),a(0)=1,a(1)=3,a(2)=8,a(3)=18} ogf A011379 19.9399 -(-2*x-4*x^2)/(1-4*x+x^4+6*x^2-4*x^3) ogf A011379 33.5353 -6*(x+1)/(2*x+1)/(x-1) lgdogf A011379 6.1998 12302*x+24604*x^2+(-6151+29734*x-6151*x^4+24604*x^3-26646*x^2)*f(x)+(-2565+10260*x-2565*x^4-15390*x^2+10260*x^3)*f(x)^2 ogf A011379 43.3986 2*(2*x+1)/(x-1)^4 ogf A011379 11.1784 {(n+2)*a(n+3)+(-5+n)*a(n+2)+(-6-2*n)*a(n+1),a(0)=0,a(1)=2,a(2)=12} ogf A011531 7.43456 (10-8*x-80*x^12+11*x^10+87*x^11-19*x^18-143*x^19+144*x^20)/(x-1)/(8*x^20+x^19-8*x^12-x^11+8*x^2-8*x-1) lgdogf A011531 14.8691 -(-1-8*x+8*x^2-x^11-8*x^12+8*x^20+x^19)/(x^2+1-2*x) ogf A011531 16.1346 -(-1-8*x+8*x^2-x^11-8*x^12+x^19+8*x^20)/(x-1)^2 ogf A011557 38.2777 -1+(1-10*x)*f(x) ogf A011557 51.037 -1/(-1+10*x) ogf A011557 47.111 -10/(-1+10*x) lgdogf A011557 61.2444 1/(1-10*x) ogf A011557 40.8296 1/10*ln(1+10*x) revegf A011557 61.2444 x/(1+10*x) revogf A011557 26.628 {a(n+1)-10*a(n),a(0)=1} ogf A011558 9.1884 -(1+2*x+3*x^6+4*x^5+2*x^7+5*x^4+3*x^2)/(-1+x)/(x+1)/(x^2+1)/(x^4+x^3+x^2+x+1) lgdogf A011558 18.6186 -(x+1)*(x^2+1)/(x-1)/(x^4+x^3+x^2+x+1) ogf A011558 28.3003 -(x+x^2+x^3+x^4)/(-1+x^5) ogf A011558 12.634 -x-x^4-x^3-x^2+(1-x-x^4-x^3-x^5-x^2)*f(x)+(1-x^5)*f(x)^2 ogf A011558 78.6118 1-x^3+x^4 ogf_with_Euler_Transform A011582 11.3909 (1+x^2+2*x^3+3*x^4+2*x^5+x^6+x^8)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A011582 11.0988 -(x+3*x^5+2*x^4+2*x^6+x^9+x^7+x^3)/(-1-x-x^9-x^2-x^3-x^10-x^4-x^5-x^6-x^7-x^8) ogf A011582 16.9746 -(x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)/(-1+x^11) ogf A011583 14.264 -(x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12)/(-1+x^13) ogf A011583 8.44758 -(x-1)*(x+1)*(x^8+2*x^6+2*x^5+3*x^4+2*x^3+2*x^2+1)/(1+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A011632 4.78791 -1+(1+x^2)*f(x) ogf A011632 5.98488 -2*x/(1+x^2) lgdogf A011632 11.9698 -x+x^3 ogf_with_Euler_Transform A011632 7.97984 1/(x^2+1) ogf A011632 2.56495 {-a(n+2)-a(n),a(0)=1,a(1)=0} ogf A011633 2.31286 -(-1-x+x^3)/(x^4+1) ogf A011634 1.74739 -(-1-2*x+9*x^8+7*x^6+8*x^7-4*x^3+10*x^9+11*x^10-3*x^2)/(-1+x)/(x^2+1+x+x^4+x^3)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011634 18.3476 -1+x^4+x^6 ogf_with_Euler_Transform A011634 3.52839 -1/(x-1)/(x^4+x^3+x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) ogf A011635 2.18775 -(x-1)*(1+x^2+x)*(x+1)/(1-x^6+x^7) ogf A011636 5.39941 (1-x^3+x^9)/(x^4+1)/(x^8-x^4+1) ogf A011636 12.8755 -x^2+x^8+x^14 ogf_with_Euler_Transform A011637 4.85693 -(-1-x^2+x^6)/(x^8+1) ogf A011637 5.66642 x-x^3-x^5-x^9+x^11 ogf_with_Euler_Transform A011638 4.79381 (x-1)*(x+1)*(1+x^2+x)*(x^2-x+1)*(x^6-x^3+1)/(-1+x^18+x^21) ogf A011638 21.3878 -x^2+x^8+x^20 ogf_with_Euler_Transform A011639 39.6258 -1+x^4+x^12 ogf_with_Euler_Transform A011639 5.51752 -1/(x-1)/(x^4+x^3+x^2+x+1)/(1+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A011640 2.65704 -(-1-x+x^3+x^4-x^6-x^7+x^9)/(x^2+1)/(x^8-x^6+x^4-x^2+1) ogf A011640 1.67974 -2+(5-4*x+4*x^2)*f(x)+(-4+6*x-2*x^4+4*x^3-8*x^2)*f(x)^2+(-2*x+1+x^4-2*x^3+3*x^2)*f(x)^3 ogf A011640 9.13356 1-x-x^2+x^5-x^10 ogf_with_Euler_Transform A011641 1.76419 -(-1+2*x+9*x^8+7*x^6-8*x^7+4*x^3-10*x^9+11*x^10-3*x^2)/(x+1)/(x^4-x^3+x^2-x+1)/(x^6-x^5+x^4-x^3+x^2-x+1) lgdogf A011641 9.17381 1-x-x^4-x^6+x^9+x^13 ogf_with_Euler_Transform A011641 3.59757 1/(x+1)/(x^4-x^3+x^2-x+1)/(1-x+x^2-x^3+x^4-x^5+x^6) ogf A011642 50.8253 -1+x^6+x^10 ogf_with_Euler_Transform A011642 7.26076 -1/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A011642 6.57739 {a(n),a(0)=-1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=1,a(7)=0,a(8)=0,a(9)=0,a(10)=1} ogf_with_Euler_Transform A011643 3.15927 -(x-1)*(1+x^2+x)*(x+1)*(x^2-x+1)*(x^2+1)/(1-x^12+x^14) ogf A011644 56.544 -1+x^4+x^16 ogf_with_Euler_Transform A011644 6.28267 -1/(x-1)/(x^4+x^3+x^2+x+1)/(1+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A011644 14.136 1/(1+x+x^2+x^3+x^4-x^17-x^18-x^19-x^20-x^21) ogf A011645 5.07217 -(-1-x^3+x^9)/(x^4+1)/(x^8-x^4+1) ogf A011647 62.4067 -1+x^4+x^18 ogf_with_Euler_Transform A011647 6.29792 -1/(x-1)/(x^4+x^3+x^2+x+1)/(x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) ogf A011647 15.6017 1/(1+x+x^2+x^3+x^4-x^19-x^20-x^21-x^22-x^23) ogf A011648 5.15874 (1-x^3+x^9-x^12+x^18-x^21+x^27)/(x^2+1)/(x^8-x^6+x^4-x^2+1)/(x^4-x^2+1)/(x^16+x^14-x^10-x^8-x^6+x^2+1) ogf A011649 4.74526 -(-1-x+x^3+x^4-x^6-x^7+x^9+x^10-x^12-x^13+x^15)/(1+x^16) ogf A011649 16.6084 1-x-x^2+x^5-x^16 ogf_with_Euler_Transform A011651 2.58209 -(-1+2*x+4*x^3+11*x^10-3*x^2+13*x^12-14*x^13-12*x^11+15*x^14)/(x+1)/(x^4-x^3+x^2-x+1)/(x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1) lgdogf A011651 15.7385 1-x-x^4+x^9-x^10+x^21 ogf_with_Euler_Transform A011651 4.86041 1/(x+1)/(x^4-x^3+x^2-x+1)/(1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10) ogf A011652 5.11547 -(x-1)*(x+1)*(1+x^2+x)*(x^6+x^3+1)*(x^6-x^3+1)/(1-x^18+x^19) ogf A011652 19.183 1-x-x^2+x^5-x^18 ogf_with_Euler_Transform A011653 74.3062 -1+x^4+x^22 ogf_with_Euler_Transform A011653 17.7689 -1/(-1-x-x^2-x^3-x^4+x^23+x^24+x^25+x^26+x^27) ogf A011654 90.2466 -1+x^6+x^16 ogf_with_Euler_Transform A011654 9.27768 -1/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(1+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A011655 25.5968 -(1+2*x^3+3*x^2)/(x-1)/(x+1)/(x^2+x+1) lgdogf A011655 44.2126 -(x+1)/(x-1)/(1+x^2+x) ogf A011655 57.2163 -(x+x^2)/(-1+x^3) ogf A011655 23.7238 x+x^2+(-1+x+x^3+x^2)*f(x)+(-1+x^3)*f(x)^2 ogf A011655 138.954 x^2-x+1 ogf_with_Euler_Transform A011655 27.7908 {-a(n+3)+a(n),a(0)=0,a(1)=1,a(2)=1} ogf A011656 36.0251 -(-x^2-x^4-x^5-x^6)/(1-x^7) ogf A011656 20.2641 -(1+x^2+x^3+x^4)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) ogf A011656 10.929 -x*(2+5*x^7+7*x^5+4*x^2+4*x^8+3*x^9+3*x)/(-1+x)/(x^4+x^3+x^2+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011657 8.22682 -(1+2*x+5*x^8+7*x^6+6*x^7+4*x^3+3*x^10)/(-1+x)/(x^4+x^2+x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011657 15.3806 -(1+x+x^2+x^4)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) ogf A011657 26.2039 -(x^2+x^3+x^4+x^6)/(-1+x^7) ogf A011658 15.0533 -(1+4*x^5+5*x^4)/(x^4+x^3+x^2+x+1)/(-1+x)/(x+1) lgdogf A011658 23.5835 -(x+1)/(x-1)/(x^4+x^3+x^2+x+1) ogf A011658 37.2372 -(x^3+x^4)/(-1+x^5) ogf A011658 33.6908 -x^3-x^4+(1-x^5)*f(x) ogf A011658 101.072 1-x+x^4 ogf_with_Euler_Transform A011659 15.0533 -(-x^3-x^4-x^5-x^6-x^8-x^10-x^11-x^14)/(1-x^15) ogf A011659 7.7748 -(1+x+x^2+x^3+x^5+x^7+x^8+x^11)/(x-1)/(x^4+x^3+x^2+x+1)/(1+x^2+x)/(1-x+x^3-x^4+x^5-x^7+x^8) ogf A011671 14.1501 -(-x^5-x^7-x^10-x^13-x^14-x^17-x^19-x^20)/(1-x^21) ogf A011671 6.26112 -(1+x^2+x^5+x^8+x^9+x^12+x^14+x^15)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(1+x^2+x)/(1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12) ogf A011672 37.2372 -(-x^5-x^8)/(1-x^9) ogf A011672 16.0797 -(x^2-x+1)*(x+1)/(x-1)/(1+x^2+x)/(x^6+x^3+1) ogf A011672 10.5598 -3*x^2*(1+3*x^6+2*x^9)/(-1+x)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^6+x^3+1) lgdogf A011672 64.3188 x^2-x^5+x^8 ogf_with_Euler_Transform A011693 6.37393 -(x+1)*(x^8-x^7+x^6+x^4+x^2-x+1)/(x-1)/(1+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A011693 17.2563 -(x^7+x^10+x^11+x^12+x^13+x^16)/(-1+x^17) ogf A011707 6.73816 -(x+1)*(x^8+x^5-x^4+x^3+1)/(x-1)/(1+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A011707 17.6877 -(x^7+x^8+x^10+x^13+x^15+x^16)/(-1+x^17) ogf A011733 9.3093 -(-x^2-x^5-x^8-x^11-3*x^19-2*x^22-2*x^36)/(1+x^3+x^6+x^9+2*x^17+2*x^20-x^23) ogf_with_Euler_Transform A011734 8.84383 -(-x-x^3-x^5-x^7-x^20-2*x^22-4*x^24-2*x^26)/(1+x^2+x^4+x^6+2*x^21+3*x^23+2*x^25) ogf_with_Euler_Transform A011735 11.9916 -(-1-x+x^24-x^2-x^3+x^21-x^22)/(x^2+1+x+x^23-x^24+x^22+x^3) ogf_with_Euler_Transform A011735 11.9916 -(-1-x-x^2+x^21-x^3-x^22+x^24)/(x^2+1+x+x^23-x^24+x^22+x^3) ogf_with_Euler_Transform A011735 13.6059 -(-1-x-x^2-x^3+2*x^24)/(x-1)/(x+1)/(x^23-x^22-x^2-1) ogf A011736 14.4389 -(-x^4-x^9-x^14-x^19-x^22)/(1+x^5+x^10+x^15-x^28) ogf_with_Euler_Transform A011738 15.3806 -(-x^2-x^5-x^8-x^11-x^24)/(1+x^3+x^6+x^9-x^28) ogf_with_Euler_Transform A011741 22.8228 -(-x^27-x^30)/(1-x^6-x^28+x^31) ogf A011741 29.4794 -(x^2+x^5+x^27)/(-1-x^3) ogf_with_Euler_Transform A011742 6.55099 (-1-2*x^4-2*x^6-2*x^2-2*x^12-2*x^14-2*x^8-2*x^10-2*x^20-2*x^22-2*x^16-2*x^18+x^25+x^27)/(-1-x^2+x^25+2*x^24) ogf A011742 22.8228 -(-x^28-x^30)/(1-x^4-x^29+x^31) ogf A011742 32.1594 -(x+x^3)/(-1-x^2+x^27) ogf_with_Euler_Transform A011744 9.5609 (-1-2*x^3-2*x^6-2*x^15-2*x^18-2*x^9-2*x^12+x^25+x^28)/(-1-x^3+2*x^21+x^25) ogf A011744 22.8228 -(-x^30-x^33)/(1-x^6-x^31+x^34) ogf A011744 29.4794 -(x^2+x^5)/(-1-x^3+x^28) ogf_with_Euler_Transform A011745 17.2563 -(-x^31-x^32)/(1-x^2+x^27-x^29-x^32+x^33) ogf A011758 10.6262 1/(1-x) ogf A011760 17.4167 (2+12*x^11-23*x^12+11*x^13)/(x-1)/(x^13-x^12-1) lgdogf A011760 30.318 -(-1-x^12+x^13)/(1-2*x+x^2) ogf A011760 35.5906 -(-1-x^12+x^13)/(x-1)^2 ogf A011761 28.4975 -(-1-4*x^2)/(1-x-x^3) ogf A011761 28.4975 -(1+4*x^2)/(-1+x+x^3) ogf A011761 15.7486 -(1+8*x+4*x^4-x^2)/(1+4*x^2)/(x^3+x-1) lgdogf A011761 8.42884 673+2692*x^2+(-700+673*x+673*x^3-108*x^2)*f(x)+(-27*x^3+27-27*x)*f(x)^2 ogf A011761 14.5963 {a(n+3)-a(n+2)-a(n),a(0)=1,a(1)=1,a(2)=5} ogf A011763 19.9838 -(365+365*x+365*x^2+366*x^3)/(-1+x^4) ogf A011763 15.4041 -(365+365*x+365*x^2+366*x^3)/(x-1)/(x+1)/(x^2+1) ogf A011763 7.17863 -(365+730*x+1098*x^2+1460*x^3+1095*x^4+730*x^5+366*x^6)/(x-1)/(x+1)/(x^2+1)/(366*x^3+365*x^2+365*x+365) lgdogf A011763 14.788 {-a(n+4)+a(n),a(0)=365,a(1)=365,a(2)=365,a(3)=366} ogf A011765 39.6269 -1/(x-1)/(x+1)/(x^2+1) ogf A011765 33.5304 -4*x^3/(x^2+1)/(x-1)/(x+1) lgdogf A011765 36.3246 -x^3*f(x)+(1-x^4)*f(x)^2 ogf A011765 290.597 x^3 ogf_with_Euler_Transform A011765 79.2537 x^3/(1-x^4) ogf A011765 23.5619 {-a(n+4),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf_with_Euler_Transform A011765 21.2632 {a(n+4)-a(n),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A011769 11.0291 -(-1+3*x+3*x^2-9*x^3-3*x^4+3*x^5)/(3*x-1)/(x+1)/(x^2-3*x+1)/(x^2+x-1) ogf A011779 27.1166 -1/(1+x^2+x)^2/(x-1)^5 ogf A011779 19.8855 -3*(1+x+3*x^2)/(x-1)/(x^2+x+1) lgdogf A011779 10.8466 1/(1-3*x+3*x^2-3*x^3+6*x^4-6*x^5+3*x^6-3*x^7+3*x^8-x^9) ogf A011779 85.2235 3+2*x^2 ogf_with_Euler_Transform A011779 7.84954 {(-n-4)*a(n+4)+3*a(n+3)+3*a(n+2)+(10+n)*a(n+1),a(0)=1,a(1)=3,a(2)=6,a(3)=12} ogf A011779 20.5712 {a(n+3),a(0)=3,a(1)=0,a(2)=2} ogf_with_Euler_Transform A011780 21.5267 -1/(x-1)^2/(x+1)^2/(2*x-1)^3 ogf A011780 12.301 1/(1-6*x+10*x^2+4*x^3-23*x^4+10*x^5+12*x^6-8*x^7) ogf A011780 6.62361 {(-n-4)*a(n+4)+(12+2*n)*a(n+3)+(6+n)*a(n+2)+(-16-2*n)*a(n+1),a(0)=1,a(1)=6,a(2)=26,a(3)=92} ogf A011781 30.0092 -1+(1-6*x)*f(x)^2 egf A011781 34.0104 -1/2*x*(-2+3*x) revegf A011781 51.0157 -3/(6*x-1) lgdegf A011781 34.0104 1/(1-6*x)^(1/2) egf A011781 13.4252 {(-6*n-9)*a(n+1)+a(n+2),a(0)=1,a(1)=3} ogf A011782 53.7925 (x-1)/(2*x-1) ogf A011782 46.6201 -(-1+x)/(1-2*x) ogf A011782 41.1354 -1+x+(1-2*x)*f(x) ogf A011782 46.6201 1/(2*x-1)/(x-1) lgdogf A011782 27.9721 1/2+x-1/2*(4*x^2+1)^(1/2) revogf A011782 22.5581 {a(n+2)-2*a(n+1),a(0)=1,a(1)=1} ogf A011783 8.71385 -(-1+2*x)/(x^2+1-3*x) ogf A011783 5.38209 -(1-2*x+2*x^2)/(2*x-1)/(x^2-3*x+1) lgdogf A011783 9.14955 -(2*x-1)/(x^2-3*x+1) ogf A011783 4.69208 -1/2*(-1-3*x+(1-2*x+5*x^2)^(1/2))/(x+2) revogf A011783 3.81231 -2+4*x+(5-12*x+2*x^2)*f(x)+(-3*x^2-3+9*x)*f(x)^2 ogf A011783 5.08308 {a(n+2)-3*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A011791 8.23387 x/(1+2*x+4*x^2+3*x^3+x^4) revogf A011795 8.665 -(3+2*x+7*x^6-4*x^5+9*x^4+4*x^3+4*x^2)/(x-1)/(x^2-x+1)/(x^4+x^3+x^2+x+1) lgdogf A011795 17.33 -(x^2-x+1)/(x^4+x^3+x^2+x+1)/(x-1)^5 ogf A011795 9.59815 -(x^5-x^6+x^7)/(-1+4*x-6*x^2+4*x^3-x^4+x^5-4*x^6+x^9+6*x^7-4*x^8) ogf A011795 41.592 3+x+x^2+x^4-x^5 ogf_with_Euler_Transform A011796 9.78563 (1+x+2*x^2+2*x^3+3*x^4+2*x^6+x^7)/(x^2-x+1)/(1+x^2+x)^2/(x+1)^3/(x-1)^6 ogf A011797 6.52295 -(4+4*x+13*x^6+6*x^5-5*x^7+6*x^4+6*x^3+9*x^8+6*x^2)/(x-1)/(x^2-x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011797 13.1877 -(x^2-x+1)^2/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^7 ogf A011797 28.8874 4+2*x+2*x^2-2*x^5+x^6 ogf_with_Euler_Transform A011800 14.2691 (-2-x^2+2*x)*f(x)+(2-4*x+2*x^2)*f(x)^2 lgdegf A011800 23.5751 1/2*(2-2*x+x^2)/(x-1)^2 lgdegf A011800 15.4922 1/exp(1/2)*exp(1/2*(x^2-x-1)/(x-1)) egf A011800 5.58997 {(5*n+n^2+6)*a(n+1)+(-12*n-2*n^2-18)*a(n+2)+(14+4*n)*a(n+3)-2*a(n+4),a(0)=1,a(1)=1,a(2)=2,a(3)=7} ogf A011819 7.81806 -(-2+9*x-23*x^2+25*x^3-19*x^4+7*x^5-x^6)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A011819 14.3054 -(2-9*x+23*x^2-25*x^3+19*x^4-7*x^5+x^6)/(x-1)^7 ogf A011819 8.00421 -(5-8*x+40*x^2-24*x^3+22*x^4-8*x^5+x^6)/(x-1)/(x^6-7*x^5+19*x^4-25*x^3+23*x^2-9*x+2) lgdogf A011820 7.2808 -(2-16*x+76*x^2-149*x^3+341*x^4-298*x^5+268*x^6+53*x^8-147*x^7-11*x^9+x^10)/(x-1)^11 ogf A011826 16.8088 -(-2+5*x-5*x^2+x^3)/(6*x^2+1-4*x+x^4-4*x^3) ogf A011826 26.7696 -(-2+5*x-5*x^2+x^3)/(x-1)^4 ogf A011826 16.8088 -(-3+5*x-7*x^2+x^3)/(x-1)/(x^3-5*x^2+5*x-2) lgdogf A011826 9.9011 -2+5*x+x^3-5*x^2+(-1+x+x^4-3*x^3+x^2)*f(x)+(1-4*x+6*x^2-4*x^3+x^4)*f(x)^2 ogf A011826 7.08608 {(750+613*n+119*n^2)*a(n+1)+(-396-720*n-198*n^2)*a(n+2)+(227*n-30+79*n^2)*a(n+3),a(0)=2,a(1)=3,a(2)=5} ogf A011827 7.71644 -(-2+11*x-26*x^2+32*x^3-25*x^4+7*x^5-x^6)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A011827 13.986 -(2-11*x+26*x^2-32*x^3+25*x^4-7*x^5+x^6)/(x-1)^7 ogf A011827 7.80616 -(3-14*x+34*x^2-28*x^3+40*x^4-8*x^5+x^6)/(x-1)/(x^6-7*x^5+25*x^4-32*x^3+26*x^2-11*x+2) lgdogf A011828 7.41564 -(2-19*x+82*x^2-210*x^3+356*x^4-400*x^5+380*x^6+69*x^8-130*x^7-11*x^9+x^10)/(x-1)^11 ogf A011842 11.4214 (x^2-x+1)*(x^4-x^3+x^2+1)/(x+1)/(x^2+1)/(x^4+1)/(x-1)^4 ogf A011842 7.85219 -(-x^10+2*x^9-x^4+x^5-2*x^6+2*x^7-3*x^8)/(1-3*x+3*x^2-x^3-x^8+3*x^9-3*x^10+x^11) ogf A011848 29.4382 -(3-2*x+5*x^2)/(x-1)/(1+x^2) lgdogf A011848 45.7927 -1/(x^2+1)/(x-1)^3 ogf A011848 117.753 3-x+x^3 ogf_with_Euler_Transform A011848 21.1351 x^3+(-1+3*x-4*x^2+4*x^3-3*x^4+x^5)*f(x) ogf A011848 24.9779 x^3/(1-3*x+4*x^2-4*x^3+3*x^4-x^5) ogf A011848 9.93096 {(n+3)*a(n+1)+(-n-1)*a(n+2)+(n+3)*a(n+3)+(-n-1)*a(n+4),a(0)=0,a(1)=0,a(2)=0,a(3)=1} ogf A011849 15.1365 (x^2-x+1)*(x^3-x^2+1)/(x^6+x^3+1)/(x-1)^4 ogf A011849 5.54105 -(18*x^9-4*x^8-13*x^10+3*x^2+5*x^11-3*x+21*x^6-7*x^5-13*x^7-x^4+3*x^3+3)/(x-1)/(x^2-x+1)/(x^3-x^2+1)/(x^6+x^3+1) lgdogf A011849 7.05225 -(x^9+x^4-x^5+2*x^7-2*x^8)/(-1+4*x-6*x^2+3*x^3+3*x^4+3*x^7-6*x^5-6*x^8+3*x^6+4*x^9-x^10) ogf A011850 7.37776 -(1-2*x+3*x^2-3*x^3+2*x^4-x^5+2*x^6+3*x^8-3*x^7-2*x^9+x^10)/(x^4+1)/(x^8+1)/(x-1)^5 ogf A011853 6.32834 -(5+4*x+14*x^6+7*x^5-5*x^7+7*x^4+7*x^3+10*x^8+7*x^2)/(x-1)/(x^2-x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011853 28.3269 5+2*x+2*x^2-2*x^5+x^6 ogf_with_Euler_Transform A011858 23.0168 -(-x^5-x^3)/(1-2*x+x^2-x^7-x^5+2*x^6) ogf A011858 12.166 -(2+4*x+2*x^5+5*x^6+9*x^4+4*x^3+4*x^2)/(x-1)/(x^2+1)/(x^4+x^3+x^2+x+1) lgdogf A011858 25.0477 -(x^2+1)/(x^4+x^3+x^2+x+1)/(x-1)^3 ogf A011858 77.4202 2+x-x^3+x^4 ogf_with_Euler_Transform A011860 22.9987 -(-x^4-x^6)/(1-2*x+x^2-x^7+2*x^8-x^9) ogf A011860 9.3511 -(2+4*x+4*x^5+11*x^6+2*x^7+7*x^8+4*x^3+4*x^4+4*x^2)/(x-1)/(x^2+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011860 20.2607 -(x^2+1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A011860 77.3591 2+x-x^3+x^6 ogf_with_Euler_Transform A011861 10.2133 -(2-2*x+7*x^8-12*x^7+19*x^6-8*x^3+13*x^4-14*x^5+7*x^2)/(x-1)/(x^2+1)/(x^2-x+1)/(x^4+1) lgdogf A011861 25.8336 -(x^2-x+1)/(x^2+1)/(x^4+1)/(x-1)^3 ogf A011861 12.7296 -(x^6-x^5+x^4)/(-1+3*x-4*x^2+4*x^3-4*x^4+4*x^5-3*x^8-4*x^6+4*x^7+x^9) ogf A011861 67.5649 2+x^2-x^5+x^7 ogf_with_Euler_Transform A011862 7.63208 -(2+2*x+7*x^12+2*x^11+2*x^10+2*x^9+13*x^8+4*x^7+4*x^6+6*x^3+4*x^4+4*x^5+2*x^2)/(x-1)/(x^2+x+1)/(x^6+x^3+1)/(x^4+1) lgdogf A011862 22.8962 -(x^4+1)/(1+x^2+x)/(x^6+x^3+1)/(x-1)^3 ogf A011862 22.3092 -(x^4+x^8)/(-1+2*x-x^2+x^9-2*x^10+x^11) ogf A011862 66.9275 2+x^3-x^7+x^8 ogf_with_Euler_Transform A011863 30.2244 -(1+x^2+x)/(x+1)/(x-1)^5 ogf A011863 16.8694 -(5+12*x+4*x^3+9*x^2)/(x-1)/(x+1)/(x^2+x+1) lgdogf A011863 16.8694 -(x+x^3+x^2)/(-1+4*x+5*x^4-5*x^2+x^6-4*x^5) ogf A011863 103.626 5-x^2+x ogf_with_Euler_Transform A011863 4.96839 {(1656+1054*n+160*n^2)*a(n+1)+(6730+2697*n+193*n^2)*a(n+2)+(2956+358*n-160*n^2)*a(n+3)+(-2118-1285*n-193*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=5,a(3)=16} ogf A011864 15.3222 -(-x^4+x^5-x^6-x^8+x^9-x^10)/(1-2*x+x^2-x^11+2*x^12-x^13) ogf A011864 12.6575 -(x^2-x+1)*(x^4+1)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^3 ogf A011864 36.3902 1+x+x^2+x^3-x^5-x^7+x^10 ogf_with_Euler_Transform A011865 6.9354 -(1+2*x+7*x^12-6*x^11+9*x^10-12*x^9+14*x^8-4*x^7+8*x^6+3*x^4-6*x^5+2*x^2)/(x-1)/(x^2+x+1)/(x^4-x^3+x^2-x+1)/(x^2+1)/(x^4-x^2+1) lgdogf A011865 15.7285 -(x^4-x^3+x^2-x+1)/(x^2+1)/(1+x^2+x)/(x^4-x^2+1)/(x-1)^3 ogf A011865 11.1493 -(x^6-x^5+x^4-x^7+x^8)/(-1+2*x-x^2+x^3-2*x^4+x^5-2*x^10-x^6+2*x^7-x^8+x^9+x^11) ogf A011865 36.6998 1+x+x^2+x^4-x^5-x^9+x^11 ogf_with_Euler_Transform A011866 21.381 -(-x^5-x^11)/(1-2*x+x^2-x^13+2*x^14-x^15) ogf A011866 10.8225 -(x^2+1)*(x^4-x^2+1)/(1+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^3 ogf A011866 58.4415 2+x^5-x^11+x^12 ogf_with_Euler_Transform A011867 12.6887 -(2+2*x+2*x^2+2*x^3+2*x^4+2*x^5+9*x^6)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011867 24.6724 -1/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^3 ogf A011867 177.641 2+x^6 ogf_with_Euler_Transform A011867 30.6278 x^5/(1-2*x+x^2-x^7+2*x^8-x^9) ogf A011868 11.2749 -(-x^5+x^7-x^8-x^10+x^11-x^13)/(1-2*x+x^2-x^15+2*x^16-x^17) ogf A011868 7.73508 -(1-x^2+x^3+x^5-x^6+x^8)/(1+x^2+x)/(x^4+x^3+x^2+x+1)/(1-x+x^3-x^4+x^5-x^7+x^8)/(x-1)^3 ogf A011869 12.8154 -(x^2-x+1)*(1-x+x^2-x^3+x^4-x^5+x^6)/(x^2+1)/(x^4+1)/(x^8+1)/(x-1)^3 ogf A011870 15.0371 -(-x^5+x^6-x^7-x^13+x^14-x^15)/(1-2*x+x^2-x^17+2*x^18-x^19) ogf A011870 8.96151 -(x^2-x+1)*(x^8+1)/(1+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^3 ogf A011871 15.7676 (1/x^10+1/x^11+1/x^9+1/x^7+1/x^8+1)/(x+1)/(x^2-x+1)*x^11 ogf_with_Euler_Transform A011871 20.5345 -(-x^5+x^6-x^7)/(1-2*x+x^2-x^9+2*x^10-x^11) ogf A011871 8.65671 -(1+2*x+9*x^10-8*x^9+11*x^8+2*x^7+2*x^6+2*x^3+2*x^4+2*x^5+2*x^2)/(x-1)/(x^2+x+1)/(x^2-x+1)/(x^6+x^3+1) lgdogf A011871 22.0746 -(x^2-x+1)/(1+x^2+x)/(x^6+x^3+1)/(x-1)^3 ogf A011872 11.5626 -(-x^5+x^6-x^7+x^8-x^9-x^13+x^14-x^15+x^16-x^17)/(1-2*x+x^2-x^19+2*x^20-x^21) ogf A011873 8.58035 -(x^2-x+1)*(x^6-x^3+1)/(x^2+1)/(x^4+x^3+x^2+x+1)/(x^8-x^6+x^4-x^2+1)/(x-1)^3 ogf A011873 26.0843 1+x+x^4+x^8-x^9-x^17+x^19 ogf_with_Euler_Transform A011874 10.9844 -(-x^6+x^8-x^9-x^15+x^16-x^18)/(1-2*x+x^2-x^21+2*x^22-x^23) ogf A011874 6.11398 -(1-x^2+x^3+x^12+x^9-x^10)/(1+x^2+x)/(x^6+x^5+x^4+x^3+x^2+x+1)/(1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12)/(x-1)^3 ogf A011875 14.6459 -(x^2-x+1)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^3 ogf A011875 20.3045 -(x^6-x^7+x^8)/(-1+2*x-x^2+x^11-2*x^12+x^13) ogf A011875 55.8373 1+x+x^2-x^5+x^10 ogf_with_Euler_Transform A011876 11.2552 -(x^6-x^7+x^8-x^10+x^11+x^15-x^16+x^18-x^19+x^20)/(-1+2*x-x^2+x^23-2*x^24+x^25) ogf A011876 35.5665 1+x+x^2-x^3+x^6-x^20+x^22 ogf_with_Euler_Transform A011877 9.31504 -(1-x+x^2-x^3+x^6-x^11+x^12-x^9+x^10)/(x^2+1)/(1+x^2+x)/(x^4-x^2+1)/(x^4+1)/(x^8-x^4+1)/(x-1)^3 ogf A011878 8.48528 -(-x^6+x^7-x^8+x^9-x^10-x^18+x^19-x^20+x^21-x^22)/(1-2*x+x^2-x^25+2*x^26-x^27) ogf A011879 12.4112 -(-x^6+x^7-x^8+x^9-x^10)/(1-2*x+x^2-x^13+2*x^14-x^15) ogf A011879 8.32647 -(x^4-x^3+x^2-x+1)/(1+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^3 ogf A011879 41.112 1+x+x^4-x^9+x^12 ogf_with_Euler_Transform A011880 9.06058 -(-x^6+x^7-x^8+x^9-x^10+x^12-x^13-x^17+x^18-x^20+x^21-x^22+x^23-x^24)/(1-2*x+x^2-x^27+2*x^28-x^29) ogf A011880 11.0992 -(x^2-x+1)*(x^16-x^13+x^11+x^5-x^3+1)/(1+x^2+x)/(x^6+x^3+1)/(x^18+x^9+1)/(x-1)^3 ogf A011883 16.8691 -(-x^6+x^7-x^9+x^11-x^12)/(1-2*x+x^2-x^15+2*x^16-x^17) ogf A011883 10.8444 -(x^2-x+1)*(x^4-x^2+1)/(1+x^2+x)/(x^4+x^3+x^2+x+1)/(1-x+x^3-x^4+x^5-x^7+x^8)/(x-1)^3 ogf A011883 47.9437 1+x^2+x^3-x^11+x^14 ogf_with_Euler_Transform A011886 22.7531 (1+3*x+2*x^3)/(x+1)/(x^2+1)/(x-1)^4 ogf A011886 13.9712 -(-2*x^6-3*x^4-x^3)/(1-3*x+3*x^2-x^3-3*x^6-x^4+x^7+3*x^5) ogf A011886 10.4784 -2*(3+6*x+3*x^5+4*x^6+12*x^4+11*x^3+9*x^2)/(x-1)/(x+1)/(2*x^3+3*x+1)/(x^2+1) lgdogf A011887 13.1858 (1+x+3*x^2-x^3+2*x^4)/(x^4+x^3+x^2+x+1)/(x-1)^4 ogf A011887 9.38988 -(-x^6+2*x^7+3*x^5+x^4+x^3)/(-1+3*x-3*x^2+x^3-3*x^6+x^5-x^8+3*x^7) ogf A011887 6.19732 -(4+12*x+21*x^6+19*x^5+x^7+23*x^4+20*x^3+8*x^8+12*x^2)/(x-1)/(x^4+x^3+x^2+x+1)/(2*x^4-x^3+3*x^2+x+1) lgdogf A011888 25.4657 (1+x^2+x)/(x+1)/(x-1)^6 ogf A011888 13.3116 -(6+14*x+5*x^3+11*x^2)/(x-1)/(x+1)/(x^2+x+1) lgdogf A011888 10.6493 -(x+x^2+x^3)/(-1+5*x-x^7-9*x^2-9*x^5+5*x^3+5*x^4+5*x^6) ogf A011888 83.6729 6+x-x^2 ogf_with_Euler_Transform A011888 4.01171 {(2170+1169*n+147*n^2)*a(n+1)+(8226+2845*n+171*n^2)*a(n+2)+(3830+421*n-147*n^2)*a(n+3)+(-2226-1255*n-171*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=6,a(3)=22} ogf A011889 11.7012 (3-x+2*x^2+x^4+x^5)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^4 ogf A011889 4.80749 -(8+10*x+39*x^6+18*x^5+3*x^7+20*x^4+16*x^3+22*x^8+9*x^10+6*x^9+12*x^2+5*x^11)/(x-1)/(x^5+x^4+2*x^2-x+3)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011889 9.39646 -(x^9+2*x^6+x^8-x^5+3*x^4)/(-1+3*x-3*x^2+x^3-3*x^8+3*x^9+x^7-x^10) ogf A011890 10.7498 (3-2*x+3*x^2-x^3+2*x^4+x^6)/(x+1)/(x^2+1)/(x^4+1)/(x-1)^4 ogf A011890 8.06236 -(x^10+3*x^6-x^7+2*x^8-2*x^5+3*x^4)/(-1+3*x-3*x^2+x^3+x^8-x^11-3*x^9+3*x^10) ogf A011891 14.2497 (2-2*x+x^2+x^3-x^4+x^5)/(x^6+x^3+1)/(x-1)^4 ogf A011891 5.3749 -(-4*x+33*x^6-8*x^5-23*x^7-8*x^4+15*x^3+9*x^9+7*x^8-7*x^10-x^2+5*x^11+6)/(x-1)/(x^5-x^4+x^3+x^2-2*x+2)/(x^6+x^3+1) lgdogf A011891 6.66021 -(x^9+x^6+x^7-x^8-2*x^5+2*x^4)/(-1+4*x-6*x^2+3*x^3+3*x^4-6*x^5+3*x^6+3*x^7-6*x^8+4*x^9-x^10) ogf A011892 18.3428 (x^3+2)/(x^4+x^3+x^2+x+1)/(x-1)^4 ogf A011892 7.76041 -(6+6*x+3*x^6+3*x^5+5*x^7+19*x^4+9*x^3+9*x^2)/(-1+x)/(x^3+2)/(x^4+x^3+x^2+x+1) lgdogf A011892 11.8689 -(x^7+2*x^4)/(-1+3*x-3*x^2+x^3-3*x^6+x^5-x^8+3*x^7) ogf A011893 6.99533 (2-x+x^2+2*x^3-2*x^4+2*x^5+x^6+x^9)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^4 ogf A011893 6.91492 -(x^10+2*x^9+x^6+x^13+2*x^7-2*x^8-x^5+2*x^4)/(-1+3*x-3*x^2+x^3-3*x^12+3*x^13+x^11-x^14) ogf A011894 19.4064 (2-x+x^2)/(x+1)/(x^2+1)/(x-1)^4 ogf A011894 10.9382 -(-x^6+x^5-2*x^4)/(1-3*x+3*x^2-x^3-3*x^6-x^4+x^7+3*x^5) ogf A011894 9.39997 -(5+5*x+5*x^5-3*x^4+14*x^3+6*x^2)/(-1+x)/(x+1)/(1+x^2)/(x^2-x+2) lgdogf A011895 7.00813 (1+x+2*x^5+x^11+2*x^9-x^10)/(1+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^4 ogf A011895 8.11468 -(-2*x^9-2*x^13+x^14-x^15-x^5-x^4)/(1-3*x+3*x^2-x^3+3*x^14-x^13+x^16-3*x^15) ogf A011896 13.9323 (1+x-x^2+2*x^3-x^4+x^5)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^4 ogf A011896 6.10877 -(4+4*x+16*x^6+9*x^5+5*x^11+9*x^2+5*x^3+11*x^4-2*x^8+12*x^7-3*x^10+14*x^9)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x^5-x^4+2*x^3-x^2+x+1) lgdogf A011896 11.6785 -(x^9-x^6+2*x^7-x^8+x^5+x^4)/(-1+3*x-3*x^2+x^3-3*x^8+3*x^9+x^7-x^10) ogf A011897 16.2021 (1+x-x^2+x^3)/(x^4+x^3+x^2+x+1)/(x-1)^4 ogf A011897 7.61303 -(4+4*x-3*x^6+7*x^5+5*x^7+11*x^4+6*x^3+6*x^2)/(x-1)/(x^3-x^2+x+1)/(x^4+x^3+x^2+x+1) lgdogf A011897 11.2836 -(x^6-x^7-x^5-x^4)/(1-3*x+3*x^2-x^3-x^5+3*x^6-3*x^7+x^8) ogf A011898 7.21977 (1+x^14+x^2+2*x^6+3*x^8+x^11+x^12-x^13-2*x^7-x^9)/(x+1)/(x^2+1)/(x^4+1)/(x^8+1)/(x-1)^4 ogf A011900 18.0707 -(1-4*x+x^2)/(-7*x^2-1+7*x+x^3) ogf A011900 10.0034 -(3-12*x-8*x^3+x^4+24*x^2)/(x-1)/(x^2-4*x+1)/(x^2+1-6*x) lgdogf A011900 18.6731 -(x^2+1-4*x)/(x-1)/(x^2-6*x+1) ogf A011900 7.46922 4-16*x+4*x^2+(37-136*x+4*x^3+13*x^2)*f(x)+(-41+287*x-287*x^2+41*x^3)*f(x)^2 ogf A011900 10.3739 {-a(n+3)+7*a(n+2)-7*a(n+1)+a(n),a(0)=1,a(1)=3,a(2)=15} ogf A011903 11.6384 (1-x+2*x^2-x^4+x^5)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^4 ogf A011903 5.22743 -(2+4*x-3*x^7+8*x^4+2*x^3+5*x^11-3*x^10+16*x^8+13*x^6+6*x^5+6*x^2)/(x-1)/(x^5-x^4+2*x^2-x+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011903 9.63808 -(x^9+2*x^6-x^8-x^5+x^4)/(-1+3*x-3*x^2+x^3-3*x^8+3*x^9+x^7-x^10) ogf A011904 7.13836 (1-x+2*x^2-x^3+x^4-x^5+2*x^6-x^8+x^9)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^4 ogf A011904 7.13836 -(2*x^10-x^9+2*x^6+x^13-x^7+x^8-x^12-x^5+x^4)/(-1+3*x-3*x^2+x^3-3*x^12+3*x^13+x^11-x^14) ogf A011906 10.5672 (-1+23*x-33*x^2+3*x^3)/(x-1)/(x^2-34*x+1)/(x^2-6*x+1) ogf A011912 17.1814 (x^2-2*x+2)/(x^4+x^3+x^2+x+1)/(x-1)^4 ogf A011912 11.352 -(2*x^6-x^7-2*x^5)/(1-3*x+3*x^2-x^3-x^5+3*x^6-3*x^7+x^8) ogf A011912 8.36463 -(4+2*x+6*x^6-11*x^5+13*x^4+3*x^3+3*x^2)/(x-1)/(x^2-2*x+2)/(x^4+x^3+x^2+x+1) lgdogf A011915 7.54915 -(6+12*x+28*x^5+29*x^4+24*x^3+12*x^6+16*x^7+5*x^8+18*x^2)/(x-1)/(x^4+x^3+x^2+x+1)/(x^4+2*x^3+2*x+1) lgdogf A011915 9.70606 -(8*x^4+4*x^3+8*x^6+4*x^7)/(-1+4*x-6*x^2+4*x^3-4*x^6-x^4+6*x^7+x^5-4*x^8+x^9) ogf A011915 16.2471 -4*(1+2*x+2*x^3+x^4)/(x^4+x^3+x^2+x+1)/(x-1)^5 ogf A011916 22.8821 (x-3)/(x-1)/(x^2-14*x+1) ogf A011916 11.2076 -2*(-22+45*x-12*x^2+x^3)/(x-1)/(x-3)/(x^2-14*x+1) lgdogf A011916 4.42879 -398943+132981*x+(-58273179+17474005*x-132981*x^3+1994715*x^2)*f(x)+(292030800*x^2+19468720-292030800*x-19468720*x^3)*f(x)^2 ogf A011916 9.46845 {-a(n+3)+15*a(n+2)-15*a(n+1)+a(n),a(0)=3,a(1)=44,a(2)=615} ogf A011917 6.50553 -(-3*x^10-5*x^9-3*x^4-x^6-6*x^7-x^8-5*x^5)/(1-4*x+6*x^2-4*x^3+x^4+4*x^8-x^7+4*x^10-6*x^9-x^11) ogf A011917 8.99294 -(3+5*x+x^2+6*x^3+x^4+5*x^5+3*x^6)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^5 ogf A011918 19.0754 -(x+5)/(x-1)/(x^2-14*x+1) ogf A011918 11.6314 -2*(38-75*x+x^3)/(x+5)/(x-1)/(x^2-14*x+1) lgdogf A011918 8.22216 {a(n+3)-15*a(n+2)+15*a(n+1)-a(n),a(0)=5,a(1)=76,a(2)=1065} ogf A011919 5.87865 -(-5*x^11-3*x^9-2*x^4-3*x^7-4*x^8-2*x^12-5*x^5)/(1-4*x+6*x^2-4*x^3+x^4-x^9+4*x^12+4*x^10-6*x^11-x^13) ogf A011919 8.73152 -(2+5*x+3*x^3+4*x^4+3*x^5+2*x^8+5*x^7)/(1+x^2+x)/(x^6+x^3+1)/(x-1)^5 ogf A011920 8.6494 -12*(1-44*x+11*x^2)/(x-1)/(x^2-14*x+1)/(x^2-194*x+1) ogf A011921 6.24077 -2*(1+x+2*x^2+x^4+2*x^5+x^6+2*x^8+x^9+x^10)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^5 ogf A011922 13.2216 -(1-12*x+3*x^2)/(-15*x^2-1+15*x+x^3) ogf A011922 13.9994 -(1-12*x+3*x^2)/(x-1)/(x^2-14*x+1) ogf A011922 5.40886 -23+276*x-69*x^2+(343-4185*x-23*x^3+1305*x^2)*f(x)+(-320+4800*x-4800*x^2+320*x^3)*f(x)^2 ogf A011922 7.80294 -3*(1-8*x+x^4-8*x^3+46*x^2)/(x-1)/(3*x^2-12*x+1)/(x^2-14*x+1) lgdogf A011922 8.49963 {-a(n+3)+15*a(n+2)-15*a(n+1)+a(n),a(0)=1,a(1)=3,a(2)=33} ogf A011924 6.64942 -(-x^10-4*x^9-x^4+x^6-4*x^7+x^8-4*x^5)/(1-4*x+6*x^2-4*x^3+x^4+4*x^8-x^7+4*x^10-6*x^9-x^11) ogf A011924 9.06739 -(1+4*x-x^2+4*x^3-x^4+4*x^5+x^6)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^5 ogf A011925 7.52993 -(-x^4+2*x^6-4*x^7-x^8-4*x^5)/(1-4*x+6*x^2-4*x^3+x^4-x^5+4*x^6-6*x^7+4*x^8-x^9) ogf A011925 11.8973 -(1+4*x-2*x^2+4*x^3+x^4)/(x^4+x^3+x^2+x+1)/(x-1)^5 ogf A011925 5.71985 -(8+16*x+6*x^6+44*x^5+28*x^7+37*x^4+32*x^3+5*x^8+24*x^2)/(x-1)/(x^4+x^3+x^2+x+1)/(x^4+4*x^3-2*x^2+4*x+1) lgdogf A011926 6.83752 -(-x^4+3*x^6-2*x^7-x^8-2*x^5)/(1-5*x+10*x^2-10*x^3+6*x^4-6*x^5+10*x^6-10*x^7+5*x^8-x^9) ogf A011926 14.8716 -(1+2*x-3*x^2+2*x^3+x^4)/(x^4+1)/(x-1)^5 ogf A011926 6.53697 -(7+2*x-23*x^6+22*x^5+12*x^7+4*x^4+4*x^3+5*x^8-3*x^2)/(x-1)/(x^4+2*x^3-3*x^2+2*x+1)/(x^4+1) lgdogf A011928 7.14628 -(-2*x^10-2*x^11+2*x^9-x^4-2*x^6+2*x^7-6*x^8-x^12-2*x^5)/(1-4*x+6*x^2-4*x^3+x^4-x^13-x^9+4*x^10-6*x^11+4*x^12) ogf A011928 10.0781 -(1+2*x+2*x^2-2*x^3+6*x^4-2*x^5+2*x^6+x^8+2*x^7)/(1+x^2+x)/(x^6+x^3+1)/(x-1)^5 ogf A011930 9.4496 -(-x^4-2*x^7-x^8-2*x^5)/(1-4*x+6*x^2-4*x^3+x^4-6*x^7-x^5+4*x^8+4*x^6-x^9) ogf A011930 15.6777 -(1+2*x+2*x^3+x^4)/(x^4+x^3+x^2+x+1)/(x-1)^5 ogf A011930 6.89821 -(6+12*x+5*x^8+12*x^6+28*x^5+16*x^7+29*x^4+24*x^3+18*x^2)/(-1+x)/(x^4+x^3+x^2+x+1)/(x^4+2*x^3+2*x+1) lgdogf A011931 6.49015 -(-x^10-x^9-x^4-3*x^6+2*x^7-3*x^8-x^5)/(1-4*x+6*x^2-4*x^3+x^4+4*x^8-x^7+4*x^10-6*x^9-x^11) ogf A011931 8.85021 -(1+x+3*x^2-2*x^3+3*x^4+x^5+x^6)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^5 ogf A011932 6.59385 -(1+x+2*x^2+x^4+2*x^5+x^6+2*x^8+x^9+x^10)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x-1)^5 ogf A011934 32.3927 (x^2+4*x+1)/(x+1)/(x-1)^4 ogf A011934 17.9959 -(-x-x^3-4*x^2)/(1-3*x+2*x^2+x^5+2*x^3-3*x^4) ogf A011934 17.6047 -(7+19*x+3*x^3+19*x^2)/(x-1)/(x+1)/(x^2+4*x+1) lgdogf A011934 5.36302 {(2115+882*n+59*n^2)*a(n+1)+(64059+27630*n+3109*n^2)*a(n+2)+(35547+8622*n-59*n^2)*a(n+3)+(-26397-18126*n-3109*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=7,a(3)=20} ogf A011938 7.05191 -(4*x^9-4*x^6+6*x^7-4*x^8+4*x^5)/(-1+4*x-6*x^2+4*x^3-x^4-4*x^8+x^11+x^7-4*x^10+6*x^9) ogf A011938 4.71979 -(6+6*x+26*x^6+12*x^5-8*x^7+12*x^4+12*x^3+27*x^8+14*x^10-8*x^9+6*x^2)/(x-1)/(2*x^4-2*x^3+3*x^2-2*x+2)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A011938 9.66795 -2*(2-2*x+3*x^2-2*x^3+2*x^4)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^5 ogf A011940 8.32518 -(3+2*x+7*x^6-4*x^5+9*x^4+4*x^3+4*x^2)/(x-1)/(x^2-x+1)/(x^4+x^3+x^2+x+1) lgdogf A011940 8.56304 -(4*x^6-4*x^7-4*x^5)/(1-4*x+6*x^2-4*x^3+x^4-x^5+4*x^6-x^9-6*x^7+4*x^8) ogf A011940 15.774 -4*(x^2-x+1)/(x^4+x^3+x^2+x+1)/(x-1)^5 ogf A011943 22.5369 -(-1+7*x)/(x^2+1-14*x) ogf A011943 22.5369 -(-1+7*x)/(x^2-14*x+1) ogf A011943 14.166 -(7-2*x+7*x^2)/(7*x-1)/(1-14*x+x^2) lgdogf A011943 8.12806 -47+329*x+(143-1330*x+47*x^2)*f(x)+(-96+1344*x-96*x^2)*f(x)^2 ogf A011943 13.4003 {a(n+2)-14*a(n+1)+a(n),a(0)=1,a(1)=7} ogf A011944 12.2046 -(-1-7*x+(6*x+1)^(1/2)*(8*x+1)^(1/2))/x revogf A011944 21.6354 -2*(-7+x)/(x^2-14*x+1) lgdogf A011944 21.6354 2*x+(-1+14*x-x^2)*f(x) ogf A011944 29.7487 2*x/(x^2+1-14*x) ogf A011944 33.9985 2/(x^2-14*x+1) ogf A011944 12.8643 {a(n+2)-14*a(n+1)+a(n),a(0)=0,a(1)=2} ogf A011945 15.2973 -(-3-7*x+(2*x+1)^(1/2)*(8*x+3)^(1/2)*3^(1/2))/x revogf A011945 34.2369 -2*(x-7)/(x^2+1-14*x) lgdogf A011945 32.6807 6*x+(-1+14*x-x^2)*f(x) ogf A011945 44.9359 6*x/(x^2+1-14*x) ogf A011945 51.3554 6/(x^2-14*x+1) ogf A011945 19.4318 {a(n+2)-14*a(n+1)+a(n),a(0)=0,a(1)=6} ogf A011960 1.62269 -(-1-3*x+2*x^6+2*x^5-2*x^4-6*x^3-4*x^2)/(-1+x)/(x+1)/(x^2+x+1)/(x^3-x-1) lgdogf A011960 3.3381 -(-1-x+x^3)/(x+1)/(1+x^2+x)/(x-1)^2 ogf A011975 11.4713 -(1+2*x+2*x^5-x^6+x^8-x^7)/(1+x^2+x)/(x^2-x+1)/(x+1)^2/(x-1)^3 ogf A011975 12.7004 -(1+2*x-x^6-x^7+x^8+2*x^5)/(x^9-1+x+x^6+x^2-x^3-x^8-x^7) ogf A011995 1.86368 25+16*x^4+40*x^2+(-10-8*x^2)*f(x)+f(x)^2 ogf A011997 1.18825 64+216*x^2+(-16-27*x^2)*f(x)+f(x)^2 ogf A012000 18.5487 -(-2*x+(-12*x^2+1)^(1/2))*x/(4*x-1)/(4*x+1) revogf A012000 31.9037 -2*(8*x-1)/(16*x^2+1-4*x) lgdogf A012000 33.2331 1+(-1+4*x-16*x^2)*f(x)^2 ogf A012000 36.2542 1/(1-4*x+16*x^2)^(1/2) ogf A012000 11.2337 {(-n-3)*a(n+3)+(10+4*n)*a(n+2)+(-32-16*n)*a(n+1),a(0)=1,a(1)=2,a(2)=-2} ogf A012019 4.90798 -2538-116*x^2+2*x^4+(11880+6369*x^2+759*x^4)*f(x)+(-11286-17358*x^2-6600*x^4)*f(x)^2+(3815*x^2+1944+1870*x^4)*f(x)^3 lgdegf A012019 37.955 1/(1+x^2)^(3/2) lgdegf A012019 11.1632 {(n+3)*a(n+3)+(4+n)*a(n+1),a(0)=1,a(1)=0,a(2)=-3/2} lgdegf A012022 4.49501 {(-300-440*n-208*n^2-32*n^3)*a(n+1)+(-85-64*n-12*n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=-5,a(2)=129/2} egf A012025 4.61691 {(300+440*n+208*n^2+32*n^3)*a(n+1)+(80+62*n+12*n^2)*a(n+2)+(n+3)*a(n+3),a(0)=1,a(1)=-4,a(2)=42} egf A012034 8.58455 {(5+4*n+n^2)*a(n+1)+(5*n+6+n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=-1} lgdegf A012125 31.0171 -6*(8*x-1)/(16*x^2+1-4*x) lgdogf A012125 35.2467 1/(1-4*x+16*x^2)^(3/2) ogf A012125 11.2381 {(n+2)*a(n+3)+(-10-4*n)*a(n+2)+(48+16*n)*a(n+1),a(0)=0,a(1)=1,a(2)=6} ogf A012150 4.92418 2538-116*x^2-2*x^4+(-11880+6369*x^2-759*x^4)*f(x)+(11286-17358*x^2+6600*x^4)*f(x)^2+(3815*x^2-1944-1870*x^4)*f(x)^3 lgdegf A012150 11.1035 {(-n-3)*a(n+3)+(4+n)*a(n+1),a(0)=1,a(1)=0,a(2)=3/2} lgdegf A012244 28.5825 -(x+1)/(x^2-1+2*x) lgdegf A012244 24.4993 -1+(1-2*x-x^2)*f(x)^2 egf A012244 27.0782 1/(1-2*x-x^2)^(1/2) egf A012244 34.2991 sin(x)+cos(x)-1 revegf A012244 8.16644 {(n^2+4*n+4)*a(n+1)+(5+2*n)*a(n+2)-a(n+3),a(0)=1,a(1)=1,a(2)=4} ogf A012245 21.7732 (1+5*x^4+23*x^22)/(1+x+x^5+x^23) lgdogf A012245 58.0619 1+x+x^5+x^23 ogf A012246 8.63446 {(5+4*n+n^2)*a(n+1)+(-5*n-6-n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=1} lgdegf A012408 11.6937 1/(1+x^2)*exp(x)*(arctan(x)+arctan(x)*x^2+1) lgdegf A012493 22.069 (x-1)^3/(-4*x^2-1+5*x+x^3) ogf A012493 15.508 -(-1+3*x-3*x^2+x^3)/(4*x^2+1-5*x-x^3) ogf A012493 15.508 -(-2-2*x+x^2)/(x-1)/(x^3-4*x^2+5*x-1) lgdogf A012493 6.83089 -23+69*x+23*x^3-69*x^2+(-17+5*x+17*x^3-28*x^2)*f(x)+(160*x^2+40-200*x-40*x^3)*f(x)^2 ogf A012493 9.25475 {a(n+4)-5*a(n+3)+4*a(n+2)-a(n+1),a(0)=1,a(1)=2,a(2)=9,a(3)=37} ogf A012584 10.2667 exp(x)/(x^2+1)*(arcsinh(x)*x^2+arcsinh(x)+(x^2+1)^(1/2)) lgdegf A012772 13.5628 -(-3+3*x-3*x^2+x^3)/(x-1)/(x^3-4*x^2+5*x-1) lgdogf A012772 18.8129 -(1-2*x+x^2)/(-4*x^2-1+5*x+x^3) ogf A012772 21.6 -(x-1)^2/(-4*x^2-1+5*x+x^3) ogf A012772 8.2141 2-4*x+2*x^2+(-13+32*x+2*x^3-19*x^2)*f(x)+(11-55*x+44*x^2-11*x^3)*f(x)^2 ogf A012772 10.8 {-a(n+3)+5*a(n+2)-4*a(n+1)+a(n),a(0)=1,a(1)=3,a(2)=12} ogf A012781 25.1596 (x-1)/(-4*x^2-1+5*x+x^3) ogf A012781 24.1532 -(-1+x)/(4*x^2+1-5*x-x^3) ogf A012781 13.7234 -(x-2)*(2*x^2-3*x+2)/(x-1)/(x^3-4*x^2+5*x-1) lgdogf A012781 10.7827 1-x+(6-2*x+x^3-4*x^2)*f(x)+(-7+7*x^3+35*x-28*x^2)*f(x)^2 ogf A012781 11.393 {a(n+3)-5*a(n+2)+4*a(n+1)-a(n),a(0)=1,a(1)=4,a(2)=16} ogf A012814 16.8176 -(x-1)*(3*x-5)/(-4*x^2-1+5*x+x^3) lgdogf A012814 26.4277 -1/(-4*x^2-1+5*x+x^3) ogf A012814 8.40881 -19+(60-95*x-19*x^3+76*x^2)*f(x)+(-164*x^2+41*x^3-41+205*x)*f(x)^2 ogf A012814 29.2096 1/(1-5*x+4*x^2-x^3) ogf A012814 10.4714 {a(n+3)-5*a(n+2)+4*a(n+1)-a(n),a(0)=1,a(1)=5,a(2)=21} ogf A012855 23.3079 (4*x-1)/(-4*x^2-1+5*x+x^3) ogf A012855 12.3675 -(-1+8*x-19*x^2+8*x^3)/(-1+4*x)/(x^3-4*x^2+5*x-1) lgdogf A012855 20.8968 -(-x+4*x^2)/(1-5*x+4*x^2-x^3) ogf A012855 10.6317 -x+4*x^2+(-6*x+1+8*x^2-x^3)*f(x)+(4*x^2+1-5*x-x^3)*f(x)^2 ogf A012855 11.654 {a(n+3)-5*a(n+2)+4*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=1} ogf A012864 18.1053 -(-1+4*x-2*x^2)/(4*x^2+1-5*x-x^3) ogf A012864 18.1053 -(2*x^2+1-4*x)/(-4*x^2-1+5*x+x^3) ogf A012864 10.3013 -(x-1)*(2*x^3-6*x^2+3*x-1)/(2*x^2-4*x+1)/(x^3-4*x^2+5*x-1) lgdogf A012864 8.07396 -10+40*x-20*x^2+(17-78*x-10*x^3+54*x^2)*f(x)+(-7+35*x-28*x^2+7*x^3)*f(x)^2 ogf A012864 11.4899 {a(n+3)-5*a(n+2)+4*a(n+1)-a(n),a(0)=1,a(1)=1,a(2)=3} ogf A012866 22.0019 (3*x-1)/(-4*x^2-1+5*x+x^3) ogf A012866 11.9177 -(-2+8*x+6*x^3-15*x^2)/(3*x-1)/(x^3-4*x^2+5*x-1) lgdogf A012866 19.7258 -(-x+3*x^2)/(4*x^2+1-5*x-x^3) ogf A012866 7.42921 16*x-48*x^2+(-16+105*x+16*x^3-139*x^2)*f(x)+(-100*x^2-25+125*x+25*x^3)*f(x)^2 ogf A012866 11.0009 {a(n+3)-5*a(n+2)+4*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=2} ogf A012880 22.8575 (2*x-1)/(-4*x^2-1+5*x+x^3) ogf A012880 12.1285 -(-3+8*x-11*x^2+4*x^3)/(-1+2*x)/(x^3-4*x^2+5*x-1) lgdogf A012880 20.4929 -(-x+2*x^2)/(1-5*x+4*x^2-x^3) ogf A012880 9.74255 -x+2*x^2+(1-8*x-x^3+10*x^2)*f(x)+(12*x^2+3-15*x-3*x^3)*f(x)^2 ogf A012880 11.4288 {a(n+3)-5*a(n+2)+4*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=3} ogf A012886 17.6237 (-1+3*x+3*x^2)/(-4*x^2-1+5*x+x^3) ogf A012886 17.6237 -(-1+3*x+3*x^2)/(4*x^2+1-5*x-x^3) ogf A012886 9.53415 -(-2+14*x+6*x^3+3*x^4-30*x^2)/(3*x^2+3*x-1)/(x^3-4*x^2+5*x-1) lgdogf A012886 6.76259 -202+606*x+606*x^2+(33-503*x-202*x^3+1315*x^2)*f(x)+(169-845*x+676*x^2-169*x^3)*f(x)^2 ogf A012886 11.1843 {a(n+3)-5*a(n+2)+4*a(n+1)-a(n),a(0)=1,a(1)=2,a(2)=3} ogf A012899 14.7597 -(-x+1+(-(x-1)*(x+1))^(1/2))/(x-1)/(x+1) lgdegf A012899 14.7597 2*x+(2-2*x^2)*f(x)+(-1-x+x^2+x^3)*f(x)^2 lgdegf A012899 5.5697 {(-n^2-1)*a(n+1)+(-3-n^2-4*n)*a(n+2)+(3*n+n^2)*a(n+3)+(7*n+12+n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=3/2,a(3)=5/6} egf A012960 23.8267 (x+2+x^2)/(1+x)/(1+x^2) lgdegf A012960 8.30324 -10-5*x^2-5*x+(9+7*x^2+7*x+5*x^3)*f(x)+(-2*x-2*x^2-2*x^3-2)*f(x)^2 lgdegf A012960 27.4007 exp(arctan(x))*(x+1) egf A012960 4.68388 {(-18*n-15*n^2-3*n^3)*a(n+1)+(-30-46*n-18*n^2-2*n^3)*a(n+2)+(1-n)*a(n+3)+(-2*n-8)*a(n+4),a(0)=1,a(1)=2,a(2)=3,a(3)=2} ogf A013069 22.6353 (x+(x^2+1)^(1/2))*(x+1) egf A013069 11.5692 (x^2+1+((1+x^2)*(x+1)^2)^(1/2))/(1+x^2)/(x+1) lgdegf A013069 14.8747 -1-2*x-x^2+(-2*x-2*x^2)*f(x)+f(x)^2 egf A013069 14.8747 -1-x^2-2*x+(-2*x-2*x^2)*f(x)+f(x)^2 egf A013078 10.3969 1/2*(x^3+2*x^2+((x^2+1)*(x^2+2+2*x)^2)^(1/2))/(x+1) egf A013078 7.26362 4+12*x^2+8*x+5*x^4+12*x^3+(8*x^2+4*x^4+12*x^3)*f(x)+(-4-8*x-4*x^2)*f(x)^2 egf A013078 7.26362 4+8*x+12*x^3+5*x^4+12*x^2+(12*x^3+4*x^4+8*x^2)*f(x)+(-4-8*x-4*x^2)*f(x)^2 egf A013080 6.97792 -4-4*x^2-8*x+(8*x^2+4*x^4+12*x^3)*f(x)+(12*x^2+4+8*x+5*x^4+12*x^3)*f(x)^2 egf A013080 6.97792 -4-8*x-4*x^2+(12*x^3+4*x^4+8*x^2)*f(x)+(4+8*x+12*x^3+5*x^4+12*x^2)*f(x)^2 egf A013080 6.53062 2*(-x^3-2*x^2+((x^2+1)*(x^2+2+2*x)^2)^(1/2))/(4+8*x+12*x^2+12*x^3+5*x^4)*(x+1) egf A013084 7.58924 -5152+(2832+768*x^4)*f(x)+(1032-1686*x^4)*f(x)^2+(651*x^4-580)*f(x)^3 lgdegf A013103 21.3116 (1+(1+x^2)^(1/2))/(1+x^2) lgdegf A013103 12.9949 -x^2+(-2-2*x^2)*f(x)+(x^4+1+2*x^2)*f(x)^2 lgdegf A013155 32.5943 (x-2)/(x-1)/(1+x) lgdegf A013155 19.107 -1-3*x-x^3-3*x^2+(1-x)*f(x)^2 egf A013155 19.107 -1-3*x^2-3*x-x^3+(1-x)*f(x)^2 egf A013155 15.8315 -1/(x-1)*(-(x-1)*(x+1))^(1/2)*(x+1) egf A013155 10.0746 {(n^2+2*n)*a(n+1)-a(n+3)+2*a(n+2),a(0)=1,a(1)=2,a(2)=3} ogf A013161 9.79695 (-2+22*x+5*x^3-x^2)/(x-1)/(x-2)/(1+x)/(x^3+3*x^2+2*x+2) lgdegf A013164 11.2493 x*(x-2)*(x^2+3*x+4)/(x-1)/(1+x)/(x^3+3*x^2+2*x+2) lgdegf A013164 3.93725 {(-400*n-127*n^2)*a(n+1)+(-1438-1093*n-201*n^2)*a(n+2)+(601*n+660+127*n^2)*a(n+3)+(1220*n+1664+201*n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=2,a(3)=-1} egf A013166 11.1441 -x*(x-2)*(x^2+3*x+4)/(x-1)/(x+1)/(x^3+3*x^2+2*x+2) lgdegf A013170 14.7542 -(1+(-(-1+x)*(x+1))^(1/2))/(-1+x)/(x+1) lgdegf A013170 14.0345 -x^2+(2-2*x^2)*f(x)+(-x^4-1+2*x^2)*f(x)^2 lgdegf A013170 5.27903 {(2+n^2+2*n)*a(n+1)+(6*n+8+n^2)*a(n+2)+(-3*n-n^2)*a(n+3)+(-7*n-12-n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=2,a(3)=11/6} egf A013174 36.9402 -2+(1-x^4)*f(x) lgdegf A013174 25.1865 -2/(x-1)/(1+x)/(1+x^2) lgdegf A013174 22.1641 exp(arctanh(x)+arctan(x)) egf A013174 9.23504 {(n+4)*a(n+4)-2*a(n+3)-a(n)*n,a(0)=1,a(1)=2,a(2)=2,a(3)=4/3} egf A013174 9.23504 {(n+4)*a(n+4)-2*a(n+3)-n*a(n),a(0)=1,a(1)=2,a(2)=2,a(3)=4/3} egf A013279 7.59045 -4-12*x^2-8*x-5*x^4-12*x^3+(8*x^2+4*x^4+12*x^3)*f(x)+(4*x^2+4+8*x)*f(x)^2 egf A013279 7.59045 -4-8*x-12*x^3-5*x^4-12*x^2+(12*x^3+4*x^4+8*x^2)*f(x)+(4*x^2+4+8*x)*f(x)^2 egf A013279 10.6558 1/2*(-x^3-2*x^2+((x^2+1)*(x^2+2+2*x)^2)^(1/2))/(x+1) egf A013281 6.87982 2*(x^3+2*x^2+((x^2+1)*(x^2+2+2*x)^2)^(1/2))/(4+8*x+12*x^2+12*x^3+5*x^4)*(x+1) egf A013281 7.2568 4*x^2+4+8*x+(12*x^3+4*x^4+8*x^2)*f(x)+(-4-8*x-12*x^3-5*x^4-12*x^2)*f(x)^2 egf A013281 7.2568 4*x^2+4+8*x+(8*x^2+4*x^4+12*x^3)*f(x)+(-4-12*x^2-8*x-5*x^4-12*x^3)*f(x)^2 egf A013299 6.9558 {(45+63*n+28*n^2+4*n^3)*a(n+1)+(-n-2)*a(n+2),a(0)=1,a(1)=6} ogf A013302 4.2918 {(-36-114*n-96*n^2-24*n^3)*a(n+1)+(93*n+90+32*n^2+4*n^3)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=0,a(2)=3} ogf A013309 5.5264 {-a(n+1)+(n+2)*a(n+2)+(-5*n-6-n^2)*a(n+3)+(26*n+24+9*n^2+n^3)*a(n+4),a(0)=1,a(1)=2,a(2)=1/2,a(3)=0} lgdegf A013326 14.2905 -(-1+x-x^2+2*x^3)/(3*x^2+1-3*x+x^4-3*x^3) ogf A013326 8.13764 -(2-4*x+2*x^6-2*x^5+2*x^3+3*x^2)/(2*x^3-x^2+x-1)/(x^4-3*x^3+3*x^2-3*x+1) lgdogf A013326 5.09487 -151+151*x+302*x^3-151*x^2+(577-879*x-1305*x^3+151*x^4+879*x^2)*f(x)+(-1278*x^2-426+1278*x-426*x^4+1278*x^3)*f(x)^2 ogf A013326 8.61633 {a(n+4)-3*a(n+3)+3*a(n+2)-3*a(n+1)+a(n),a(0)=1,a(1)=2,a(2)=4,a(3)=7} ogf A013378 19.9719 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A013397 14.5981 -(x-1+(-(x-1)*(x+1))^(1/2))/(x-1)/(x+1) lgdegf A013397 14.2331 -2*x+(2-2*x^2)*f(x)+(1+x-x^2-x^3)*f(x)^2 lgdegf A013397 4.99408 {(5+n^2+4*n)*a(n+1)+(5+n^2+4*n)*a(n+2)+(-7*n-12-n^2)*a(n+3)+(-7*n-12-n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=1/2,a(3)=-1/6} egf A013430 13.8606 -(-1+(-(x-1)*(x+1))^(1/2))/(x-1)/(x+1) lgdegf A013430 13.5052 x^2+(2-2*x^2)*f(x)+(1-2*x^2+x^4)*f(x)^2 lgdegf A013430 4.2476 {(-n-n^2-n^3-n^4)*a(n)+(-15*n-8-6*n^3-12*n^2-n^4)*a(n+1)+(2*n-4+2*n^2)*a(n+2)+(3*n+n^2)*a(n+3),a(0)=1,a(1)=0,a(2)=0,a(3)=-1} ogf A013430 4.83213 {(2+n^2+2*n)*a(n+1)+(-6*n-8-n^2)*a(n+2)+(-3*n-n^2)*a(n+3)+(7*n+12+n^2)*a(n+4),a(0)=1,a(1)=0,a(2)=0,a(3)=-1/6} egf A013458 21.3259 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A013459 23.285 -x*(x-1)/(x+1)/(1+x^2) lgdegf A013459 23.285 1/(x+1)*exp(arctan(x)) egf A013459 7.53338 15*x^2-15*x+(15+13*x^2+17*x+15*x^3)*f(x)+(-2-2*x-2*x^2-2*x^3)*f(x)^2 lgdegf A013459 5.17444 {(-16*n-7*n^2-n^3-12)*a(n+1)+(-4*n-3-n^2)*a(n+2)+(-n-3)*a(n+3)-a(n+4),a(0)=1,a(1)=0,a(2)=1,a(3)=-4} ogf A013459 5.69189 {(-n-4)*a(n+4)+(-n-3)*a(n+3)+(-1-n)*a(n+2)+(-n-2)*a(n+1),a(0)=1,a(1)=0,a(2)=1/2,a(3)=-2/3} egf A013461 19.5075 -(-1+(1+x^2)^(1/2))/(1+x^2) lgdegf A013461 13.1675 x^2+(2+2*x^2)*f(x)+(-1-2*x^2-x^4)*f(x)^2 lgdegf A013462 29.4304 2*x^2+(1-x^4)*f(x) lgdegf A013462 21.1899 2*x^2/(x-1)/(x+1)/(1+x^2) lgdegf A013462 8.5443 {(-n-4)*a(n+4)-2*a(n+1)+a(n)*n,a(0)=1,a(1)=0,a(2)=0,a(3)=-2/3} egf A013462 8.5443 {(-n-4)*a(n+4)-2*a(n+1)+n*a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=-2/3} egf A013468 5.441 {a(n+1)+(-n-2)*a(n+2)+(5*n+6+n^2)*a(n+3)+(-26*n-24-9*n^2-n^3)*a(n+4),a(0)=-1,a(1)=-2,a(2)=-1/2,a(3)=0} lgdegf A013492 11.1363 (-x^2-1+((1+x^2)*(x+1)^2)^(1/2))/(1+x^2)/(x+1) lgdegf A013492 22.2726 (x+(x^2+1)^(1/2))/(x+1) egf A013492 13.4808 1+(2*x^2+2*x)*f(x)+(-1-2*x-x^2)*f(x)^2 egf A013492 7.4242 {-a(n)*n-a(n+1)*n+(-n-3)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=0,a(2)=1/2} egf A013523 8.80926 1-12*x+2*x^4+(-3+36*x-4*x^4)*f(x)+(3-36*x+2*x^4)*f(x)^2+(12*x-1)*f(x)^3 ogf A013524 10.0064 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A013528 5.56867 1-12*x+2*x^4+(-3+36*x-4*x^4)*f(x)+(3-36*x+2*x^4)*f(x)^2+(12*x-1)*f(x)^3 ogf A013539 3.59468 1144-41*x-1308736*x^4+(3432-123*x-2617472*x^4)*f(x)+(3432-123*x-1308736*x^4)*f(x)^2+(-41*x+1144)*f(x)^3 ogf A013545 2.88651 935-83*x-874225*x^4+(2805-249*x-1748450*x^4)*f(x)+(2805-249*x-874225*x^4)*f(x)^2+(-83*x+935)*f(x)^3 ogf A013549 1.56779 2+x+4*x^2+24*x^3 ogf_with_Euler_Transform A013571 12.1781 -1/(1+x^2)*exp(-x)*(arctan(x)+arctan(x)*x^2-1) lgdegf A013574 4.21252 (3+x+2*x^2)/(x^2+1)/(x-1)^2 ogf A013574 2.18727 -(7-x+4*x^4+3*x^3+11*x^2)/(-1+x)/(1+x^2)/(2*x^2+x+3) lgdogf A013574 1.17256 {(-6*n-25)*a(n+1)+(6*n+19)*a(n+2)+(-6*n-25)*a(n+3)+(6*n+19)*a(n+4),a(0)=3,a(1)=7,a(2)=10,a(3)=12} ogf A013575 2.32892 (-13+x+2*x^4-5*x^3+3*x^2)/(-1+x)/(x^4-x^3-x^2+x+6) lgdogf A013575 4.65785 (6+x-x^2-x^3+x^4)/(x-1)^2 ogf A013575 1.11967 -4458-743*x+743*x^3-743*x^4+743*x^2+(-61-1620*x+134*x^3-134*x^4+877*x^2)*f(x)+(134-268*x+134*x^2)*f(x)^2 ogf A013575 1.84835 {a(n+5)-2*a(n+4)+a(n+3),a(0)=6,a(1)=13,a(2)=19,a(3)=24,a(4)=30} ogf A013654 22.4941 -(-2-6*x)/(-2*x^2+1-x-x^5+2*x^3+x^4) ogf A013654 31.1457 -2*(3*x+1)/(x+1)^2/(x-1)^3 ogf A013654 22.4941 -4*(1+2*x+3*x^2)/(x-1)/(3*x+1)/(x+1) lgdogf A013654 8.89877 {(-n-4)*a(n+4)+(-5-3*n)*a(n+3)+(10+n)*a(n+2)+(15+3*n)*a(n+1),a(0)=2,a(1)=8,a(2)=12,a(3)=24} ogf A013655 56.8088 (x-3)/(x^2+x-1) ogf A013655 29.3838 -(-2-6*x+x^2)/(x-3)/(x^2+x-1) lgdogf A013655 53.2582 -(3-x)/(x^2-1+x) ogf A013655 14.4429 -735+245*x+(506-332*x-245*x^2)*f(x)+(87*x^2-87+87*x)*f(x)^2 ogf A013655 23.6703 1/2/(x-1)*(-3-x+(9+2*x+5*x^2)^(1/2)) revogf A013655 24.3466 {-a(n+2)+a(n+1)+a(n),a(0)=3,a(1)=2} ogf A013656 25.0703 -(7*x+11*x^2)/(-1+3*x-3*x^2+x^3) ogf A013656 47.1911 -(7+11*x)/(x-1)^3 ogf A013656 29.7129 -2*(16+11*x)/(11*x+7)/(x-1) lgdogf A013656 6.46974 -21569275*x-33894575*x^2+(3081325-5563011*x-3081325*x^3+15028347*x^2)*f(x)+(-525852+1577556*x-1577556*x^2+525852*x^3)*f(x)^2 ogf A013656 15.1368 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=7,a(2)=32} ogf A013698 5.40976 -800+5832*x+(100+8748*x^2-1944*x)*f(x)+(-1188*x^2+80*x+4374*x^3)*f(x)^2+(16*x^2+729*x^4-216*x^3)*f(x)^3 lgdogf A013698 6.79519 {(990+897*n+270*n^2+27*n^3)*a(n+1)+(-140*n-144-42*n^2-4*n^3)*a(n+2),a(0)=1,a(1)=8} ogf A013708 34.8771 -3+(1-9*x)*f(x) ogf A013708 47.5597 -3/(-1+9*x) ogf A013708 47.5597 -9/(-1+9*x) lgdogf A013708 40.2428 1/3*x/(1+3*x) revogf A013708 40.2428 1/9*ln(1+3*x) revegf A013708 58.1286 3/(1-9*x) ogf A013708 23.7799 {a(n+1)-9*a(n),a(0)=3} ogf A013709 41.1268 -16/(16*x-1) lgdogf A013709 30.8451 -4+(1-16*x)*f(x) ogf A013709 41.1268 -4/(-1+16*x) ogf A013709 35.2515 1/16*ln(1+4*x) revegf A013709 37.9632 1/4*x/(1+4*x) revogf A013709 49.3521 4/(1-16*x) ogf A013709 21.4574 {a(n+1)-16*a(n),a(0)=4} ogf A013710 37.2878 -25/(-1+25*x) lgdogf A013710 30.2963 -5+(1-25*x)*f(x) ogf A013710 40.3951 -5/(-1+25*x) ogf A013710 34.6244 1/25*ln(1+5*x) revegf A013710 37.2878 1/5*x/(1+5*x) revogf A013710 48.4741 5/(1-25*x) ogf A013710 21.0757 {a(n+1)-25*a(n),a(0)=5} ogf A013711 41.0374 -36/(-1+36*x) lgdogf A013711 33.3429 -6+(1-36*x)*f(x) ogf A013711 44.4572 -6/(-1+36*x) ogf A013711 38.1061 1/36*ln(1+6*x) revegf A013711 41.0374 1/6*x/(6*x+1) revogf A013711 53.3486 6/(1-36*x) ogf A013711 23.195 {a(n+1)-36*a(n),a(0)=6} ogf A013712 43.9537 -49/(-1+49*x) lgdogf A013712 35.7124 -7+(1-49*x)*f(x) ogf A013712 47.6165 -7/(-1+49*x) ogf A013712 40.8142 1/49*ln(1+7*x) revegf A013712 43.9537 1/7*x/(1+7*x) revogf A013712 57.1399 7/(1-49*x) ogf A013712 24.8434 {a(n+1)-49*a(n),a(0)=7} ogf A013713 39.7889 -64/(-1+64*x) lgdogf A013713 32.3285 -8+(1-64*x)*f(x) ogf A013713 43.1046 -8/(-1+64*x) ogf A013713 36.9468 1/64*ln(8*x+1) revegf A013713 39.7889 1/8*x/(8*x+1) revogf A013713 51.7256 8/(1-64*x) ogf A013713 22.4894 {a(n+1)-64*a(n),a(0)=8} ogf A013714 41.819 -81/(-1+81*x) lgdogf A013714 33.9779 -9+(1-81*x)*f(x) ogf A013714 45.3039 -9/(-1+81*x) ogf A013714 38.8319 1/81*ln(1+9*x) revegf A013714 41.819 1/9*x/(1+9*x) revogf A013714 54.3646 9/(1-81*x) ogf A013714 23.6368 {a(n+1)-81*a(n),a(0)=9} ogf A013715 23.0544 -10+(1-100*x)*f(x) ogf A013715 29.6414 -10/(-1+100*x) ogf A013715 27.6653 -100/(-1+100*x) lgdogf A013715 27.6653 1/10*x/(1+10*x) revogf A013715 25.9362 1/100*ln(1+10*x) revegf A013715 34.5817 10/(1-100*x) ogf A013715 16.5992 {a(n+1)-100*a(n),a(0)=10} ogf A013716 23.0544 -11+(1-121*x)*f(x) ogf A013716 29.6414 -11/(-1+121*x) ogf A013716 27.6653 -121/(-1+121*x) lgdogf A013716 27.6653 1/11*x/(1+11*x) revogf A013716 25.9362 1/121*ln(1+11*x) revegf A013716 34.5817 11/(1-121*x) ogf A013716 16.5992 {a(n+1)-121*a(n),a(0)=11} ogf A013717 23.8827 -12+(1-144*x)*f(x) ogf A013717 30.7064 -12/(-1+144*x) ogf A013717 28.6593 -144/(-1+144*x) lgdogf A013717 28.6593 1/12*x/(1+12*x) revogf A013717 26.8681 1/144*ln(1+12*x) revegf A013717 35.8241 12/(1-144*x) ogf A013717 17.1956 {a(n+1)-144*a(n),a(0)=12} ogf A013718 24.573 -13+(1-169*x)*f(x) ogf A013718 31.5939 -13/(-1+169*x) ogf A013718 29.4876 -169/(-1+169*x) lgdogf A013718 29.4876 1/13*x/(1+13*x) revogf A013718 27.6446 1/169*ln(1+13*x) revegf A013718 36.8595 13/(1-169*x) ogf A013718 17.6926 {a(n+1)-169*a(n),a(0)=13} ogf A013719 25.2633 -14+(1-196*x)*f(x) ogf A013719 32.4813 -14/(-1+196*x) ogf A013719 30.3159 -196/(-1+196*x) lgdogf A013719 30.3159 1/14*x/(1+14*x) revogf A013719 28.4212 1/196*ln(1+14*x) revegf A013719 37.8949 14/(1-196*x) ogf A013719 18.1895 {a(n+1)-196*a(n),a(0)=14} ogf A013720 25.6774 -15+(1-225*x)*f(x) ogf A013720 33.0138 -15/(-1+225*x) ogf A013720 30.8129 -225/(-1+225*x) lgdogf A013720 30.8129 1/15*x/(1+15*x) revogf A013720 28.8871 1/225*ln(1+15*x) revegf A013720 38.5161 15/(1-225*x) ogf A013720 18.4877 {a(n+1)-225*a(n),a(0)=15} ogf A013721 26.3677 -16+(1-256*x)*f(x) ogf A013721 33.9013 -16/(-1+256*x) ogf A013721 31.6412 -256/(-1+256*x) lgdogf A013721 31.6412 1/16*x/(1+16*x) revogf A013721 29.6636 1/256*ln(1+16*x) revegf A013721 39.5515 16/(1-256*x) ogf A013721 18.9847 {a(n+1)-256*a(n),a(0)=16} ogf A013722 21.8475 -17+(1-289*x)*f(x) ogf A013722 28.0897 -17/(-1+289*x) ogf A013722 26.217 -289/(-1+289*x) lgdogf A013722 26.217 1/17*x/(1+17*x) revogf A013722 24.5785 1/289*ln(1+17*x) revegf A013722 32.7713 17/(1-289*x) ogf A013722 15.7302 {a(n+1)-289*a(n),a(0)=17} ogf A013723 22.2472 -18+(1-324*x)*f(x) ogf A013723 28.6035 -18/(-1+324*x) ogf A013723 26.6966 -324/(-1+324*x) lgdogf A013723 26.6966 1/18*x/(1+18*x) revogf A013723 25.0281 1/324*ln(1+18*x) revegf A013723 33.3708 18/(1-324*x) ogf A013723 16.018 {a(n+1)-324*a(n),a(0)=18} ogf A013724 22.6468 -19+(1-361*x)*f(x) ogf A013724 29.1174 -19/(-1+361*x) ogf A013724 27.1762 -361/(-1+361*x) lgdogf A013724 27.1762 1/19*x/(1+19*x) revogf A013724 25.4777 1/361*ln(1+19*x) revegf A013724 33.9703 19/(1-361*x) ogf A013724 16.3057 {a(n+1)-361*a(n),a(0)=19} ogf A013725 23.0465 -20+(1-400*x)*f(x) ogf A013725 29.6312 -20/(-1+400*x) ogf A013725 27.6558 -400/(-1+400*x) lgdogf A013725 27.6558 1/20*x/(1+20*x) revogf A013725 25.9273 1/400*ln(1+20*x) revegf A013725 34.5697 20/(1-400*x) ogf A013725 16.5935 {a(n+1)-400*a(n),a(0)=20} ogf A013726 23.3129 -21+(1-441*x)*f(x) ogf A013726 29.9737 -21/(-1+441*x) ogf A013726 27.9755 -441/(-1+441*x) lgdogf A013726 27.9755 1/21*x/(1+21*x) revogf A013726 26.227 1/441*ln(1+21*x) revegf A013726 34.9694 21/(1-441*x) ogf A013726 16.7853 {a(n+1)-441*a(n),a(0)=21} ogf A013727 23.8458 -22+(1-484*x)*f(x) ogf A013727 30.6589 -22/(-1+484*x) ogf A013727 28.6149 -484/(-1+484*x) lgdogf A013727 28.6149 1/22*x/(1+22*x) revogf A013727 26.8265 1/484*ln(1+22*x) revegf A013727 35.7687 22/(1-484*x) ogf A013727 17.169 {a(n+1)-484*a(n),a(0)=22} ogf A013728 23.979 -23+(1-529*x)*f(x) ogf A013728 30.8301 -23/(-1+529*x) ogf A013728 28.7748 -529/(-1+529*x) lgdogf A013728 28.7748 1/23*x/(1+23*x) revogf A013728 26.9764 1/529*ln(1+23*x) revegf A013728 35.9685 23/(1-529*x) ogf A013728 17.2649 {a(n+1)-529*a(n),a(0)=23} ogf A013729 24.2454 -24+(1-576*x)*f(x) ogf A013729 31.1727 -24/(-1+576*x) ogf A013729 29.0945 -576/(-1+576*x) lgdogf A013729 29.0945 1/24*x/(1+24*x) revogf A013729 27.2761 1/576*ln(1+24*x) revegf A013729 36.3681 24/(1-576*x) ogf A013729 17.4567 {a(n+1)-576*a(n),a(0)=24} ogf A013730 41.3411 -2+(1-8*x)*f(x) ogf A013730 56.3742 -2/(-1+8*x) ogf A013730 56.3742 -8/(-1+8*x) lgdogf A013730 47.7012 1/2*x/(1+4*x) revogf A013730 47.7012 1/8*ln(1+4*x) revegf A013730 68.9018 2/(1-8*x) ogf A013730 28.1871 {a(n+1)-8*a(n),a(0)=2} ogf A013731 42.5394 -4+(1-8*x)*f(x) ogf A013731 58.0082 -4/(-1+8*x) ogf A013731 58.0082 -8/(-1+8*x) lgdogf A013731 49.0839 1/4*x/(2*x+1) revogf A013731 49.0839 1/8*ln(1+2*x) revegf A013731 70.8989 4/(1-8*x) ogf A013731 29.0041 {a(n+1)-8*a(n),a(0)=4} ogf A013732 43.0818 -27/(-1+27*x) lgdogf A013732 35.0039 -3+(1-27*x)*f(x) ogf A013732 46.6719 -3/(-1+27*x) ogf A013732 40.0045 1/27*ln(1+9*x) revegf A013732 43.0818 1/3*x/(1+9*x) revogf A013732 56.0063 3/(1-27*x) ogf A013732 24.3506 {a(n+1)-27*a(n),a(0)=3} ogf A013733 36.217 -9+(1-27*x)*f(x) ogf A013733 48.2893 -9/(-1+27*x) ogf A013733 41.3908 1/27*ln(1+3*x) revegf A013733 44.5747 1/9*x/(1+3*x) revogf A013733 57.9471 9/(1-27*x) ogf A013733 25.1944 {a(n+1)-27*a(n),a(0)=9} ogf A013734 31.9986 -4+(1-64*x)*f(x) ogf A013734 42.6648 -4/(-1+64*x) ogf A013734 39.3829 -64/(-1+64*x) lgdogf A013734 36.5698 1/4*x/(1+16*x) revogf A013734 34.1318 1/64*ln(1+16*x) revegf A013734 51.1978 4/(1-64*x) ogf A013734 22.2599 {a(n+1)-64*a(n),a(0)=4} ogf A013735 31.3582 -16+(1-64*x)*f(x) ogf A013735 41.0069 -16/(-1+64*x) ogf A013735 41.0069 -64/(-1+64*x) lgdogf A013735 38.0779 1/16*x/(1+4*x) revogf A013735 38.0779 1/64*ln(1+4*x) revegf A013735 48.4627 16/(1-64*x) ogf A013735 22.2121 {a(n+1)-64*a(n),a(0)=16} ogf A013736 32.4894 -125/(-1+125*x) lgdogf A013736 28.6671 -5+(1-125*x)*f(x) ogf A013736 37.4877 -5/(-1+125*x) ogf A013736 30.4588 1/125*ln(1+25*x) revegf A013736 34.81 1/5*x/(1+25*x) revogf A013736 44.3037 5/(1-125*x) ogf A013736 20.3059 {a(n+1)-125*a(n),a(0)=5} ogf A013737 34.1993 -125/(-1+125*x) lgdogf A013737 28.4994 -25+(1-125*x)*f(x) ogf A013737 36.6421 -25/(-1+125*x) ogf A013737 34.1993 1/125*ln(1+5*x) revegf A013737 36.6421 1/25*x/(1+5*x) revogf A013737 42.7492 25/(1-125*x) ogf A013737 20.5196 {a(n+1)-125*a(n),a(0)=25} ogf A013738 29.9846 -216/(-1+216*x) lgdogf A013738 26.457 -6+(1-216*x)*f(x) ogf A013738 34.5976 -6/(-1+216*x) ogf A013738 28.1105 1/216*ln(1+36*x) revegf A013738 32.1263 1/6*x/(1+36*x) revogf A013738 40.8881 6/(1-216*x) ogf A013738 18.7404 {a(n+1)-216*a(n),a(0)=6} ogf A013739 31.3099 -216/(-1+216*x) lgdogf A013739 26.0916 -36+(1-216*x)*f(x) ogf A013739 33.5463 -36/(-1+216*x) ogf A013739 31.3099 1/216*ln(1+6*x) revegf A013739 33.5463 1/36*x/(6*x+1) revogf A013739 39.1373 36/(1-216*x) ogf A013739 18.7859 {a(n+1)-216*a(n),a(0)=36} ogf A013740 32.1382 -343/(-1+343*x) lgdogf A013740 28.3572 -7+(1-343*x)*f(x) ogf A013740 37.0825 -7/(-1+343*x) ogf A013740 30.1295 1/343*ln(1+49*x) revegf A013740 34.4338 1/7*x/(1+49*x) revogf A013740 43.8248 7/(1-343*x) ogf A013740 20.0864 {a(n+1)-343*a(n),a(0)=7} ogf A013741 33.7948 -343/(-1+343*x) lgdogf A013741 28.1623 -49+(1-343*x)*f(x) ogf A013741 36.2087 -49/(-1+343*x) ogf A013741 33.7948 1/343*ln(1+7*x) revegf A013741 36.2087 1/49*x/(1+7*x) revogf A013741 42.2435 49/(1-343*x) ogf A013741 20.2769 {a(n+1)-343*a(n),a(0)=49} ogf A013742 34.1261 -512/(-1+512*x) lgdogf A013742 30.1113 -8+(1-512*x)*f(x) ogf A013742 39.3763 -8/(-1+512*x) ogf A013742 31.9932 1/512*ln(1+64*x) revegf A013742 36.5637 1/8*x/(1+64*x) revogf A013742 46.5356 8/(1-512*x) ogf A013742 21.3288 {a(n+1)-512*a(n),a(0)=8} ogf A013743 35.9484 -512/(-1+512*x) lgdogf A013743 29.957 -64+(1-512*x)*f(x) ogf A013743 38.5161 -64/(-1+512*x) ogf A013743 35.9484 1/512*ln(8*x+1) revegf A013743 38.5161 1/64*x/(8*x+1) revogf A013743 44.9355 64/(1-512*x) ogf A013743 21.569 {a(n+1)-512*a(n),a(0)=64} ogf A013744 29.0945 -729/(-1+729*x) lgdogf A013744 25.6716 -9+(1-729*x)*f(x) ogf A013744 33.5706 -9/(-1+729*x) ogf A013744 27.2761 1/729*ln(1+81*x) revegf A013744 31.1727 1/9*x/(1+81*x) revogf A013744 39.6743 9/(1-729*x) ogf A013744 18.1841 {a(n+1)-729*a(n),a(0)=9} ogf A013745 30.853 -729/(-1+729*x) lgdogf A013745 25.7108 -81+(1-729*x)*f(x) ogf A013745 33.0568 -81/(-1+729*x) ogf A013745 30.853 1/729*ln(1+9*x) revegf A013745 33.0568 1/81*x/(1+9*x) revogf A013745 38.5662 81/(1-729*x) ogf A013745 18.5118 {a(n+1)-729*a(n),a(0)=81} ogf A013746 19.875 -10+(1-1000*x)*f(x) ogf A013746 25.175 -10/(-1+1000*x) ogf A013746 22.2132 -1000/(-1+1000*x) lgdogf A013746 23.6015 1/10*x/(1+100*x) revogf A013746 20.9792 1/1000*ln(1+100*x) revegf A013746 29.0481 10/(1-1000*x) ogf A013746 14.524 {a(n+1)-1000*a(n),a(0)=10} ogf A013747 20.0325 -100+(1-1000*x)*f(x) ogf A013747 25.0407 -100/(-1+1000*x) ogf A013747 23.5677 -1000/(-1+1000*x) lgdogf A013747 25.0407 1/100*x/(1+10*x) revogf A013747 23.5677 1/1000*ln(1+10*x) revegf A013747 28.6179 100/(1-1000*x) ogf A013747 14.8389 {a(n+1)-1000*a(n),a(0)=100} ogf A013748 25.2411 -11+(1-1331*x)*f(x) ogf A013748 31.972 -11/(-1+1331*x) ogf A013748 28.2106 -1331/(-1+1331*x) lgdogf A013748 29.9737 1/11*x/(1+121*x) revogf A013748 26.6433 1/1331*ln(1+121*x) revegf A013748 36.8908 11/(1-1331*x) ogf A013748 18.4454 {a(n+1)-1331*a(n),a(0)=11} ogf A013749 25.2978 -121+(1-1331*x)*f(x) ogf A013749 31.6223 -121/(-1+1331*x) ogf A013749 29.7622 -1331/(-1+1331*x) lgdogf A013749 31.6223 1/121*x/(1+11*x) revogf A013749 29.7622 1/1331*ln(1+11*x) revegf A013749 36.1398 121/(1-1331*x) ogf A013749 18.7391 {a(n+1)-1331*a(n),a(0)=121} ogf A013750 20.7233 -12+(1-1728*x)*f(x) ogf A013750 26.2495 -12/(-1+1728*x) ogf A013750 23.1613 -1728/(-1+1728*x) lgdogf A013750 24.6089 1/12*x/(1+144*x) revogf A013750 21.8746 1/1728*ln(1+144*x) revegf A013750 30.2879 12/(1-1728*x) ogf A013750 15.144 {a(n+1)-1728*a(n),a(0)=12} ogf A013751 16.3693 -144+(1-1728*x)*f(x) ogf A013751 20.4616 -144/(-1+1728*x) ogf A013751 19.258 -1728/(-1+1728*x) lgdogf A013751 20.4616 1/144*x/(1+12*x) revogf A013751 19.258 1/1728*ln(1+12*x) revegf A013751 23.3847 144/(1-1728*x) ogf A013751 12.1254 {a(n+1)-1728*a(n),a(0)=144} ogf A013752 16.537 -13+(1-2197*x)*f(x) ogf A013752 20.9468 -13/(-1+2197*x) ogf A013752 18.4825 -2197/(-1+2197*x) lgdogf A013752 19.6377 1/13*x/(1+169*x) revogf A013752 17.4557 1/2197*ln(1+169*x) revegf A013752 24.1694 13/(1-2197*x) ogf A013752 12.0847 {a(n+1)-2197*a(n),a(0)=13} ogf A013753 32.6766 -169+(1-2197*x)*f(x) ogf A013753 40.8457 -169/(-1+2197*x) ogf A013753 38.443 -2197/(-1+2197*x) lgdogf A013753 40.8457 1/169*x/(1+13*x) revogf A013753 38.443 1/2197*ln(1+13*x) revegf A013753 46.6808 169/(1-2197*x) ogf A013753 24.2049 {a(n+1)-2197*a(n),a(0)=169} ogf A013754 33.7425 -14+(1-2744*x)*f(x) ogf A013754 42.7405 -14/(-1+2744*x) ogf A013754 37.7122 -2744/(-1+2744*x) lgdogf A013754 40.0692 1/14*x/(1+196*x) revogf A013754 35.617 1/2744*ln(1+196*x) revegf A013754 49.3159 14/(1-2744*x) ogf A013754 24.658 {a(n+1)-2744*a(n),a(0)=14} ogf A013755 27.5758 -196+(1-2744*x)*f(x) ogf A013755 34.4698 -196/(-1+2744*x) ogf A013755 32.4422 -2744/(-1+2744*x) lgdogf A013755 34.4698 1/196*x/(1+14*x) revogf A013755 32.4422 1/2744*ln(1+14*x) revegf A013755 39.3941 196/(1-2744*x) ogf A013755 20.4266 {a(n+1)-2744*a(n),a(0)=196} ogf A013756 28.0176 -15+(1-3375*x)*f(x) ogf A013756 35.4889 -15/(-1+3375*x) ogf A013756 31.3138 -3375/(-1+3375*x) lgdogf A013756 33.2709 1/15*x/(1+225*x) revogf A013756 29.5741 1/3375*ln(1+225*x) revegf A013756 40.9488 15/(1-3375*x) ogf A013756 20.4744 {a(n+1)-3375*a(n),a(0)=15} ogf A013757 22.5654 -225+(1-3375*x)*f(x) ogf A013757 28.2067 -225/(-1+3375*x) ogf A013757 26.5475 -3375/(-1+3375*x) lgdogf A013757 28.2067 1/225*x/(1+15*x) revogf A013757 26.5475 1/3375*ln(1+15*x) revegf A013757 32.2363 225/(1-3375*x) ogf A013757 16.7151 {a(n+1)-3375*a(n),a(0)=225} ogf A013758 22.9047 -16+(1-4096*x)*f(x) ogf A013758 29.0126 -16/(-1+4096*x) ogf A013758 25.5994 -4096/(-1+4096*x) lgdogf A013758 27.1993 1/16*x/(1+256*x) revogf A013758 24.1772 1/4096*ln(1+256*x) revegf A013758 33.4761 16/(1-4096*x) ogf A013758 16.7381 {a(n+1)-4096*a(n),a(0)=16} ogf A013759 13.7243 -256+(1-4096*x)*f(x) ogf A013759 17.1554 -256/(-1+4096*x) ogf A013759 16.1462 -4096/(-1+4096*x) lgdogf A013759 17.1554 1/256*x/(1+16*x) revogf A013759 16.1462 1/4096*ln(1+16*x) revegf A013759 19.6061 256/(1-4096*x) ogf A013759 10.1662 {a(n+1)-4096*a(n),a(0)=256} ogf A013760 13.5711 -17+(1-4913*x)*f(x) ogf A013760 17.19 -17/(-1+4913*x) ogf A013760 15.1677 -4913/(-1+4913*x) lgdogf A013760 16.1157 1/17*x/(1+289*x) revogf A013760 14.325 1/4913*ln(1+289*x) revegf A013760 19.8347 17/(1-4913*x) ogf A013760 9.91733 {a(n+1)-4913*a(n),a(0)=17} ogf A013761 23.4864 -289+(1-4913*x)*f(x) ogf A013761 29.358 -289/(-1+4913*x) ogf A013761 27.6311 -4913/(-1+4913*x) lgdogf A013761 29.358 1/289*x/(1+17*x) revogf A013761 27.6311 1/4913*ln(1+17*x) revegf A013761 33.552 289/(1-4913*x) ogf A013761 17.3973 {a(n+1)-4913*a(n),a(0)=289} ogf A013762 18.5029 -18+(1-5832*x)*f(x) ogf A013762 23.437 -18/(-1+5832*x) ogf A013762 20.6797 -5832/(-1+5832*x) lgdogf A013762 21.9722 1/18*x/(1+324*x) revogf A013762 19.5308 1/5832*ln(1+324*x) revegf A013762 27.0427 18/(1-5832*x) ogf A013762 13.5214 {a(n+1)-5832*a(n),a(0)=18} ogf A013763 18.7862 -324+(1-5832*x)*f(x) ogf A013763 23.4828 -324/(-1+5832*x) ogf A013763 22.1014 -5832/(-1+5832*x) lgdogf A013763 23.4828 1/324*x/(1+18*x) revogf A013763 22.1014 1/5832*ln(1+18*x) revegf A013763 26.8375 324/(1-5832*x) ogf A013763 13.9157 {a(n+1)-5832*a(n),a(0)=324} ogf A013764 18.7342 -19+(1-6859*x)*f(x) ogf A013764 23.73 -19/(-1+6859*x) ogf A013764 20.9382 -6859/(-1+6859*x) lgdogf A013764 22.2469 1/19*x/(1+361*x) revogf A013764 19.775 1/6859*ln(1+361*x) revegf A013764 27.3807 19/(1-6859*x) ogf A013764 13.6904 {a(n+1)-6859*a(n),a(0)=19} ogf A013765 19.1158 -361+(1-6859*x)*f(x) ogf A013765 23.8948 -361/(-1+6859*x) ogf A013765 22.4892 -6859/(-1+6859*x) lgdogf A013765 23.8948 1/361*x/(1+19*x) revogf A013765 22.4892 1/6859*ln(1+19*x) revegf A013765 27.3083 361/(1-6859*x) ogf A013765 14.1599 {a(n+1)-6859*a(n),a(0)=361} ogf A013766 24.6014 -20+(1-8000*x)*f(x) ogf A013766 31.1617 -20/(-1+8000*x) ogf A013766 27.4956 -8000/(-1+8000*x) lgdogf A013766 29.2141 1/20*x/(1+400*x) revogf A013766 25.9681 1/8000*ln(1+400*x) revegf A013766 35.9558 20/(1-8000*x) ogf A013766 17.9779 {a(n+1)-8000*a(n),a(0)=20} ogf A013767 24.868 -400+(1-8000*x)*f(x) ogf A013767 31.085 -400/(-1+8000*x) ogf A013767 29.2564 -8000/(-1+8000*x) lgdogf A013767 31.085 1/400*x/(1+20*x) revogf A013767 29.2564 1/8000*ln(1+20*x) revegf A013767 35.5257 400/(1-8000*x) ogf A013767 18.4207 {a(n+1)-8000*a(n),a(0)=400} ogf A013768 25.3285 -21+(1-9261*x)*f(x) ogf A013768 32.0828 -21/(-1+9261*x) ogf A013768 28.3083 -9261/(-1+9261*x) lgdogf A013768 30.0776 1/21*x/(1+441*x) revogf A013768 26.7356 1/9261*ln(1+441*x) revegf A013768 37.0186 21/(1-9261*x) ogf A013768 18.5093 {a(n+1)-9261*a(n),a(0)=21} ogf A013769 25.2134 -441+(1-9261*x)*f(x) ogf A013769 31.5167 -441/(-1+9261*x) ogf A013769 29.6628 -9261/(-1+9261*x) lgdogf A013769 31.5167 1/441*x/(1+21*x) revogf A013769 29.6628 1/9261*ln(1+21*x) revegf A013769 36.0191 441/(1-9261*x) ogf A013769 18.6766 {a(n+1)-9261*a(n),a(0)=441} ogf A013770 25.3285 -10648/(-1+10648*x) lgdogf A013770 24.0621 -22+(1-10648*x)*f(x) ogf A013770 30.0776 -22/(-1+10648*x) ogf A013770 25.3285 1/10648*ln(1+484*x) revegf A013770 30.0776 1/22*x/(1+484*x) revogf A013770 34.3744 22/(1-10648*x) ogf A013770 17.8238 {a(n+1)-10648*a(n),a(0)=22} ogf A013771 26.5404 -10648/(-1+10648*x) lgdogf A013771 24.0127 -484+(1-10648*x)*f(x) ogf A013771 29.6628 -484/(-1+10648*x) ogf A013771 28.0148 1/10648*ln(1+22*x) revegf A013771 31.5167 1/484*x/(1+22*x) revogf A013771 33.6178 484/(1-10648*x) ogf A013771 18.0095 {a(n+1)-10648*a(n),a(0)=484} ogf A013772 25.5709 -12167/(-1+12167*x) lgdogf A013772 24.2923 -23+(1-12167*x)*f(x) ogf A013772 30.3654 -23/(-1+12167*x) ogf A013772 25.5709 1/12167*ln(1+529*x) revegf A013772 30.3654 1/23*x/(1+529*x) revogf A013772 34.7033 23/(1-12167*x) ogf A013772 17.9943 {a(n+1)-12167*a(n),a(0)=23} ogf A013773 21.2783 -12167/(-1+12167*x) lgdogf A013773 19.2518 -529+(1-12167*x)*f(x) ogf A013773 23.7817 -529/(-1+12167*x) ogf A013773 22.4605 1/12167*ln(1+23*x) revegf A013773 25.268 1/529*x/(1+23*x) revogf A013773 26.9526 529/(1-12167*x) ogf A013773 14.4389 {a(n+1)-12167*a(n),a(0)=529} ogf A013774 20.1219 -13824/(-1+13824*x) lgdogf A013774 19.1158 -24+(1-13824*x)*f(x) ogf A013774 23.8948 -24/(-1+13824*x) ogf A013774 20.1219 1/13824*ln(1+576*x) revegf A013774 23.8948 1/24*x/(1+576*x) revogf A013774 27.3083 24/(1-13824*x) ogf A013774 14.1599 {a(n+1)-13824*a(n),a(0)=24} ogf A013775 16.3072 -13824/(-1+13824*x) lgdogf A013775 14.7541 -576+(1-13824*x)*f(x) ogf A013775 18.2257 -576/(-1+13824*x) ogf A013775 17.2131 1/13824*ln(1+24*x) revegf A013775 19.3648 1/576*x/(1+24*x) revogf A013775 20.6558 576/(1-13824*x) ogf A013775 11.0656 {a(n+1)-13824*a(n),a(0)=576} ogf A013776 36.6835 -16/(-1+16*x) lgdogf A013776 29.8053 -2+(1-16*x)*f(x) ogf A013776 39.7405 -2/(-1+16*x) ogf A013776 34.0632 1/16*ln(8*x+1) revegf A013776 36.6835 1/2*x/(8*x+1) revogf A013776 47.6885 2/(1-16*x) ogf A013776 20.7342 {a(n+1)-16*a(n),a(0)=2} ogf A013777 41.8199 -16/(16*x-1) lgdogf A013777 31.3649 -8+(1-16*x)*f(x) ogf A013777 41.8199 -8/(-1+16*x) ogf A013777 35.8456 1/16*ln(1+2*x) revegf A013777 38.603 1/8*x/(2*x+1) revogf A013777 50.1839 8/(1-16*x) ogf A013777 21.8191 {a(n+1)-16*a(n),a(0)=8} ogf A013778 33.1532 -3+(1-81*x)*f(x) ogf A013778 44.2043 -3/(-1+81*x) ogf A013778 40.8039 -81/(-1+81*x) lgdogf A013778 37.8894 1/3*x/(1+27*x) revogf A013778 35.3634 1/81*ln(1+27*x) revegf A013778 53.0451 3/(1-81*x) ogf A013778 23.0631 {a(n+1)-81*a(n),a(0)=3} ogf A013779 28.0636 -27+(1-81*x)*f(x) ogf A013779 36.6985 -27/(-1+81*x) ogf A013779 36.6985 -81/(-1+81*x) lgdogf A013779 34.0772 1/27*x/(1+3*x) revogf A013779 34.0772 1/81*ln(1+3*x) revegf A013779 43.371 27/(1-81*x) ogf A013779 19.8784 {a(n+1)-81*a(n),a(0)=27} ogf A013780 30.4816 -256/(-1+256*x) lgdogf A013780 26.8955 -4+(1-256*x)*f(x) ogf A013780 35.171 -4/(-1+256*x) ogf A013780 28.5765 1/256*ln(1+64*x) revegf A013780 32.6588 1/4*x/(1+64*x) revogf A013780 41.5658 4/(1-256*x) ogf A013780 19.051 {a(n+1)-256*a(n),a(0)=4} ogf A013781 32.8008 -256/(-1+256*x) lgdogf A013781 27.334 -64+(1-256*x)*f(x) ogf A013781 35.1437 -64/(-1+256*x) ogf A013781 32.8008 1/256*ln(1+4*x) revegf A013781 35.1437 1/64*x/(1+4*x) revogf A013781 41.001 64/(1-256*x) ogf A013781 19.6805 {a(n+1)-256*a(n),a(0)=64} ogf A013782 24.9664 -5+(1-625*x)*f(x) ogf A013782 32.6483 -5/(-1+625*x) ogf A013782 28.2952 1/5*x/(1+125*x) revogf A013782 24.9664 1/625*ln(1+125*x) revegf A013782 38.5844 5/(1-625*x) ogf A013782 17.6845 {a(n+1)-625*a(n),a(0)=5} ogf A013783 24.3576 -125+(1-625*x)*f(x) ogf A013783 30.853 -125/(-1+625*x) ogf A013783 30.853 -625/(-1+625*x) lgdogf A013783 30.853 1/125*x/(1+5*x) revogf A013783 30.853 1/625*ln(1+5*x) revegf A013783 35.5996 125/(1-625*x) ogf A013783 17.7998 {a(n+1)-625*a(n),a(0)=125} ogf A013784 27.5053 -1296/(-1+1296*x) lgdogf A013784 25.9773 -6+(1-1296*x)*f(x) ogf A013784 33.3993 -6/(-1+1296*x) ogf A013784 25.9773 1/1296*ln(1+216*x) revegf A013784 31.1727 1/6*x/(1+216*x) revogf A013784 38.9659 6/(1-1296*x) ogf A013784 18.7036 {a(n+1)-1296*a(n),a(0)=6} ogf A013785 30.0443 -1296/(-1+1296*x) lgdogf A013785 25.5376 -216+(1-1296*x)*f(x) ogf A013785 31.922 -216/(-1+1296*x) ogf A013785 31.922 1/1296*ln(1+6*x) revegf A013785 34.0502 1/216*x/(6*x+1) revogf A013785 36.4823 216/(1-1296*x) ogf A013785 18.9168 {a(n+1)-1296*a(n),a(0)=216} ogf A013786 29.6211 -2401/(-1+2401*x) lgdogf A013786 27.9755 -7+(1-2401*x)*f(x) ogf A013786 35.9685 -7/(-1+2401*x) ogf A013786 27.9755 1/2401*ln(1+343*x) revegf A013786 33.5706 1/7*x/(1+343*x) revogf A013786 41.9633 7/(1-2401*x) ogf A013786 20.1424 {a(n+1)-2401*a(n),a(0)=7} ogf A013787 32.3011 -2401/(-1+2401*x) lgdogf A013787 27.456 -343+(1-2401*x)*f(x) ogf A013787 34.3199 -343/(-1+2401*x) ogf A013787 34.3199 1/2401*ln(1+7*x) revegf A013787 36.6079 1/343*x/(1+7*x) revogf A013787 39.2228 343/(1-2401*x) ogf A013787 20.3377 {a(n+1)-2401*a(n),a(0)=343} ogf A013788 31.5959 -4096/(-1+4096*x) lgdogf A013788 29.8405 -8+(1-4096*x)*f(x) ogf A013788 38.3664 -8/(-1+4096*x) ogf A013788 29.8405 1/4096*ln(1+512*x) revegf A013788 35.8086 1/8*x/(1+512*x) revogf A013788 44.7608 8/(1-4096*x) ogf A013788 21.4852 {a(n+1)-4096*a(n),a(0)=8} ogf A013789 27.4956 -4096/(-1+4096*x) lgdogf A013789 23.3713 -512+(1-4096*x)*f(x) ogf A013789 29.2141 -512/(-1+4096*x) ogf A013789 29.2141 1/4096*ln(8*x+1) revegf A013789 31.1617 1/512*x/(8*x+1) revogf A013789 33.3876 512/(1-4096*x) ogf A013789 17.3121 {a(n+1)-4096*a(n),a(0)=512} ogf A013790 26.4121 -6561/(-1+6561*x) lgdogf A013790 24.9447 -9+(1-6561*x)*f(x) ogf A013790 32.0718 -9/(-1+6561*x) ogf A013790 24.9447 1/6561*ln(1+729*x) revegf A013790 29.9337 1/9*x/(1+729*x) revogf A013790 37.4171 9/(1-6561*x) ogf A013790 17.9602 {a(n+1)-6561*a(n),a(0)=9} ogf A013791 28.9855 -6561/(-1+6561*x) lgdogf A013791 24.6377 -729+(1-6561*x)*f(x) ogf A013791 30.7971 -729/(-1+6561*x) ogf A013791 30.7971 1/6561*ln(1+9*x) revegf A013791 32.8503 1/729*x/(1+9*x) revogf A013791 35.1967 729/(1-6561*x) ogf A013791 18.2502 {a(n+1)-6561*a(n),a(0)=729} ogf A013792 24.0621 -10+(1-10000*x)*f(x) ogf A013792 30.0776 -10/(-1+10000*x) ogf A013792 25.3285 -10000/(-1+10000*x) lgdogf A013792 28.3083 1/10*x/(1+1000*x) revogf A013792 24.0621 1/10000*ln(1+1000*x) revegf A013792 34.3744 10/(1-10000*x) ogf A013792 17.8238 {a(n+1)-10000*a(n),a(0)=10} ogf A013793 18.7762 -1000+(1-10000*x)*f(x) ogf A013793 22.9487 -1000/(-1+10000*x) ogf A013793 21.7409 -10000/(-1+10000*x) lgdogf A013793 24.2987 1/1000*x/(1+10*x) revogf A013793 22.9487 1/10000*ln(1+10*x) revegf A013793 25.8173 1000/(1-10000*x) ogf A013793 14.244 {a(n+1)-10000*a(n),a(0)=1000} ogf A013794 24.5226 -11+(1-14641*x)*f(x) ogf A013794 30.6532 -11/(-1+14641*x) ogf A013794 25.8132 -14641/(-1+14641*x) lgdogf A013794 28.8501 1/11*x/(1+1331*x) revogf A013794 24.5226 1/14641*ln(1+1331*x) revegf A013794 35.0323 11/(1-14641*x) ogf A013794 18.1649 {a(n+1)-14641*a(n),a(0)=11} ogf A013795 19.0759 -1331+(1-14641*x)*f(x) ogf A013795 23.3149 -1331/(-1+14641*x) ogf A013795 22.0878 -14641/(-1+14641*x) lgdogf A013795 24.6864 1/1331*x/(1+11*x) revogf A013795 23.3149 1/14641*ln(1+11*x) revegf A013795 26.2293 1331/(1-14641*x) ogf A013795 14.4713 {a(n+1)-14641*a(n),a(0)=1331} ogf A013796 25.2134 -12+(1-20736*x)*f(x) ogf A013796 31.5167 -12/(-1+20736*x) ogf A013796 26.5404 -20736/(-1+20736*x) lgdogf A013796 29.6628 1/12*x/(1+1728*x) revogf A013796 25.2134 1/20736*ln(1+1728*x) revegf A013796 36.0191 12/(1-20736*x) ogf A013796 18.6766 {a(n+1)-20736*a(n),a(0)=12} ogf A013797 19.6751 -1728+(1-20736*x)*f(x) ogf A013797 24.0474 -1728/(-1+20736*x) ogf A013797 22.7817 -20736/(-1+20736*x) lgdogf A013797 25.4619 1/1728*x/(1+12*x) revogf A013797 24.0474 1/20736*ln(1+12*x) revegf A013797 27.0533 1728/(1-20736*x) ogf A013797 14.9259 {a(n+1)-20736*a(n),a(0)=1728} ogf A013798 20.1046 -13+(1-28561*x)*f(x) ogf A013798 25.1307 -13/(-1+28561*x) ogf A013798 21.1627 -28561/(-1+28561*x) lgdogf A013798 23.6524 1/13*x/(1+2197*x) revogf A013798 20.1046 1/28561*ln(1+2197*x) revegf A013798 28.7208 13/(1-28561*x) ogf A013798 14.8923 {a(n+1)-28561*a(n),a(0)=13} ogf A013799 20.2743 -2197+(1-28561*x)*f(x) ogf A013799 24.7798 -2197/(-1+28561*x) ogf A013799 23.4756 -28561/(-1+28561*x) lgdogf A013799 26.2374 1/2197*x/(1+13*x) revogf A013799 24.7798 1/28561*ln(1+13*x) revegf A013799 27.8772 2197/(1-28561*x) ogf A013799 15.3805 {a(n+1)-28561*a(n),a(0)=2197} ogf A013800 20.6539 -14+(1-38416*x)*f(x) ogf A013800 25.8173 -14/(-1+38416*x) ogf A013800 21.7409 -38416/(-1+38416*x) lgdogf A013800 24.2987 1/14*x/(1+2744*x) revogf A013800 20.6539 1/38416*ln(1+2744*x) revegf A013800 29.5055 14/(1-38416*x) ogf A013800 15.2992 {a(n+1)-38416*a(n),a(0)=14} ogf A013801 20.8736 -2744+(1-38416*x)*f(x) ogf A013801 25.5122 -2744/(-1+38416*x) ogf A013801 24.1694 -38416/(-1+38416*x) lgdogf A013801 27.0129 1/2744*x/(1+14*x) revogf A013801 25.5122 1/38416*ln(1+14*x) revegf A013801 28.7012 2744/(1-38416*x) ogf A013801 15.8351 {a(n+1)-38416*a(n),a(0)=2744} ogf A013802 21.0933 -15+(1-50625*x)*f(x) ogf A013802 26.3666 -15/(-1+50625*x) ogf A013802 22.2035 -50625/(-1+50625*x) lgdogf A013802 24.8157 1/15*x/(1+3375*x) revogf A013802 21.0933 1/50625*ln(1+3375*x) revegf A013802 30.1333 15/(1-50625*x) ogf A013802 15.6247 {a(n+1)-50625*a(n),a(0)=15} ogf A013803 21.373 -3375+(1-50625*x)*f(x) ogf A013803 26.1225 -3375/(-1+50625*x) ogf A013803 24.7476 -50625/(-1+50625*x) lgdogf A013803 27.6591 1/3375*x/(1+15*x) revogf A013803 26.1225 1/50625*ln(1+15*x) revegf A013803 29.3878 3375/(1-50625*x) ogf A013803 16.214 {a(n+1)-50625*a(n),a(0)=3375} ogf A013804 21.6426 -16+(1-65536*x)*f(x) ogf A013804 27.0533 -16/(-1+65536*x) ogf A013804 22.7817 -65536/(-1+65536*x) lgdogf A013804 25.4619 1/16*x/(1+4096*x) revogf A013804 21.6426 1/65536*ln(1+4096*x) revegf A013804 30.918 16/(1-65536*x) ogf A013804 16.0316 {a(n+1)-65536*a(n),a(0)=16} ogf A013805 21.8723 -4096+(1-65536*x)*f(x) ogf A013805 26.7328 -4096/(-1+65536*x) ogf A013805 25.3259 -65536/(-1+65536*x) lgdogf A013805 28.3054 1/4096*x/(1+16*x) revogf A013805 26.7328 1/65536*ln(1+16*x) revegf A013805 30.0744 4096/(1-65536*x) ogf A013805 16.5928 {a(n+1)-65536*a(n),a(0)=4096} ogf A013806 21.9722 -17+(1-83521*x)*f(x) ogf A013806 27.4653 -17/(-1+83521*x) ogf A013806 23.1286 -83521/(-1+83521*x) lgdogf A013806 25.8496 1/17*x/(1+4913*x) revogf A013806 21.9722 1/83521*ln(1+4913*x) revegf A013806 31.3889 17/(1-83521*x) ogf A013806 16.2757 {a(n+1)-83521*a(n),a(0)=17} ogf A013807 22.3717 -4913+(1-83521*x)*f(x) ogf A013807 27.3432 -4913/(-1+83521*x) ogf A013807 25.9041 -83521/(-1+83521*x) lgdogf A013807 28.9516 1/4913*x/(1+17*x) revogf A013807 27.3432 1/83521*ln(1+17*x) revegf A013807 30.7611 4913/(1-83521*x) ogf A013807 16.9716 {a(n+1)-83521*a(n),a(0)=4913} ogf A013808 21.5537 -104976/(-1+104976*x) lgdogf A013808 21.5537 -18+(1-104976*x)*f(x) ogf A013808 26.6251 -18/(-1+104976*x) ogf A013808 21.5537 1/104976*ln(1+5832*x) revegf A013808 26.6251 1/18*x/(1+5832*x) revogf A013808 30.1752 18/(1-104976*x) ogf A013808 16.1653 {a(n+1)-104976*a(n),a(0)=18} ogf A013809 23.437 -104976/(-1+104976*x) lgdogf A013809 21.399 -5832+(1-104976*x)*f(x) ogf A013809 25.9041 -5832/(-1+104976*x) ogf A013809 25.9041 1/104976*ln(1+18*x) revegf A013809 28.9516 1/5832*x/(1+18*x) revogf A013809 28.9516 5832/(1-104976*x) ogf A013809 16.4059 {a(n+1)-104976*a(n),a(0)=5832} ogf A013810 21.7629 -130321/(-1+130321*x) lgdogf A013810 21.7629 -19+(1-130321*x)*f(x) ogf A013810 26.8836 -19/(-1+130321*x) ogf A013810 21.7629 1/130321*ln(1+6859*x) revegf A013810 26.8836 1/19*x/(1+6859*x) revogf A013810 30.4681 19/(1-130321*x) ogf A013810 16.3222 {a(n+1)-130321*a(n),a(0)=19} ogf A013811 24.1694 -130321/(-1+130321*x) lgdogf A013811 22.0677 -6859+(1-130321*x)*f(x) ogf A013811 26.7136 -6859/(-1+130321*x) ogf A013811 26.7136 1/130321*ln(1+19*x) revegf A013811 29.8563 1/6859*x/(1+19*x) revogf A013811 29.8563 6859/(1-130321*x) ogf A013811 16.9186 {a(n+1)-130321*a(n),a(0)=6859} ogf A013812 22.0768 -160000/(-1+160000*x) lgdogf A013812 22.0768 -20+(1-160000*x)*f(x) ogf A013812 27.2714 -20/(-1+160000*x) ogf A013812 22.0768 1/160000*ln(1+8000*x) revegf A013812 27.2714 1/20*x/(1+8000*x) revogf A013812 30.9076 20/(1-160000*x) ogf A013812 16.5576 {a(n+1)-160000*a(n),a(0)=20} ogf A013813 24.5879 -160000/(-1+160000*x) lgdogf A013813 22.4499 -8000+(1-160000*x)*f(x) ogf A013813 27.1761 -8000/(-1+160000*x) ogf A013813 27.1761 1/160000*ln(1+20*x) revegf A013813 30.3733 1/8000*x/(1+20*x) revogf A013813 30.3733 8000/(1-160000*x) ogf A013813 17.2116 {a(n+1)-160000*a(n),a(0)=8000} ogf A013814 22.4953 -194481/(-1+194481*x) lgdogf A013814 22.4953 -21+(1-194481*x)*f(x) ogf A013814 27.7884 -21/(-1+194481*x) ogf A013814 22.4953 1/194481*ln(1+9261*x) revegf A013814 27.7884 1/21*x/(1+9261*x) revogf A013814 31.4935 21/(1-194481*x) ogf A013814 16.8715 {a(n+1)-194481*a(n),a(0)=21} ogf A013815 24.9018 -194481/(-1+194481*x) lgdogf A013815 22.7365 -9261+(1-194481*x)*f(x) ogf A013815 27.5231 -9261/(-1+194481*x) ogf A013815 27.5231 1/194481*ln(1+21*x) revegf A013815 30.7611 1/9261*x/(1+21*x) revogf A013815 30.7611 9261/(1-194481*x) ogf A013815 17.4313 {a(n+1)-194481*a(n),a(0)=9261} ogf A013816 22.8092 -22+(1-234256*x)*f(x) ogf A013816 28.1761 -22/(-1+234256*x) ogf A013816 22.8092 -234256/(-1+234256*x) lgdogf A013816 26.6108 1/22*x/(1+10648*x) revogf A013816 21.7725 1/234256*ln(1+10648*x) revegf A013816 31.9329 22/(1-234256*x) ogf A013816 17.1069 {a(n+1)-234256*a(n),a(0)=22} ogf A013817 16.8088 -10648+(1-234256*x)*f(x) ogf A013817 20.1706 -10648/(-1+234256*x) ogf A013817 19.2101 -234256/(-1+234256*x) lgdogf A013817 22.4117 1/10648*x/(1+22*x) revogf A013817 21.2322 1/234256*ln(1+22*x) revegf A013817 22.4117 10648/(1-234256*x) ogf A013817 13.0133 {a(n+1)-234256*a(n),a(0)=10648} ogf A013818 23.1231 -23+(1-279841*x)*f(x) ogf A013818 28.5639 -23/(-1+279841*x) ogf A013818 23.1231 -279841/(-1+279841*x) lgdogf A013818 26.977 1/23*x/(1+12167*x) revogf A013818 22.0721 1/279841*ln(1+12167*x) revegf A013818 32.3724 23/(1-279841*x) ogf A013818 17.3423 {a(n+1)-279841*a(n),a(0)=23} ogf A013819 16.9821 -12167+(1-279841*x)*f(x) ogf A013819 20.3785 -12167/(-1+279841*x) ogf A013819 19.4081 -279841/(-1+279841*x) lgdogf A013819 22.6428 1/12167*x/(1+23*x) revogf A013819 21.4511 1/279841*ln(1+23*x) revegf A013819 22.6428 12167/(1-279841*x) ogf A013819 13.1474 {a(n+1)-279841*a(n),a(0)=12167} ogf A013820 23.3324 -24+(1-331776*x)*f(x) ogf A013820 28.8224 -24/(-1+331776*x) ogf A013820 23.3324 -331776/(-1+331776*x) lgdogf A013820 27.2211 1/24*x/(1+13824*x) revogf A013820 22.2718 1/331776*ln(1+13824*x) revegf A013820 32.6653 24/(1-331776*x) ogf A013820 17.4993 {a(n+1)-331776*a(n),a(0)=24} ogf A013821 17.242 -13824+(1-331776*x)*f(x) ogf A013821 20.6904 -13824/(-1+331776*x) ogf A013821 19.7052 -331776/(-1+331776*x) lgdogf A013821 22.9894 1/13824*x/(1+24*x) revogf A013821 21.7794 1/331776*ln(1+24*x) revegf A013821 22.9894 13824/(1-331776*x) ogf A013821 13.3487 {a(n+1)-331776*a(n),a(0)=13824} ogf A013822 30.9733 -2+(1-32*x)*f(x) ogf A013822 41.2978 -2/(-1+32*x) ogf A013822 38.121 -32/(-1+32*x) lgdogf A013822 35.3981 1/2*x/(1+16*x) revogf A013822 33.0382 1/32*ln(1+16*x) revegf A013822 49.5573 2/(1-32*x) ogf A013822 21.5467 {a(n+1)-32*a(n),a(0)=2} ogf A013823 39.5792 -32/(-1+32*x) lgdogf A013823 32.1581 -4+(1-32*x)*f(x) ogf A013823 42.8775 -4/(-1+32*x) ogf A013823 36.7521 1/32*ln(8*x+1) revegf A013823 39.5792 1/4*x/(8*x+1) revogf A013823 51.453 4/(1-32*x) ogf A013823 22.3708 {a(n+1)-32*a(n),a(0)=4} ogf A013824 39.5792 -32/(-1+32*x) lgdogf A013824 32.1581 -8+(1-32*x)*f(x) ogf A013824 42.8775 -8/(-1+32*x) ogf A013824 36.7521 1/32*ln(1+4*x) revegf A013824 39.5792 1/8*x/(1+4*x) revogf A013824 51.453 8/(1-32*x) ogf A013824 22.3708 {a(n+1)-32*a(n),a(0)=8} ogf A013825 31.5408 -16+(1-32*x)*f(x) ogf A013825 41.2457 -16/(-1+32*x) ogf A013825 41.2457 -32/(-1+32*x) lgdogf A013825 38.2996 1/16*x/(2*x+1) revogf A013825 38.2996 1/32*ln(1+2*x) revegf A013825 48.7449 16/(1-32*x) ogf A013825 22.3414 {a(n+1)-32*a(n),a(0)=16} ogf A013826 29.8189 -243/(-1+243*x) lgdogf A013826 26.3108 -3+(1-243*x)*f(x) ogf A013826 34.4064 -3/(-1+243*x) ogf A013826 27.9552 1/243*ln(1+81*x) revegf A013826 31.9488 1/3*x/(1+81*x) revogf A013826 40.6622 3/(1-243*x) ogf A013826 18.6368 {a(n+1)-243*a(n),a(0)=3} ogf A013827 30.8129 -243/(-1+243*x) lgdogf A013827 27.1878 -9+(1-243*x)*f(x) ogf A013827 35.5533 -9/(-1+243*x) ogf A013827 28.8871 1/243*ln(1+27*x) revegf A013827 33.0138 1/9*x/(1+27*x) revogf A013827 42.0176 9/(1-243*x) ogf A013827 19.2581 {a(n+1)-243*a(n),a(0)=9} ogf A013828 31.6412 -243/(-1+243*x) lgdogf A013828 26.3677 -27+(1-243*x)*f(x) ogf A013828 33.9013 -27/(-1+243*x) ogf A013828 31.6412 1/243*ln(1+9*x) revegf A013828 33.9013 1/27*x/(1+9*x) revogf A013828 39.5515 27/(1-243*x) ogf A013828 18.9847 {a(n+1)-243*a(n),a(0)=27} ogf A013829 32.6352 -243/(-1+243*x) lgdogf A013829 27.196 -81+(1-243*x)*f(x) ogf A013829 34.9662 -81/(-1+243*x) ogf A013829 32.6352 1/243*ln(1+3*x) revegf A013829 34.9662 1/81*x/(1+3*x) revogf A013829 40.7939 81/(1-243*x) ogf A013829 19.5811 {a(n+1)-243*a(n),a(0)=81} ogf A013830 26.2358 -1024/(-1+1024*x) lgdogf A013830 24.7783 -4+(1-1024*x)*f(x) ogf A013830 31.8578 -4/(-1+1024*x) ogf A013830 24.7783 1/1024*ln(1+256*x) revegf A013830 29.734 1/4*x/(1+256*x) revogf A013830 37.1675 4/(1-1024*x) ogf A013830 17.8404 {a(n+1)-1024*a(n),a(0)=4} ogf A013831 27.7874 -1024/(-1+1024*x) lgdogf A013831 24.8624 -16+(1-1024*x)*f(x) ogf A013831 31.4924 -16/(-1+1024*x) ogf A013831 27.7874 1/1024*ln(1+64*x) revegf A013831 31.4924 1/16*x/(1+64*x) revogf A013831 36.3374 16/(1-1024*x) ogf A013831 18.1687 {a(n+1)-1024*a(n),a(0)=16} ogf A013832 27.7874 -1024/(-1+1024*x) lgdogf A013832 24.8624 -64+(1-1024*x)*f(x) ogf A013832 31.4924 -64/(-1+1024*x) ogf A013832 27.7874 1/1024*ln(1+16*x) revegf A013832 31.4924 1/64*x/(1+16*x) revogf A013832 36.3374 64/(1-1024*x) ogf A013832 18.1687 {a(n+1)-1024*a(n),a(0)=64} ogf A013833 29.339 -1024/(-1+1024*x) lgdogf A013833 24.9382 -256+(1-1024*x)*f(x) ogf A013833 31.1727 -256/(-1+1024*x) ogf A013833 31.1727 1/1024*ln(1+4*x) revegf A013833 33.2509 1/256*x/(1+4*x) revogf A013833 35.6259 256/(1-1024*x) ogf A013833 18.4727 {a(n+1)-1024*a(n),a(0)=256} ogf A013834 30.4674 -3125/(-1+3125*x) lgdogf A013834 28.7748 -5+(1-3125*x)*f(x) ogf A013834 36.9962 -5/(-1+3125*x) ogf A013834 28.7748 1/3125*ln(1+625*x) revegf A013834 34.5298 1/5*x/(1+625*x) revogf A013834 43.1622 5/(1-3125*x) ogf A013834 20.7179 {a(n+1)-3125*a(n),a(0)=5} ogf A013835 28.0176 -25+(1-3125*x)*f(x) ogf A013835 35.4889 -25/(-1+3125*x) ogf A013835 31.3138 -3125/(-1+3125*x) lgdogf A013835 33.2709 1/25*x/(1+125*x) revogf A013835 29.5741 1/3125*ln(1+125*x) revegf A013835 40.9488 25/(1-3125*x) ogf A013835 20.4744 {a(n+1)-3125*a(n),a(0)=25} ogf A013836 22.3351 -125+(1-3125*x)*f(x) ogf A013836 27.9189 -125/(-1+3125*x) ogf A013836 26.2766 -3125/(-1+3125*x) lgdogf A013836 27.9189 1/125*x/(1+25*x) revogf A013836 26.2766 1/3125*ln(1+25*x) revegf A013836 31.9073 125/(1-3125*x) ogf A013836 16.5445 {a(n+1)-3125*a(n),a(0)=125} ogf A013837 26.9538 -3125/(-1+3125*x) lgdogf A013837 22.9108 -625+(1-3125*x)*f(x) ogf A013837 28.6385 -625/(-1+3125*x) ogf A013837 28.6385 1/3125*ln(1+5*x) revegf A013837 30.5477 1/625*x/(1+5*x) revogf A013837 32.7297 625/(1-3125*x) ogf A013837 16.9709 {a(n+1)-3125*a(n),a(0)=625} ogf A013838 25.2006 -6+(1-7776*x)*f(x) ogf A013838 32.4007 -6/(-1+7776*x) ogf A013838 26.683 -7776/(-1+7776*x) lgdogf A013838 28.3506 1/6*x/(1+1296*x) revogf A013838 23.8742 1/7776*ln(1+1296*x) revegf A013838 37.8009 6/(1-7776*x) ogf A013838 18.1444 {a(n+1)-7776*a(n),a(0)=6} ogf A013839 24.8437 -36+(1-7776*x)*f(x) ogf A013839 31.4687 -36/(-1+7776*x) ogf A013839 27.7665 -7776/(-1+7776*x) lgdogf A013839 29.5019 1/36*x/(1+216*x) revogf A013839 26.2239 1/7776*ln(1+216*x) revegf A013839 36.3101 36/(1-7776*x) ogf A013839 18.155 {a(n+1)-7776*a(n),a(0)=36} ogf A013840 24.5226 -216+(1-7776*x)*f(x) ogf A013840 30.6532 -216/(-1+7776*x) ogf A013840 28.8501 -7776/(-1+7776*x) lgdogf A013840 30.6532 1/216*x/(1+36*x) revogf A013840 28.8501 1/7776*ln(1+36*x) revegf A013840 35.0323 216/(1-7776*x) ogf A013840 18.1649 {a(n+1)-7776*a(n),a(0)=216} ogf A013841 24.232 -1296+(1-7776*x)*f(x) ogf A013841 29.9337 -1296/(-1+7776*x) ogf A013841 29.9337 -7776/(-1+7776*x) lgdogf A013841 31.8045 1/1296*x/(6*x+1) revogf A013841 31.8045 1/7776*ln(1+6*x) revegf A013841 33.9248 1296/(1-7776*x) ogf A013841 18.174 {a(n+1)-7776*a(n),a(0)=1296} ogf A013842 25.6921 -16807/(-1+16807*x) lgdogf A013842 25.6921 -7+(1-16807*x)*f(x) ogf A013842 32.5433 -7/(-1+16807*x) ogf A013842 24.4075 1/16807*ln(1+2401*x) revegf A013842 30.5093 1/7*x/(1+2401*x) revogf A013842 37.5499 7/(1-16807*x) ogf A013842 18.775 {a(n+1)-16807*a(n),a(0)=7} ogf A013843 26.7828 -16807/(-1+16807*x) lgdogf A013843 25.4436 -49+(1-16807*x)*f(x) ogf A013843 31.8045 -49/(-1+16807*x) ogf A013843 26.7828 1/16807*ln(1+343*x) revegf A013843 31.8045 1/49*x/(1+343*x) revogf A013843 36.348 49/(1-16807*x) ogf A013843 18.8471 {a(n+1)-16807*a(n),a(0)=49} ogf A013844 21.6253 -16807/(-1+16807*x) lgdogf A013844 19.5657 -343+(1-16807*x)*f(x) ogf A013844 24.1694 -343/(-1+16807*x) ogf A013844 22.8267 1/16807*ln(1+49*x) revegf A013844 25.68 1/343*x/(1+49*x) revogf A013844 27.392 343/(1-16807*x) ogf A013844 14.6743 {a(n+1)-16807*a(n),a(0)=343} ogf A013845 22.5504 -16807/(-1+16807*x) lgdogf A013845 19.4754 -2401+(1-16807*x)*f(x) ogf A013845 23.8032 -2401/(-1+16807*x) ogf A013845 25.2034 1/16807*ln(1+7*x) revegf A013845 26.7786 1/2401*x/(1+7*x) revogf A013845 26.7786 2401/(1-16807*x) ogf A013845 14.7744 {a(n+1)-16807*a(n),a(0)=2401} ogf A013846 21.0471 -32768/(-1+32768*x) lgdogf A013846 21.0471 -8+(1-32768*x)*f(x) ogf A013846 26.6596 -8/(-1+32768*x) ogf A013846 19.9947 1/32768*ln(1+4096*x) revegf A013846 24.9934 1/8*x/(1+4096*x) revogf A013846 30.7611 8/(1-32768*x) ogf A013846 15.3805 {a(n+1)-32768*a(n),a(0)=8} ogf A013847 21.9722 -32768/(-1+32768*x) lgdogf A013847 20.8736 -64+(1-32768*x)*f(x) ogf A013847 26.092 -64/(-1+32768*x) ogf A013847 21.9722 1/32768*ln(1+512*x) revegf A013847 26.092 1/64*x/(1+512*x) revogf A013847 29.8194 64/(1-32768*x) ogf A013847 15.4619 {a(n+1)-32768*a(n),a(0)=64} ogf A013848 23.013 -32768/(-1+32768*x) lgdogf A013848 20.8213 -512+(1-32768*x)*f(x) ogf A013848 25.7204 -512/(-1+32768*x) ogf A013848 24.2915 1/32768*ln(1+64*x) revegf A013848 27.3279 1/512*x/(1+64*x) revogf A013848 29.1498 512/(1-32768*x) ogf A013848 15.616 {a(n+1)-32768*a(n),a(0)=512} ogf A013849 24.0538 -32768/(-1+32768*x) lgdogf A013849 20.7737 -4096+(1-32768*x)*f(x) ogf A013849 25.3901 -4096/(-1+32768*x) ogf A013849 26.8836 1/32768*ln(8*x+1) revegf A013849 28.5639 1/4096*x/(8*x+1) revogf A013849 28.5639 4096/(1-32768*x) ogf A013849 15.7594 {a(n+1)-32768*a(n),a(0)=4096} ogf A013850 22.3191 -59049/(-1+59049*x) lgdogf A013850 22.3191 -9+(1-59049*x)*f(x) ogf A013850 28.2709 -9/(-1+59049*x) ogf A013850 21.2032 1/59049*ln(1+6561*x) revegf A013850 26.504 1/9*x/(1+6561*x) revogf A013850 32.6203 9/(1-59049*x) ogf A013850 16.3101 {a(n+1)-59049*a(n),a(0)=9} ogf A013851 23.2443 -59049/(-1+59049*x) lgdogf A013851 22.0821 -81+(1-59049*x)*f(x) ogf A013851 27.6026 -81/(-1+59049*x) ogf A013851 23.2443 1/59049*ln(1+729*x) revegf A013851 27.6026 1/81*x/(1+729*x) revogf A013851 31.5458 81/(1-59049*x) ogf A013851 16.3571 {a(n+1)-59049*a(n),a(0)=81} ogf A013852 24.2851 -59049/(-1+59049*x) lgdogf A013852 21.9722 -729+(1-59049*x)*f(x) ogf A013852 27.1421 -729/(-1+59049*x) ogf A013852 25.6342 1/59049*ln(1+81*x) revegf A013852 28.8385 1/729*x/(1+81*x) revogf A013852 30.7611 729/(1-59049*x) ogf A013852 16.4792 {a(n+1)-59049*a(n),a(0)=729} ogf A013853 25.2102 -59049/(-1+59049*x) lgdogf A013853 21.7725 -6561+(1-59049*x)*f(x) ogf A013853 26.6108 -6561/(-1+59049*x) ogf A013853 28.1761 1/59049*ln(1+9*x) revegf A013853 29.9371 1/6561*x/(1+9*x) revogf A013853 29.9371 6561/(1-59049*x) ogf A013853 16.517 {a(n+1)-59049*a(n),a(0)=6561} ogf A013854 21.5537 -10+(1-100000*x)*f(x) ogf A013854 26.6251 -10/(-1+100000*x) ogf A013854 21.5537 -100000/(-1+100000*x) lgdogf A013854 25.146 1/10*x/(1+10000*x) revogf A013854 20.574 1/100000*ln(1+10000*x) revegf A013854 30.1752 10/(1-100000*x) ogf A013854 16.1653 {a(n+1)-100000*a(n),a(0)=10} ogf A013855 21.4728 -100+(1-100000*x)*f(x) ogf A013855 26.2446 -100/(-1+100000*x) ogf A013855 22.4953 -100000/(-1+100000*x) lgdogf A013855 26.2446 1/100*x/(1+1000*x) revogf A013855 22.4953 1/100000*ln(1+1000*x) revegf A013855 29.5251 100/(1-100000*x) ogf A013855 16.2897 {a(n+1)-100000*a(n),a(0)=100} ogf A013856 21.399 -1000+(1-100000*x)*f(x) ogf A013856 25.9041 -1000/(-1+100000*x) ogf A013856 23.437 -100000/(-1+100000*x) lgdogf A013856 27.3432 1/1000*x/(1+100*x) revogf A013856 24.6089 1/100000*ln(1+100*x) revegf A013856 28.9516 1000/(1-100000*x) ogf A013856 16.4059 {a(n+1)-100000*a(n),a(0)=1000} ogf A013857 16.2023 -10000+(1-100000*x)*f(x) ogf A013857 19.4428 -10000/(-1+100000*x) ogf A013857 18.5169 -100000/(-1+100000*x) lgdogf A013857 21.6031 1/10000*x/(1+10*x) revogf A013857 20.4661 1/100000*ln(1+10*x) revegf A013857 21.6031 10000/(1-100000*x) ogf A013857 12.5437 {a(n+1)-100000*a(n),a(0)=10000} ogf A013858 21.9722 -11+(1-161051*x)*f(x) ogf A013858 27.1421 -11/(-1+161051*x) ogf A013858 21.9722 -161051/(-1+161051*x) lgdogf A013858 25.6342 1/11*x/(1+14641*x) revogf A013858 20.9735 1/161051*ln(1+14641*x) revegf A013858 30.7611 11/(1-161051*x) ogf A013858 16.4792 {a(n+1)-161051*a(n),a(0)=11} ogf A013859 21.8723 -121+(1-161051*x)*f(x) ogf A013859 26.7328 -121/(-1+161051*x) ogf A013859 22.9139 -161051/(-1+161051*x) lgdogf A013859 26.7328 1/121*x/(1+1331*x) revogf A013859 22.9139 1/161051*ln(1+1331*x) revegf A013859 30.0744 121/(1-161051*x) ogf A013859 16.5928 {a(n+1)-161051*a(n),a(0)=121} ogf A013860 21.7811 -1331+(1-161051*x)*f(x) ogf A013860 26.3666 -1331/(-1+161051*x) ogf A013860 23.8555 -161051/(-1+161051*x) lgdogf A013860 27.8315 1/1331*x/(1+121*x) revogf A013860 25.0483 1/161051*ln(1+121*x) revegf A013860 29.4686 1331/(1-161051*x) ogf A013860 16.6989 {a(n+1)-161051*a(n),a(0)=1331} ogf A013861 16.4622 -14641+(1-161051*x)*f(x) ogf A013861 19.7547 -14641/(-1+161051*x) ogf A013861 18.814 -161051/(-1+161051*x) lgdogf A013861 21.9496 1/14641*x/(1+11*x) revogf A013861 20.7944 1/161051*ln(1+11*x) revegf A013861 21.9496 14641/(1-161051*x) ogf A013861 12.745 {a(n+1)-161051*a(n),a(0)=14641} ogf A013862 22.7046 -12+(1-248832*x)*f(x) ogf A013862 28.0469 -12/(-1+248832*x) ogf A013862 22.7046 -248832/(-1+248832*x) lgdogf A013862 26.4887 1/12*x/(1+20736*x) revogf A013862 21.6726 1/248832*ln(1+20736*x) revegf A013862 31.7864 12/(1-248832*x) ogf A013862 17.0285 {a(n+1)-248832*a(n),a(0)=12} ogf A013863 22.5714 -144+(1-248832*x)*f(x) ogf A013863 27.5873 -144/(-1+248832*x) ogf A013863 23.6463 -248832/(-1+248832*x) lgdogf A013863 27.5873 1/144*x/(1+1728*x) revogf A013863 23.6463 1/248832*ln(1+1728*x) revegf A013863 31.0357 144/(1-248832*x) ogf A013863 17.1232 {a(n+1)-248832*a(n),a(0)=144} ogf A013864 22.6409 -1728+(1-248832*x)*f(x) ogf A013864 27.4074 -1728/(-1+248832*x) ogf A013864 24.7972 -248832/(-1+248832*x) lgdogf A013864 28.9301 1/1728*x/(1+144*x) revogf A013864 26.0371 1/248832*ln(1+144*x) revegf A013864 30.6318 1728/(1-248832*x) ogf A013864 17.358 {a(n+1)-248832*a(n),a(0)=1728} ogf A013865 17.0687 -20736+(1-248832*x)*f(x) ogf A013865 20.4825 -20736/(-1+248832*x) ogf A013865 19.5071 -248832/(-1+248832*x) lgdogf A013865 22.7583 1/20736*x/(1+12*x) revogf A013865 21.5605 1/248832*ln(1+12*x) revegf A013865 22.7583 20736/(1-248832*x) ogf A013865 13.2145 {a(n+1)-248832*a(n),a(0)=20736} ogf A013866 23.3324 -13+(1-371293*x)*f(x) ogf A013866 28.8224 -13/(-1+371293*x) ogf A013866 23.3324 -371293/(-1+371293*x) lgdogf A013866 27.2211 1/13*x/(1+28561*x) revogf A013866 22.2718 1/371293*ln(1+28561*x) revegf A013866 32.6653 13/(1-371293*x) ogf A013866 17.4993 {a(n+1)-371293*a(n),a(0)=13} ogf A013867 23.2706 -169+(1-371293*x)*f(x) ogf A013867 28.4418 -169/(-1+371293*x) ogf A013867 28.4418 1/169*x/(1+2197*x) revogf A013867 24.3787 1/371293*ln(1+2197*x) revegf A013867 31.997 169/(1-371293*x) ogf A013867 17.6535 {a(n+1)-371293*a(n),a(0)=169} ogf A013868 17.5396 -2197+(1-371293*x)*f(x) ogf A013868 21.2322 -2197/(-1+371293*x) ogf A013868 19.2101 -371293/(-1+371293*x) lgdogf A013868 22.4117 1/2197*x/(1+169*x) revogf A013868 20.1706 1/371293*ln(1+169*x) revegf A013868 23.7301 2197/(1-371293*x) ogf A013868 13.447 {a(n+1)-371293*a(n),a(0)=2197} ogf A013869 17.5886 -28561+(1-371293*x)*f(x) ogf A013869 21.1063 -28561/(-1+371293*x) ogf A013869 20.1013 -371293/(-1+371293*x) lgdogf A013869 23.4515 1/28561*x/(1+13*x) revogf A013869 22.2172 1/371293*ln(1+13*x) revegf A013869 23.4515 28561/(1-371293*x) ogf A013869 13.617 {a(n+1)-371293*a(n),a(0)=28561} ogf A013870 23.9602 -14+(1-537824*x)*f(x) ogf A013870 29.5978 -14/(-1+537824*x) ogf A013870 23.9602 -537824/(-1+537824*x) lgdogf A013870 27.9535 1/14*x/(1+38416*x) revogf A013870 22.8711 1/537824*ln(1+38416*x) revegf A013870 33.5442 14/(1-537824*x) ogf A013870 17.9701 {a(n+1)-537824*a(n),a(0)=14} ogf A013871 23.9697 -196+(1-537824*x)*f(x) ogf A013871 29.2963 -196/(-1+537824*x) ogf A013871 25.1111 -537824/(-1+537824*x) lgdogf A013871 29.2963 1/196*x/(1+2744*x) revogf A013871 25.1111 1/537824*ln(1+2744*x) revegf A013871 32.9583 196/(1-537824*x) ogf A013871 18.1839 {a(n+1)-537824*a(n),a(0)=196} ogf A013872 17.9917 -2744+(1-537824*x)*f(x) ogf A013872 21.7794 -2744/(-1+537824*x) ogf A013872 19.7052 -537824/(-1+537824*x) lgdogf A013872 22.9894 1/2744*x/(1+196*x) revogf A013872 20.6904 1/537824*ln(1+196*x) revegf A013872 24.3417 2744/(1-537824*x) ogf A013872 13.7936 {a(n+1)-537824*a(n),a(0)=2744} ogf A013873 18.0218 -38416+(1-537824*x)*f(x) ogf A013873 21.6262 -38416/(-1+537824*x) ogf A013873 20.5964 -537824/(-1+537824*x) lgdogf A013873 24.0291 1/38416*x/(1+14*x) revogf A013873 22.7644 1/537824*ln(1+14*x) revegf A013873 24.0291 38416/(1-537824*x) ogf A013873 13.9524 {a(n+1)-537824*a(n),a(0)=38416} ogf A013874 24.5879 -15+(1-759375*x)*f(x) ogf A013874 30.3733 -15/(-1+759375*x) ogf A013874 24.5879 -759375/(-1+759375*x) lgdogf A013874 28.6859 1/15*x/(1+50625*x) revogf A013874 23.4703 1/759375*ln(1+50625*x) revegf A013874 34.4231 15/(1-759375*x) ogf A013874 18.441 {a(n+1)-759375*a(n),a(0)=15} ogf A013875 24.469 -225+(1-759375*x)*f(x) ogf A013875 29.9066 -225/(-1+759375*x) ogf A013875 25.6342 -759375/(-1+759375*x) lgdogf A013875 29.9066 1/225*x/(1+3375*x) revogf A013875 25.6342 1/759375*ln(1+3375*x) revegf A013875 33.6449 225/(1-759375*x) ogf A013875 18.5627 {a(n+1)-759375*a(n),a(0)=225} ogf A013876 18.4437 -3375+(1-759375*x)*f(x) ogf A013876 22.3266 -3375/(-1+759375*x) ogf A013876 20.2003 -759375/(-1+759375*x) lgdogf A013876 23.567 1/3375*x/(1+225*x) revogf A013876 21.2103 1/759375*ln(1+225*x) revegf A013876 24.9533 3375/(1-759375*x) ogf A013876 14.1402 {a(n+1)-759375*a(n),a(0)=3375} ogf A013877 18.455 -50625+(1-759375*x)*f(x) ogf A013877 22.146 -50625/(-1+759375*x) ogf A013877 21.0915 -759375/(-1+759375*x) lgdogf A013877 24.6067 1/50625*x/(1+15*x) revogf A013877 23.3116 1/759375*ln(1+15*x) revegf A013877 24.6067 50625/(1-759375*x) ogf A013877 14.2878 {a(n+1)-759375*a(n),a(0)=50625} ogf A013878 23.1186 -1048576/(-1+1048576*x) lgdogf A013878 24.1694 -16+(1-1048576*x)*f(x) ogf A013878 29.5404 -16/(-1+1048576*x) ogf A013878 23.1186 1/1048576*ln(1+65536*x) revegf A013878 29.5404 1/16*x/(1+65536*x) revogf A013878 33.233 16/(1-1048576*x) ogf A013878 18.3354 {a(n+1)-1048576*a(n),a(0)=16} ogf A013879 23.9784 -1048576/(-1+1048576*x) lgdogf A013879 23.9784 -256+(1-1048576*x)*f(x) ogf A013879 29.0264 -256/(-1+1048576*x) ogf A013879 25.0683 1/1048576*ln(1+4096*x) revegf A013879 30.639 1/256*x/(1+4096*x) revogf A013879 32.4413 256/(1-1048576*x) ogf A013879 18.3834 {a(n+1)-1048576*a(n),a(0)=256} ogf A013880 18.715 -1048576/(-1+1048576*x) lgdogf A013880 17.9352 -4096+(1-1048576*x)*f(x) ogf A013880 21.5222 -4096/(-1+1048576*x) ogf A013880 20.4973 1/1048576*ln(1+256*x) revegf A013880 23.9136 1/4096*x/(1+256*x) revogf A013880 23.9136 4096/(1-1048576*x) ogf A013880 13.8853 {a(n+1)-1048576*a(n),a(0)=4096} ogf A013881 19.4382 -1048576/(-1+1048576*x) lgdogf A013881 17.8832 -65536+(1-1048576*x)*f(x) ogf A013881 21.2895 -65536/(-1+1048576*x) ogf A013881 22.354 1/1048576*ln(1+16*x) revegf A013881 24.8378 1/65536*x/(1+16*x) revogf A013881 23.5305 65536/(1-1048576*x) ogf A013881 13.9712 {a(n+1)-1048576*a(n),a(0)=65536} ogf A013882 23.4052 -1419857/(-1+1419857*x) lgdogf A013882 24.469 -17+(1-1419857*x)*f(x) ogf A013882 29.9066 -17/(-1+1419857*x) ogf A013882 23.4052 1/1419857*ln(1+83521*x) revegf A013882 29.9066 1/17*x/(1+83521*x) revogf A013882 33.6449 17/(1-1419857*x) ogf A013882 18.5627 {a(n+1)-1419857*a(n),a(0)=17} ogf A013883 24.456 -1419857/(-1+1419857*x) lgdogf A013883 24.456 -289+(1-1419857*x)*f(x) ogf A013883 29.6046 -289/(-1+1419857*x) ogf A013883 25.5677 1/1419857*ln(1+4913*x) revegf A013883 31.2494 1/289*x/(1+4913*x) revogf A013883 33.0875 289/(1-1419857*x) ogf A013883 18.7496 {a(n+1)-1419857*a(n),a(0)=289} ogf A013884 19.167 -1419857/(-1+1419857*x) lgdogf A013884 18.3684 -4913+(1-1419857*x)*f(x) ogf A013884 22.0421 -4913/(-1+1419857*x) ogf A013884 20.9924 1/1419857*ln(1+289*x) revegf A013884 24.4912 1/4913*x/(1+289*x) revogf A013884 24.4912 4913/(1-1419857*x) ogf A013884 14.2207 {a(n+1)-1419857*a(n),a(0)=4913} ogf A013885 20.0711 -1419857/(-1+1419857*x) lgdogf A013885 18.4654 -83521+(1-1419857*x)*f(x) ogf A013885 21.9827 -83521/(-1+1419857*x) ogf A013885 23.0818 1/1419857*ln(1+17*x) revegf A013885 25.6464 1/83521*x/(1+17*x) revogf A013885 24.2966 83521/(1-1419857*x) ogf A013885 14.4261 {a(n+1)-1419857*a(n),a(0)=83521} ogf A013886 24.9684 -18+(1-1889568*x)*f(x) ogf A013886 30.5169 -18/(-1+1889568*x) ogf A013886 23.8828 -1889568/(-1+1889568*x) lgdogf A013886 28.9108 1/18*x/(1+104976*x) revogf A013886 22.8877 1/1889568*ln(1+104976*x) revegf A013886 34.3316 18/(1-1889568*x) ogf A013886 18.9416 {a(n+1)-1889568*a(n),a(0)=18} ogf A013887 18.715 -1889568/(-1+1889568*x) lgdogf A013887 18.715 -324+(1-1889568*x)*f(x) ogf A013887 22.655 -324/(-1+1889568*x) ogf A013887 19.5656 1/1889568*ln(1+5832*x) revegf A013887 23.9136 1/324*x/(1+5832*x) revogf A013887 25.3202 324/(1-1889568*x) ogf A013887 14.3481 {a(n+1)-1889568*a(n),a(0)=324} ogf A013888 19.6191 -1889568/(-1+1889568*x) lgdogf A013888 18.8016 -5832+(1-1889568*x)*f(x) ogf A013888 22.5619 -5832/(-1+1889568*x) ogf A013888 21.4875 1/1889568*ln(1+324*x) revegf A013888 25.0688 1/5832*x/(1+324*x) revogf A013888 25.0688 5832/(1-1889568*x) ogf A013888 14.5561 {a(n+1)-1889568*a(n),a(0)=5832} ogf A013889 18.1551 -104976+(1-1889568*x)*f(x) ogf A013889 21.456 -104976/(-1+1889568*x) ogf A013889 20.5232 -1889568/(-1+1889568*x) lgdogf A013889 24.8438 1/104976*x/(1+18*x) revogf A013889 23.6016 1/1889568*ln(1+18*x) revegf A013889 23.6016 104976/(1-1889568*x) ogf A013889 14.304 {a(n+1)-1889568*a(n),a(0)=104976} ogf A013890 25.4678 -19+(1-2476099*x)*f(x) ogf A013890 31.1273 -19/(-1+2476099*x) ogf A013890 24.3605 -2476099/(-1+2476099*x) lgdogf A013890 29.489 1/19*x/(1+130321*x) revogf A013890 23.3455 1/2476099*ln(1+130321*x) revegf A013890 35.0182 19/(1-2476099*x) ogf A013890 19.3204 {a(n+1)-2476099*a(n),a(0)=19} ogf A013891 18.9862 -2476099/(-1+2476099*x) lgdogf A013891 18.9862 -361+(1-2476099*x)*f(x) ogf A013891 22.9833 -361/(-1+2476099*x) ogf A013891 19.8492 1/2476099*ln(1+6859*x) revegf A013891 24.2601 1/361*x/(1+6859*x) revogf A013891 25.6872 361/(1-2476099*x) ogf A013891 14.5561 {a(n+1)-2476099*a(n),a(0)=361} ogf A013892 19.9807 -2476099/(-1+2476099*x) lgdogf A013892 19.1482 -6859+(1-2476099*x)*f(x) ogf A013892 22.9778 -6859/(-1+2476099*x) ogf A013892 21.8836 1/2476099*ln(1+361*x) revegf A013892 25.5309 1/6859*x/(1+361*x) revogf A013892 25.5309 6859/(1-2476099*x) ogf A013892 14.8244 {a(n+1)-2476099*a(n),a(0)=6859} ogf A013893 18.475 -130321+(1-2476099*x)*f(x) ogf A013893 21.8341 -130321/(-1+2476099*x) ogf A013893 20.8848 -2476099/(-1+2476099*x) lgdogf A013893 25.2816 1/130321*x/(1+19*x) revogf A013893 24.0175 1/2476099*ln(1+19*x) revegf A013893 24.0175 130321/(1-2476099*x) ogf A013893 14.5561 {a(n+1)-2476099*a(n),a(0)=130321} ogf A013894 25.7674 -20+(1-3200000*x)*f(x) ogf A013894 31.4935 -20/(-1+3200000*x) ogf A013894 24.6471 -3200000/(-1+3200000*x) lgdogf A013894 29.8359 1/20*x/(1+160000*x) revogf A013894 23.6201 1/3200000*ln(1+160000*x) revegf A013894 35.4302 20/(1-3200000*x) ogf A013894 19.5477 {a(n+1)-3200000*a(n),a(0)=20} ogf A013895 19.4382 -3200000/(-1+3200000*x) lgdogf A013895 19.4382 -400+(1-3200000*x)*f(x) ogf A013895 23.5305 -400/(-1+3200000*x) ogf A013895 20.3218 1/3200000*ln(1+8000*x) revegf A013895 24.8378 1/400*x/(1+8000*x) revogf A013895 26.2988 400/(1-3200000*x) ogf A013895 14.9027 {a(n+1)-3200000*a(n),a(0)=400} ogf A013896 20.1615 -3200000/(-1+3200000*x) lgdogf A013896 19.3215 -8000+(1-3200000*x)*f(x) ogf A013896 23.1858 -8000/(-1+3200000*x) ogf A013896 22.0817 1/3200000*ln(1+400*x) revegf A013896 25.762 1/8000*x/(1+400*x) revogf A013896 25.762 8000/(1-3200000*x) ogf A013896 14.9586 {a(n+1)-3200000*a(n),a(0)=8000} ogf A013897 18.7949 -160000+(1-3200000*x)*f(x) ogf A013897 22.2122 -160000/(-1+3200000*x) ogf A013897 21.2465 -3200000/(-1+3200000*x) lgdogf A013897 25.7194 1/160000*x/(1+20*x) revogf A013897 24.4334 1/3200000*ln(1+20*x) revegf A013897 24.4334 160000/(1-3200000*x) ogf A013897 14.8081 {a(n+1)-3200000*a(n),a(0)=160000} ogf A013898 26.1669 -21+(1-4084101*x)*f(x) ogf A013898 31.9818 -21/(-1+4084101*x) ogf A013898 25.0292 -4084101/(-1+4084101*x) lgdogf A013898 30.2985 1/21*x/(1+194481*x) revogf A013898 23.9863 1/4084101*ln(1+194481*x) revegf A013898 35.9795 21/(1-4084101*x) ogf A013898 19.8507 {a(n+1)-4084101*a(n),a(0)=21} ogf A013899 19.6191 -4084101/(-1+4084101*x) lgdogf A013899 19.6191 -441+(1-4084101*x)*f(x) ogf A013899 23.7494 -441/(-1+4084101*x) ogf A013899 20.5108 1/4084101*ln(1+9261*x) revegf A013899 25.0688 1/441*x/(1+9261*x) revogf A013899 26.5434 441/(1-4084101*x) ogf A013899 15.0413 {a(n+1)-4084101*a(n),a(0)=441} ogf A013900 20.6136 -4084101/(-1+4084101*x) lgdogf A013900 19.7547 -9261+(1-4084101*x)*f(x) ogf A013900 23.7056 -9261/(-1+4084101*x) ogf A013900 22.5768 1/4084101*ln(1+441*x) revegf A013900 26.3396 1/9261*x/(1+441*x) revogf A013900 26.3396 9261/(1-4084101*x) ogf A013900 15.2939 {a(n+1)-4084101*a(n),a(0)=9261} ogf A013901 19.0349 -194481+(1-4084101*x)*f(x) ogf A013901 22.4958 -194481/(-1+4084101*x) ogf A013901 21.5177 -4084101/(-1+4084101*x) lgdogf A013901 26.0477 1/194481*x/(1+21*x) revogf A013901 24.7453 1/4084101*ln(1+21*x) revegf A013901 24.7453 194481/(1-4084101*x) ogf A013901 14.9972 {a(n+1)-4084101*a(n),a(0)=194481} ogf A013902 26.6663 -22+(1-5153632*x)*f(x) ogf A013902 32.5921 -22/(-1+5153632*x) ogf A013902 25.5069 -5153632/(-1+5153632*x) lgdogf A013902 30.8767 1/22*x/(1+234256*x) revogf A013902 24.4441 1/5153632*ln(1+234256*x) revegf A013902 36.6661 22/(1-5153632*x) ogf A013902 20.2296 {a(n+1)-5153632*a(n),a(0)=22} ogf A013903 19.8903 -484+(1-5153632*x)*f(x) ogf A013903 24.0777 -484/(-1+5153632*x) ogf A013903 19.8903 -5153632/(-1+5153632*x) lgdogf A013903 24.0777 1/484*x/(1+10648*x) revogf A013903 19.8903 1/5153632*ln(1+10648*x) revegf A013903 26.9104 484/(1-5153632*x) ogf A013903 15.2492 {a(n+1)-5153632*a(n),a(0)=484} ogf A013904 19.2972 -10648+(1-5153632*x)*f(x) ogf A013904 22.9729 -10648/(-1+5153632*x) ogf A013904 20.9752 -5153632/(-1+5153632*x) lgdogf A013904 25.3911 1/10648*x/(1+484*x) revogf A013904 22.9729 1/5153632*ln(1+484*x) revegf A013904 25.3911 10648/(1-5153632*x) ogf A013904 15.0759 {a(n+1)-5153632*a(n),a(0)=10648} ogf A013905 19.3548 -234256+(1-5153632*x)*f(x) ogf A013905 22.8738 -234256/(-1+5153632*x) ogf A013905 21.8793 -5153632/(-1+5153632*x) lgdogf A013905 26.4855 1/234256*x/(1+22*x) revogf A013905 25.1612 1/5153632*ln(1+22*x) revegf A013905 25.1612 234256/(1-5153632*x) ogf A013905 15.2492 {a(n+1)-5153632*a(n),a(0)=234256} ogf A013906 26.9659 -23+(1-6436343*x)*f(x) ogf A013906 32.9583 -23/(-1+6436343*x) ogf A013906 25.7935 -6436343/(-1+6436343*x) lgdogf A013906 31.2237 1/23*x/(1+279841*x) revogf A013906 24.7187 1/6436343*ln(1+279841*x) revegf A013906 37.0781 23/(1-6436343*x) ogf A013906 20.4569 {a(n+1)-6436343*a(n),a(0)=23} ogf A013907 20.1615 -529+(1-6436343*x)*f(x) ogf A013907 24.4061 -529/(-1+6436343*x) ogf A013907 20.1615 -6436343/(-1+6436343*x) lgdogf A013907 24.4061 1/529*x/(1+12167*x) revogf A013907 20.1615 1/6436343*ln(1+12167*x) revegf A013907 27.2774 529/(1-6436343*x) ogf A013907 15.4572 {a(n+1)-6436343*a(n),a(0)=529} ogf A013908 19.4636 -12167+(1-6436343*x)*f(x) ogf A013908 23.1709 -12167/(-1+6436343*x) ogf A013908 25.6099 1/12167*x/(1+529*x) revogf A013908 23.1709 1/6436343*ln(1+529*x) revegf A013908 25.6099 12167/(1-6436343*x) ogf A013908 15.2059 {a(n+1)-6436343*a(n),a(0)=12167} ogf A013909 19.6747 -279841+(1-6436343*x)*f(x) ogf A013909 23.2519 -279841/(-1+6436343*x) ogf A013909 22.241 -6436343/(-1+6436343*x) lgdogf A013909 26.9233 1/279841*x/(1+23*x) revogf A013909 25.5771 1/6436343*ln(1+23*x) revegf A013909 25.5771 279841/(1-6436343*x) ogf A013909 15.5013 {a(n+1)-6436343*a(n),a(0)=279841} ogf A013910 14.5059 -24+(1-7962624*x)*f(x) ogf A013910 17.7294 -24/(-1+7962624*x) ogf A013910 16.7963 1/24*x/(1+331776*x) revogf A013910 13.2971 1/7962624*ln(1+331776*x) revegf A013910 19.9456 24/(1-7962624*x) ogf A013911 20.5232 -576+(1-7962624*x)*f(x) ogf A013911 24.8438 -576/(-1+7962624*x) ogf A013911 20.5232 -7962624/(-1+7962624*x) lgdogf A013911 24.8438 1/576*x/(1+13824*x) revogf A013911 20.5232 1/7962624*ln(1+13824*x) revegf A013911 27.7666 576/(1-7962624*x) ogf A013911 15.7344 {a(n+1)-7962624*a(n),a(0)=576} ogf A013912 19.7131 -13824+(1-7962624*x)*f(x) ogf A013912 23.468 -13824/(-1+7962624*x) ogf A013912 21.4273 -7962624/(-1+7962624*x) lgdogf A013912 25.9383 1/13824*x/(1+576*x) revogf A013912 23.468 1/7962624*ln(1+576*x) revegf A013912 25.9383 13824/(1-7962624*x) ogf A013912 15.4009 {a(n+1)-7962624*a(n),a(0)=13824} ogf A013913 19.9146 -331776+(1-7962624*x)*f(x) ogf A013913 23.5355 -331776/(-1+7962624*x) ogf A013913 22.5122 -7962624/(-1+7962624*x) lgdogf A013913 27.2516 1/331776*x/(1+24*x) revogf A013913 25.889 1/7962624*ln(1+24*x) revegf A013913 25.889 331776/(1-7962624*x) ogf A013913 15.6903 {a(n+1)-7962624*a(n),a(0)=331776} ogf A013915 19.2899 (-3+6*x+2*x^3-4*x^2)/(x^2+x-1)/(x-1)^2 ogf A013915 17.0469 -(3-6*x+4*x^2-2*x^3)/(-2*x^2-1+3*x+x^4-x^3) ogf A013915 10.7797 -(3-x+2*x^5-16*x^2+20*x^3-6*x^4)/(x-1)/(x^2+x-1)/(2*x^3-4*x^2+6*x-3) lgdogf A013915 6.10847 -11520+23040*x+7680*x^3-15360*x^2+(3549-10938*x+4034*x^3-3840*x^4+7292*x^2)*f(x)+(194*x^2+97-291*x-97*x^4+97*x^3)*f(x)^2 ogf A013915 9.04959 {a(n)*n+a(n+1)+(-2*n+1)*a(n+2)+(n-1)*a(n+3),a(0)=3,a(1)=3,a(2)=7,a(3)=10,a(4)=16} ogf A013938 6.08347 (1+x+x^3+x^14+2*x^15+x^2+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13)/(x+1)/(x^2+1)/(x^4+1)/(x^8+1)/(x-1)^2 ogf A013945 10.4347 -(2+22*x+2*x^4+20*x^3+x^6+6*x^5+7*x^2)/(x-1)/(x+1)/(x^5+3*x^4-x^3+2*x^2+2*x+3) lgdogf A013945 16.6104 -(3+2*x+3*x^4+x^5+2*x^2-x^3)/(-1-3*x^4+3*x^2+x^6) ogf A013945 18.4979 -(3+2*x-x^3+2*x^2+3*x^4+x^5)/(x-1)^3/(x+1)^3 ogf A013950 13.5491 -(1+x-x^8-x^6+2*x^2+x^3)/(-x^2-1+x+x^4-x^5+2*x^3-2*x^7+x^6) ogf A013950 11.9313 -(1+x^2+x)*(x^6-x^5+x^4-x^2-1)/(x-1)/(x+1)/(x^2+1)/(-1+x-x^2+2*x^3) ogf A013977 14.3914 (1+8*x+58*x^3+21*x^2+47*x^4+35*x^5+21*x^6+x^7)/(1+x^2+x)^2/(x-1)^4 ogf A013977 10.3243 -(1+8*x+47*x^4+x^7+35*x^5+21*x^2+58*x^3+21*x^6)/(-x^2-1+2*x-x^8-4*x^4+2*x^3-x^6+2*x^5+2*x^7) ogf A013977 7.19569 -(10+60*x+307*x^6+580*x^5+149*x^7+511*x^4+x^9+402*x^3+44*x^8+240*x^2)/(x-1)/(x^2+x+1)/(x^7+21*x^6+35*x^5+47*x^4+58*x^3+21*x^2+8*x+1) lgdogf A013978 7.93152 (1+18*x^3+8*x^2+21*x^4+19*x^5+21*x^6+7*x^7+x^8)/(x+1)^2/(1+x^2+x)^2/(x-1)^4 ogf A013978 6.26173 -(1+21*x^4+x^8+7*x^7+19*x^5+8*x^2+18*x^3+21*x^6)/(2*x^3-1+2*x^2-x^10-4*x^5-x^4+2*x^7-x^6+2*x^8) ogf A013979 41.2278 -1/(x+1)/(-1+x+x^3) ogf A013979 24.479 -x*(2+4*x^2+3*x)/(x+1)/(x^3+x-1) lgdogf A013979 14.7798 1+(-3+x^3+x^4+x^2)*f(x)+(-2*x^3-2*x^4+2-2*x^2)*f(x)^2 ogf A013979 46.0781 1/(1-x^2-x^3-x^4) ogf A013979 14.2423 {a(n+4)-a(n+2)-a(n+1)-a(n),a(0)=1,a(1)=0,a(2)=1,a(3)=1} ogf A013982 25.7474 -1/(-1+x^2+x^3+x^4+x^5) ogf A013982 13.7719 -x*(2+5*x^3+4*x^2+3*x)/(-1+x^2+x^3+x^4+x^5) lgdogf A013982 28.1996 1/(1-x^2-x^3-x^4-x^5) ogf A013983 27.9026 -1/(x+1)/(x^5+x^3+x-1) ogf A013983 12.7887 -x*(2+6*x^4+5*x^3+4*x^2+3*x)/(x+1)/(x^5+x^3+x-1) lgdogf A013983 24.5543 1/(1-x^2-x^3-x^4-x^5-x^6) ogf A013984 20.0348 -1/(-1+x^2+x^3+x^4+x^5+x^6+x^7) ogf A013984 9.85838 -x*(2+7*x^5+6*x^4+5*x^3+4*x^2+3*x)/(-1+x^2+x^3+x^4+x^5+x^6+x^7) lgdogf A013984 21.4165 1/(1-x^2-x^3-x^4-x^5-x^6-x^7) ogf A013985 24.0265 -1/(x+1)/(x^7+x^5+x^3+x-1) ogf A013985 9.76077 -x*(2+7*x^5+6*x^4+8*x^6+5*x^3+4*x^2+3*x)/(x+1)/(x^7+x^5+x^3+x-1) lgdogf A013985 18.93 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8) ogf A013986 16.1103 -1/(-1+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) ogf A013986 7.56988 -x*(2+7*x^5+6*x^4+8*x^6+5*x^3+4*x^2+9*x^7+3*x)/(-1+x^8+x^2+x^9+x^3+x^4+x^5+x^6+x^7) lgdogf A013986 16.9811 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9) ogf A013987 26.1188 -1/(x+1)/(x^9+x^7+x^5+x^3+x-1) ogf A013987 9.67362 -x*(2+7*x^5+6*x^4+8*x^6+5*x^3+4*x^2+10*x^8+9*x^7+3*x)/(x+1)/(x^9+x^7+x^5+x^3+x-1) lgdogf A013987 18.6563 1/(1-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10) ogf A013989 19.8581 (2+4*x+x^3+2*x^2)/(x^2+1+x) lgdegf A013989 7.44679 -20-20*x^2-40*x-10*x^3+(16+16*x^2+22*x+3*x^3)*f(x)+(-3*x-3*x^2-3)*f(x)^2 lgdegf A013989 20.6219 exp(1/2*x*(x+2))*(1+x^2+x) egf A013989 7.65955 {(-12-7*n-n^2)*a(n+1)+(-4-n)*a(n+2)+(n+3)*a(n+3),a(0)=1,a(1)=2,a(2)=6} ogf A013991 7.50681 (-1+5*x-2*x^3-4*x^2+12*x^4-15*x^5+7*x^6)/(x^2-x+1)/(7*x^4-9*x^3+5*x-1) ogf A013991 6.48737 -(1-5*x-12*x^4+15*x^5+4*x^2+2*x^3-7*x^6)/(-6*x^2-1+6*x+16*x^4-4*x^3+7*x^6-16*x^5) ogf A013999 4.32448 {(-4-n)*a(n+1)+(13*n+18+2*n^2)*a(n+2)+(-41*n-42-12*n^2-n^3)*a(n+3)+(26*n+24+9*n^2+n^3)*a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=4/3} egf A013999 6.87482 {(n+4)*a(n+1)+(-2*n-9)*a(n+2)+(n+7)*a(n+3)-a(n+4),a(0)=1,a(1)=1,a(2)=2,a(3)=8} ogf A014003 7.6527 -(-9+3*x+2*x^3-4*x^2-6*x^4-x^5-2*x^6+6*x^7)/(-x^7+1-2*x+x^8+x^2-x^3+x^4-x^5) ogf A014003 7.6527 -(-9+3*x-6*x^4+6*x^7-x^5-4*x^2+2*x^3-2*x^6)/(-x^7+1-2*x+x^8+x^2-x^3+x^4-x^5) ogf A014009 5.3884 (-3+2*x+2*x^3+x^11-2*x^10+2*x^9+x^2-x^4-2*x^5+x^6-x^7+x^8)/(x^2-1+2*x+x^8-x^4+x^9+x^3-x^10+x^6+x^11-x^5) ogf A014010 13.8749 -(-2+2*x^4+x^2)/(3*x^5+1-3*x-x^2+x^3-x^4) ogf A014010 12.1036 -(-2+x^2+2*x^4)/(x-1)/(3*x^4+2*x^3+3*x^2+2*x-1) ogf A014010 6.6926 -(6+2*x+6*x^8-3*x^2-11*x^4+2*x^5+7*x^6)/(x-1)/(2*x^4+x^2-2)/(3*x^4+2*x^3+3*x^2+2*x-1) lgdogf A014011 12.4761 -(-1-x^4+x^8-x^14-x^2-x^24+x^20+x^16+x^6)/(2*x^7+1-2*x+x^2-x^8-x^6) ogf A014011 11.2959 -(1+x^24-x^16-x^20+x^14+x^2+x^4-x^6-x^8)/(x+1)/(1+x^2+x)/(x^2-x+1)/(x-1)^3 ogf A014016 50.6827 -(-1-x)/(1-x^7) ogf A014016 13.1076 -(2*x+3*x^2+4*x^3+5*x^4+6*x^5+1)/(x^6+x^5+x^4+x^3+x^2+x+1) lgdogf A014016 126.707 -1+x^6 ogf_with_Euler_Transform A014016 26.2152 -1/(-1-x-x^2-x^3-x^4-x^5-x^6) ogf A014016 28.157 1/(x^6+x^5+x^4+x^3+x^2+x+1) ogf A014016 13.1076 {a(n+7),a(0)=-1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=1} ogf_with_Euler_Transform A014017 50.0967 -1+(1+x^4)*f(x) ogf A014017 68.3137 -1/(-1-x^4) ogf A014017 53.6751 -4*x^3/(1+x^4) lgdogf A014017 93.9314 -x^3+x^7 ogf_with_Euler_Transform A014017 83.4946 1/(1-x^4) ogf A014017 83.4946 1/(x^4+1) ogf A014017 17.4756 {-a(n+4)-a(n),a(0)=0,a(1)=0,a(2)=0,a(3)=-4} lgdogf A014017 8.94584 {a(n+1)+(154*n+120+71*n^2+14*n^3+n^4)*a(n+5),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=-1/24} egf A014017 11.5608 {a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=-1,a(4)=0,a(5)=0,a(6)=0,a(7)=1} ogf_with_Euler_Transform A014018 43.9445 -(-1-x^3)/(1-x^9) ogf A014018 49.8038 -1/(-1-x^3-x^6) ogf A014018 26.6806 -3*x^2*(1+2*x^3)/(1+x^3+x^6) lgdogf A014018 93.3821 -x^2+x^8 ogf_with_Euler_Transform A014018 57.4659 1/(x^6+x^3+1) ogf A014018 10.3758 {a(n+1),a(0)=0,a(1)=0,a(2)=-1,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=1} ogf_with_Euler_Transform A014019 51.8545 -(-1-x)/(1-x^5) ogf A014019 37.0389 -1/(-1+x-x^2+x^3-x^4) ogf A014019 15.5564 1+(-x^2+x-2+x^3-x^4)*f(x)+(x^2-x^3+1-x+x^4)*f(x)^2 ogf A014019 70.7107 1-x-x^4+x^9 ogf_with_Euler_Transform A014019 40.9378 1/(x^4-x^3+x^2-x+1) ogf A014019 11.9664 {-a(n+4)+a(n+3)-a(n+2)+a(n+1)-a(n),a(0)=1,a(1)=-1,a(2)=1,a(3)=-1} lgdogf A014020 46.4164 -(-1-x)/(1-x^11) ogf A014020 7.42662 -(5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A014020 106.095 -1+x^10 ogf_with_Euler_Transform A014020 16.1448 -1/(-1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10) ogf A014020 16.8787 1/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A014020 8.7372 {a(n),a(0)=-1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=1} ogf_with_Euler_Transform A014021 45.237 -(-1-x^2)/(1-x^6) ogf A014021 51.2686 -1/(-1+x^2-x^4) ogf A014021 28.4825 -2*x*(-1+2*x^2)/(1-x^2+x^4) lgdogf A014021 17.8844 -2+(2*x^4+3-2*x^2)*f(x)+(-x^4-1+x^2)*f(x)^2 ogf A014021 59.1561 1/(x^4-x^2+1) ogf A014021 40.4752 x^11-x*(-1+x^2+x^4) ogf_with_Euler_Transform A014021 15.3806 {-a(n+4)+a(n+2)-a(n),a(0)=0,a(1)=2,a(2)=0,a(3)=-2} lgdogf A014022 46.1417 -(-1-x)/(1-x^13) ogf A014022 5.85927 -(1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x^12+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^11+x^9+x^10+1) lgdogf A014022 105.467 -1+x^12 ogf_with_Euler_Transform A014022 7.30958 {a(n),a(0)=-1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=0,a(11)=0,a(12)=1} ogf_with_Euler_Transform A014023 50.6827 -(-1-x)/(1-x^7) ogf A014023 13.1076 -(2*x-3*x^2+4*x^3-5*x^4+6*x^5-1)/(x^2+1-x+x^4-x^3+x^6-x^5) lgdogf A014023 26.2152 -1/(-1+x-x^2+x^3-x^4+x^5-x^6) ogf A014023 63.3533 1-x-x^6+x^13 ogf_with_Euler_Transform A014023 28.157 1/(1-x+x^2-x^3+x^4-x^5+x^6) ogf A014024 15.5564 -(-1-x^5)/(1-x+x^3-x^4+x^6-x^7+x^9-x^10+x^12-x^13) ogf A014024 55.5584 1-x^2-x^4+x^14 ogf_with_Euler_Transform A014024 28.8081 1/(1-x+x^3-x^4+x^5-x^7+x^8) ogf A014025 84.8009 -1/(-1-x^8) ogf A014025 66.6292 -8*x^7/(1+x^8) lgdogf A014025 103.645 -x^7+x^15 ogf_with_Euler_Transform A014025 103.645 1/(1-x^8) ogf A014025 103.645 1/(x^8+1) ogf A014026 45.5924 -(-1-x)/(1-x^17) ogf A014026 104.211 -1+x^16 ogf_with_Euler_Transform A014027 43.686 -(-1-x^3)/(1-x^9) ogf A014027 49.5108 -1/(-1+x^3-x^6) ogf A014027 25.609 -3*x^2*(-1+2*x^3)/(1-x^3+x^6) lgdogf A014027 57.1279 1/(x^6-x^3+1) ogf A014028 45.5924 -(-1-x)/(1-x^19) ogf A014028 104.211 -1+x^18 ogf_with_Euler_Transform A014029 41.259 -(-1-x^2)/(1-x^10) ogf A014029 32.2897 -1/(-1+x^2-x^4+x^6-x^8) ogf A014029 15.8013 -2*x*(-1+2*x^2-3*x^4+4*x^6)/(1-x^2+x^4-x^6+x^8) lgdogf A014029 35.3649 1/(x^8-x^6+x^4-x^2+1) ogf A014029 53.0473 x-x^3-x^9+x^19 ogf_with_Euler_Transform A014030 8.73839 -(-1+6*x^5-8*x^7-4*x^3+9*x^8-11*x^10+12*x^11+3*x^2)/(x^3+1-x+x^12+x^6-x^4+x^9-x^8-x^11) lgdogf A014030 54.3028 1-x^2-x^6+x^20 ogf_with_Euler_Transform A014030 20.547 1/(1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12) ogf A014031 46.4164 -(-1-x)/(1-x^11) ogf A014031 7.35309 -(-5*x^4+6*x^5-1-7*x^6+8*x^7+2*x-9*x^8-3*x^2+10*x^9+4*x^3)/(x^2+1-x+x^8+x^4-x^9-x^3+x^10+x^6-x^5-x^7) lgdogf A014031 16.1448 -1/(-1+x-x^2+x^3-x^4+x^5-x^6+x^7-x^8+x^9-x^10) ogf A014031 57.1279 1-x-x^10+x^21 ogf_with_Euler_Transform A014031 16.8787 1/(1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10) ogf A014032 45.3178 -(-1-x)/(1-x^23) ogf A014032 103.583 -1+x^22 ogf_with_Euler_Transform A014033 40.7707 -(-1-x^4)/(1-x^12) ogf A014033 48.9249 -1/(-1+x^4-x^8) ogf A014033 25.306 -4*x^3*(-1+2*x^4)/(1-x^4+x^8) lgdogf A014033 56.4518 1/(x^8-x^4+1) ogf A014033 43.169 x^3-x^7-x^11+x^23 ogf_with_Euler_Transform A014034 40.2825 -(-1-x^5)/(1-x^25) ogf A014034 27.8879 -1/(-1-x^5-x^10-x^15-x^20) ogf A014034 13.6808 -5*x^4*(1+2*x^5+3*x^10+4*x^15)/(1+x^5+x^10+x^15+x^20) lgdogf A014034 80.5649 -x^4+x^24 ogf_with_Euler_Transform A014034 30.2118 1/(1+x^5+x^10+x^15+x^20) ogf A014035 5.77853 -(-1-7*x^6+8*x^7+2*x-9*x^8-3*x^2+10*x^9+4*x^3-11*x^10-5*x^4+12*x^11+6*x^5)/(1+x^6-x^7+x^8-x^9+x^10-x^11-x+x^2-x^3+x^4-x^5+x^12) lgdogf A014035 45.8671 -(-1-x)/(1-x^13) ogf A014036 40.0383 -(-1-x^9)/(1-x^27) ogf A014036 45.0431 -1/(-1-x^9-x^18) ogf A014036 24.8514 -9*x^8*(1+2*x^9)/(1+x^9+x^18) lgdogf A014036 51.4778 1/(x^18+x^9+1) ogf A014037 40.7707 -(-1-x^2)/(1-x^14) ogf A014037 22.2386 -1/(-1+x^2-x^4+x^6-x^8+x^10-x^12) ogf A014037 10.4839 -2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A014037 23.6733 1/(x^12-x^10+x^8-x^6+x^4-x^2+1) ogf A014038 45.0431 -(-1-x)/(1-x^29) ogf A014039 15.6442 -(-1-x^5)/(1-x+x^3-x^4+x^6-x^7+x^9-x^10+x^12-x^13) ogf A014039 12.8231 -(1-4*x^3-3*x^2-5*x^4+7*x^6+8*x^7)/(-x^3+1+x-x^5-x^4+x^8+x^7) lgdogf A014039 28.9708 1/(1+x-x^3-x^4-x^5+x^7+x^8) ogf A014039 28.9708 1/(x^8+x^7-x^5-x^4-x^3+x+1) ogf A014040 45.0431 -(-1-x)/(1-x^31) ogf A014041 60.0575 -1/(-1-x^16) ogf A014041 42.3935 -16*x^15/(1+x^16) lgdogf A014041 72.069 1/(1+x^16) ogf A014041 72.069 1/(1-x^16) ogf A014042 11.1501 1/(1-x+x^3-x^4+x^6-x^7+x^9-x^10+x^11-x^13+x^14-x^16+x^17-x^19+x^20) ogf A014043 45.3178 -(-1-x)/(1-x^17) ogf A014044 9.85934 1/(1-x+x^5-x^6+x^7-x^8+x^10-x^11+x^12-x^13+x^14-x^16+x^17-x^18+x^19-x^23+x^24) ogf A014045 40.2825 -(-1-x^6)/(1-x^18) ogf A014045 45.3178 -1/(-1+x^6-x^12) ogf A014045 24.1695 -6*x^5*(-1+2*x^6)/(1-x^6+x^12) lgdogf A014045 51.7917 1/(1-x^6+x^12) ogf A014047 45.3178 -(-1-x)/(1-x^19) ogf A014049 40.2825 -(-1-x^4)/(1-x^20) ogf A014049 29.0034 -1/(-1+x^4-x^8+x^12-x^16) ogf A014049 13.9439 -4*x^3*(-1+2*x^4-3*x^8+4*x^12)/(1-x^4+x^8-x^12+x^16) lgdogf A014049 31.5254 1/(1-x^4+x^8-x^12+x^16) ogf A014051 8.73839 -(1+6*x^5-8*x^7-4*x^3-9*x^8+11*x^10+12*x^11-3*x^2)/(-x^3+1+x+x^12+x^6-x^4-x^9-x^8+x^11) lgdogf A014051 20.547 1/(1+x-x^3-x^4+x^6-x^8-x^9+x^11+x^12) ogf A014053 40.2825 -(-1-x^2)/(1-x^22) ogf A014053 6.09314 -2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10-7*x^12+8*x^14-9*x^16+10*x^18)/(1-x^2+x^4-x^6+x^8-x^10+x^12-x^14+x^16-x^18+x^20) lgdogf A014054 9.65623 -3*x^2*(-1+3*x^6-4*x^9+5*x^12-7*x^18+8*x^21)/(1-x^3+x^9-x^12+x^15-x^21+x^24) lgdogf A014054 22.2386 1/(1-x^3+x^9-x^12+x^15-x^21+x^24) ogf A014055 45.3178 -(-1-x)/(1-x^23) ogf A014057 40.2825 -(-1-x^8)/(1-x^24) ogf A014057 45.3178 -1/(-1+x^8-x^16) ogf A014057 24.1695 -8*x^7*(-1+2*x^8)/(1-x^8+x^16) lgdogf A014057 51.7917 1/(1-x^8+x^16) ogf A014059 40.2825 -(-1-x^5)/(1-x^25) ogf A014059 27.8879 -1/(-1+x^5-x^10+x^15-x^20) ogf A014059 13.4275 -5*x^4*(-1+2*x^5-3*x^10+4*x^15)/(1-x^5+x^10-x^15+x^20) lgdogf A014059 30.2118 1/(1-x^5+x^10-x^15+x^20) ogf A014060 16.3083 -(1+x+x^2-2*x^36-2*x^35-2*x^34)/(x^17-1+x^34) ogf A014061 40.2825 -(-1-x^2)/(1-x^26) ogf A014063 39.7942 -(-1-x^9)/(1-x^27) ogf A014063 44.7685 -1/(-1+x^9-x^18) ogf A014063 23.8765 -9*x^8*(-1+2*x^9)/(1-x^9+x^18) lgdogf A014063 51.164 1/(1-x^9+x^18) ogf A014064 9.39314 1/(1-x+x^5-x^6+x^10-x^12+x^15-x^17+x^20-x^23+x^25-x^28+x^30-x^34+x^35-x^39+x^40) ogf A014065 39.7942 -(-1-x^4)/(1-x^28) ogf A014065 9.42494 -4*x^3*(-1+2*x^4-3*x^8+4*x^12-5*x^16+6*x^20)/(1-x^4+x^8-x^12+x^16-x^20+x^24) lgdogf A014066 16.3083 -(1+x+x^2-2*x^40-2*x^39-2*x^38)/(x^19-1+x^38) ogf A014067 44.7685 -(-1-x)/(1-x^29) ogf A014069 10.46 -2*x*(1-3*x^4-4*x^6-5*x^8+7*x^12+8*x^14)/(1+x^2-x^6-x^8-x^10+x^14+x^16) lgdogf A014069 23.2082 1/(1+x^2-x^6-x^8-x^10+x^14+x^16) ogf A014069 23.2082 1/(x^16+x^14-x^10-x^8-x^6+x^2+1) ogf A014071 44.7685 -(-1-x)/(1-x^31) ogf A014072 7.06559 -3*x^2*(-1+3*x^6-4*x^9+6*x^15-8*x^21+9*x^24-11*x^30+12*x^33)/(1-x^3+x^9-x^12+x^18-x^24+x^27-x^33+x^36) lgdogf A014075 11.0845 1/(1+x-x^3-x^4+x^6+x^7-x^9-x^10-x^11+x^13+x^14-x^16-x^17+x^19+x^20) ogf A014077 124.647 1/(1-x) ogf A014079 9.85934 1/(1+x-x^5-x^6-x^7-x^8+x^10+x^11+x^12+x^13+x^14-x^16-x^17-x^18-x^19+x^23+x^24) ogf A014084 9.12266 -5*x^4*(-1+3*x^10-4*x^15+5*x^20-7*x^30+8*x^35)/(1-x^5+x^15-x^20+x^25-x^35+x^40) lgdogf A014093 7.4885 -2*x*(1-3*x^4-4*x^6+6*x^10-8*x^14-9*x^16+11*x^20+12*x^22)/(1+x^2-x^6-x^8+x^12-x^16-x^18+x^22+x^24) lgdogf A014093 17.4732 1/(1+x^2-x^6-x^8+x^12-x^16-x^18+x^22+x^24) ogf A014094 7.5204 -(x-1)*(x^4+x^3+x^2+x+1)*(1+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A014094 72.9479 1-x^4-x^16 ogf_with_Euler_Transform A014095 11.3051 (1-3*x-17*x^3+13*x^2+44*x^4-17*x^5+13*x^6-3*x^7+x^8)/(x+1)^4/(x-1)^8 ogf A014095 5.86829 -(1+26*x-88*x^6+362*x^5+74*x^7-62*x^4+238*x^3+4*x^9-11*x^8-32*x^2)/(x-1)/(x+1)/(x^8-3*x^7+13*x^6-17*x^5+44*x^4-17*x^3+13*x^2-3*x+1) lgdogf A014097 29.134 -(1+4*x^3)/(-1+x+x^4) ogf A014097 14.2282 -(1+4*x^6-4*x^3+12*x^2)/(4*x^3+1)/(x^4+x-1) lgdogf A014097 7.37126 -10193-40772*x^3+(10476-10193*x+1132*x^3-10193*x^4)*f(x)+(283*x^4-283+283*x)*f(x)^2 ogf A014097 12.486 {-a(n+4)+a(n+3)+a(n),a(0)=1,a(1)=1,a(2)=1,a(3)=5} ogf A014098 28.7851 -(1+3*x^3)/(-1+x+x^4) ogf A014098 14.3926 -(1+3*x^6-2*x^3+9*x^2)/(3*x^3+1)/(x^4+x-1) lgdogf A014098 7.85049 -2743-8229*x^3+(2894-2743*x+453*x^3-2743*x^4)*f(x)+(151*x^4-151+151*x)*f(x)^2 ogf A014098 12.3365 {-a(n+4)+a(n+3)+a(n),a(0)=1,a(1)=1,a(2)=1,a(3)=4} ogf A014099 9.78498 -3*x^2*(1-3*x^6-4*x^9-5*x^12+7*x^18+8*x^21)/(1+x^3-x^9-x^12-x^15+x^21+x^24) lgdogf A014099 22.2386 1/(1+x^3-x^9-x^12-x^15+x^21+x^24) ogf A014100 8.6855 -(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) ogf A014100 73.8268 1-x^6-x^12 ogf_with_Euler_Transform A014101 29.6867 -(1+2*x^3)/(-1+x+x^4) ogf A014101 17.3172 -(1+6*x^2+2*x^6)/(2*x^3+1)/(x^4+x-1) lgdogf A014101 10.22 -80-160*x^3+(89-80*x+18*x^3-80*x^4)*f(x)+(9*x^4-9+9*x)*f(x)^2 ogf A014103 64.2936 24/(1-x^2) ogf_with_Euler_Transform A014103 22.962 {a(n+2)-a(n),a(0)=24,a(1)=0} ogf_with_Euler_Transform A014104 6.81756 -(x-1)*(x^4+x^3+x^2+x+1)*(x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) ogf A014104 72.9479 1-x^4-x^18 ogf_with_Euler_Transform A014105 26.8183 -(3*x+x^2)/(-1+3*x-3*x^2+x^3) ogf A014105 55.5522 -(3+x)/(x-1)^3 ogf A014105 8.18663 -10101*x-3367*x^2+(3367-4197*x-3367*x^3+12069*x^2)*f(x)+(-1968+5904*x-5904*x^2+1968*x^3)*f(x)^2 ogf A014105 38.8865 -2*(5+x)/(x+3)/(x-1) lgdogf A014105 14.6742 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=3,a(2)=10} ogf A014106 55.8272 (-5+x)/(x-1)^3 ogf A014106 26.9511 -(5*x-x^2)/(-1+3*x-3*x^2+x^3) ogf A014106 39.079 -2*(x-7)/(x-1)/(x-5) lgdogf A014106 8.5888 -8235*x+1647*x^2+(1647-2621*x-1647*x^3+4477*x^2)*f(x)+(-464+1392*x-1392*x^2+464*x^3)*f(x)^2 ogf A014106 14.7468 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=5,a(2)=14} ogf A014107 46.4544 -(-1+5*x)/(x-1)^3 ogf A014107 20.2494 -(x-x^2+6*x^3-2*x^4)/(-1+3*x-3*x^2+x^3) ogf A014107 32.9052 -2*(1+5*x)/(5*x-1)/(x-1) lgdogf A014107 9.87156 117*x-585*x^2+(117-431*x-117*x^3+751*x^2)*f(x)+(-80+240*x-240*x^2+80*x^3)*f(x)^2 ogf A014107 14.6245 {-a(n+3)+3*a(n+2)-3*a(n+1)+a(n),a(0)=0,a(1)=-1,a(2)=2} ogf A014111 16.3083 -(1+x+x^2-2*x^36-2*x^35-2*x^34)/(x^17-1+x^34) ogf A014112 25.0503 -(-1+x+x^3-3*x^2)/(x+1)/(x-1)^4 ogf A014112 16.5225 -(1-x+3*x^2-x^3)/(-2*x^2-1+3*x+3*x^4-x^5-2*x^3) ogf A014112 14.652 -2*(-1-4*x+x^4-3*x^3-x^2)/(x-1)/(x+1)/(x^3-3*x^2+x-1) lgdogf A014112 6.16316 {(-144-75*n-9*n^2)*a(n+1)+(-12+17*n+5*n^2)*a(n+2)+(96+63*n+9*n^2)*a(n+3)+(-29*n-36-5*n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=7,a(3)=14} ogf A014113 26.4366 -(4*x+1)/(x+1)/(2*x-1) lgdogf A014113 34.2121 -2*x/(-1+x+2*x^2) ogf A014113 36.3503 -2/(x+1)/(2*x-1) ogf A014113 18.1752 1/4/x*(-x-2+(9*x^2+4*x+4)^(1/2)) revogf A014113 13.8477 4*x+(-2+4*x+4*x^2)*f(x)+(2*x^2-1+x)*f(x)^2 ogf A014113 15.7191 {-a(n+2)+a(n+1)+2*a(n),a(0)=0,a(1)=2} ogf A014119 9.39314 1/(1+x-x^5-x^6+x^10-x^12-x^15+x^17+x^20+x^23-x^25-x^28+x^30-x^34-x^35+x^39+x^40) ogf A014123 16.3083 -(1+x+x^2-2*x^40-2*x^39-2*x^38)/(x^19-1+x^38) ogf A014124 72.9479 1-x^4-x^22 ogf_with_Euler_Transform A014125 20.0508 -1/(-1+3*x-3*x^2+2*x^3-3*x^4+3*x^5-x^6) ogf A014125 26.0661 -3*(1+x+2*x^2)/(x-1)/(x^2+x+1) lgdogf A014125 41.157 1/(x^2+x+1)/(x-1)^4 ogf A014125 156.396 3+x^2 ogf_with_Euler_Transform A014125 10.4264 {(-n-4)*a(n+4)+3*a(n+3)+3*a(n+2)+(7+n)*a(n+1),a(0)=1,a(1)=3,a(2)=6,a(3)=11} ogf A014125 26.9649 {a(n+3),a(0)=3,a(1)=0,a(2)=1} ogf_with_Euler_Transform A014126 25.8618 (x^2+1)/(x+1)/(x^2+x+1)/(x-1)^4 ogf A014126 22.9061 -(1+x^2)/(-1+2*x-x^3-x^4+2*x^6-x^7) ogf A014126 12.5268 -(2+8*x+5*x^5+13*x^3+7*x^4+13*x^2)/(x-1)/(x+1)/(x^2+1)/(x^2+x+1) lgdogf A014126 61.6704 2+2*x+x^2-x^3 ogf_with_Euler_Transform A014126 21.668 {a(n+4),a(0)=2,a(1)=2,a(2)=1,a(3)=-1} ogf_with_Euler_Transform A014128 7.03112 -(x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) ogf A014128 73.8268 1-x^6-x^16 ogf_with_Euler_Transform A014129 9.47375 -4*x^3*(1-3*x^8-4*x^12-5*x^16+7*x^24+8*x^28)/(1+x^4-x^12-x^16-x^20+x^28+x^32) lgdogf A014129 21.4553 1/(1+x^4-x^12-x^16-x^20+x^28+x^32) ogf A014130 8.86581 {(2*n^2+15*n+25)*a(n+1)-a(n+2),a(0)=1,a(1)=12} ogf A014131 16.3754 -2*(-1-x+3*x^2)/(x-1)/(2*x-1)/(x+1) lgdogf A014131 21.2273 -6*x+(1-2*x-x^2+2*x^3)*f(x) ogf A014131 24.9191 -6*x/(-1+2*x+x^2-2*x^3) ogf A014131 27.2923 6/(x-1)/(2*x-1)/(x+1) ogf A014131 10.6137 {-a(n+3)+2*a(n+2)+a(n+1)-2*a(n),a(0)=0,a(1)=6,a(2)=12} ogf A014135 7.17905 -3*x^2*(1-3*x^6-4*x^9+6*x^15-8*x^21-9*x^24+11*x^30+12*x^33)/(1+x^3-x^9-x^12+x^18-x^24-x^27+x^33+x^36) lgdogf A014137 23.5711 1+(-1+x)*f(x)+(x+x^3-2*x^2)*f(x)^2 ogf A014137 23.5711 1+(-1+x)*f(x)+(x^3+x-2*x^2)*f(x)^2 ogf A014137 11.6147 {(-4*n-10)*a(n+1)+(5*n+14)*a(n+2)+(-n-4)*a(n+3),a(0)=1,a(1)=2,a(2)=4} ogf A014138 13.3247 -x+(1-3*x+2*x^2)*f(x)+(-x+2*x^2-x^3)*f(x)^2 ogf A014138 8.30378 {(-4*n-10)*a(n+1)+(5*n+14)*a(n+2)+(-n-4)*a(n+3),a(0)=0,a(1)=1,a(2)=3} ogf A014140 11.5247 3+25*x^2-16*x+(-1-29*x^2+10*x+20*x^3)*f(x)+(6*x^2+4*x^4-9*x^3-x)*f(x)^2 lgdogf A014140 8.79843 {(4*n+14)*a(n+1)+(-33-9*n)*a(n+2)+(6*n+24)*a(n+3)+(-n-5)*a(n+4),a(0)=1,a(1)=3,a(2)=7,a(3)=16} ogf A014140 8.79843 {(4*n+14)*a(n+1)+(-9*n-33)*a(n+2)+(6*n+24)*a(n+3)+(-n-5)*a(n+4),a(0)=1,a(1)=3,a(2)=7,a(3)=16} ogf A014142 73.8268 1-x^6-x^18 ogf_with_Euler_Transform A014143 7.90099 -8-36*x^2+32*x+(2+38*x^2-16*x-24*x^3)*f(x)+(-6*x^2+x+9*x^3-4*x^4)*f(x)^2 lgdogf A014143 6.05182 {(4*n+18)*a(n+1)+(-9*n-42)*a(n+2)+(6*n+30)*a(n+3)+(-n-6)*a(n+4),a(0)=1,a(1)=4,a(2)=12,a(3)=34} ogf A014144 6.62858 {(-n-3)*a(n+1)+(2*n+7)*a(n+2)+(-n-5)*a(n+3)+a(n+4),a(0)=0,a(1)=1,a(2)=3,a(3)=7} ogf A014145 7.23074 {(-n-4)*a(n+1)+(2*n+9)*a(n+2)+(-n-6)*a(n+3)+a(n+4),a(0)=0,a(1)=1,a(2)=4,a(3)=13} ogf A014151 11.5985 -4-49*x^2+26*x+(1+39*x^2-12*x-28*x^3)*f(x)+(-6*x^2+x+9*x^3-4*x^4)*f(x)^2 lgdogf A014151 6.7346 {(90+38*n+4*n^2)*a(n+1)+(-168-79*n-9*n^2)*a(n+2)+(104+50*n+6*n^2)*a(n+3)+(-9*n-20-n^2)*a(n+4),a(0)=1,a(1)=4,a(2)=11,a(3)=27} ogf A014152 7.41025 -(x-1)*(x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)*(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) ogf A014152 68.7132 1-x^10-x^12 ogf_with_Euler_Transform A014152 7.3383 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1,a(11)=0,a(12)=-1} ogf_with_Euler_Transform A014153 53.2278 -(-3+2*x)/(1-x) ogf_with_Euler_Transform A014153 27.5316 {a(n+2)-a(n+1),a(0)=3,a(1)=1} ogf_with_Euler_Transform A014159 9.23961 -5*x^4*(1-3*x^10-4*x^15-5*x^20+7*x^30+8*x^35)/(1+x^5-x^15-x^20-x^25+x^35+x^40) lgdogf A014160 40.3264 -(-4+3*x)/(1-x) ogf_with_Euler_Transform A014160 20.8585 {a(n+2)-a(n+1),a(0)=4,a(1)=1} ogf_with_Euler_Transform A014161 39.6054 -(-5+4*x)/(1-x) ogf_with_Euler_Transform A014161 20.4855 {a(n+2)-a(n+1),a(0)=5,a(1)=1} ogf_with_Euler_Transform A014162 18.4992 -(-4+2*x+5*x^2)/(x-1)/(x^2+x-1) lgdogf A014162 18.4992 -x/(-1+4*x-x^5-5*x^2+x^3+2*x^4) ogf A014162 30.183 1/(x^2+x-1)/(x-1)^3 ogf A014162 6.99361 {(-3-n)*a(n+4)+(8+2*n)*a(n+3)-2*a(n+2)+(-5-n)*a(n+1),a(0)=0,a(1)=1,a(2)=4,a(3)=11} ogf A014162 6.99361 {(-n-3)*a(n+4)+(8+2*n)*a(n+3)-2*a(n+2)+(-5-n)*a(n+1),a(0)=0,a(1)=1,a(2)=4,a(3)=11} ogf A014166 19.7177 -(-5+3*x+6*x^2)/(x-1)/(x^2+x-1) lgdogf A014166 30.5625 -1/(x^2+x-1)/(x-1)^4 ogf A014166 17.4643 x/(1-5*x+3*x^5+9*x^2-6*x^3-x^4-x^6) ogf A014166 7.45427 {(-3-n)*a(n+4)+(9+2*n)*a(n+3)-3*a(n+2)+(-6-n)*a(n+1),a(0)=0,a(1)=1,a(2)=5,a(3)=16} ogf A014170 73.8268 1-x^6-x^22 ogf_with_Euler_Transform A014177 8.04826 4*x^3*(-1+2*x^4+7*x^24-8*x^28+9*x^32)/(x^4+1)/(x^8-x^4+1)/(1-x^4+x^8-x^12+x^16-x^20+x^24) lgdogf A014179 7.55296 (x+1)*(x^4-x^3+x^2-x+1)*(x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1) ogf A014181 6.30275 -(10*x^9-11)*(9*x^8+8*x^7+7*x^6+6*x^5+5*x^4+4*x^3+3*x^2+2*x+1)/(x-1)/(10*x^9-1)/(x^2+x+1)/(x^6+x^3+1) ogf A014182 72.5085 -1+exp(-x) lgdegf A014182 21.326 {a(n)+(n+1)*a(n+1),a(0)=0,a(1)=-1} lgdegf A014189 10.2328 -6*x^5*(5*x^24+x^18+x^12-1)*(3*x^12+x^6-1)/(1-2*x^12-x^18-2*x^24+x^36) lgdogf A014191 8.73659 (x+1)*(x^6-x^5+x^4-x^3+x^2-x+1)*(x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1) ogf A014196 68.7132 1-x^10-x^16 ogf_with_Euler_Transform A014199 6.84042 (x+1)*(x^4-x^3+x^2-x+1)*(x^18-x^17+x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1) ogf A014205 40.4779 (-1-2*x+x^2)/(x-1)^5 ogf A014205 24.5321 -(-7-6*x+3*x^2)/(x-1)/(x^2-2*x-1) lgdogf A014205 17.2246 -(x+2*x^2-x^3)/(-1+5*x-10*x^2+x^5+10*x^3-5*x^4) ogf A014205 9.41347 {(-3-n)*a(n+4)+(5-n)*a(n+3)+(9+3*n)*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=1,a(2)=7,a(3)=24} ogf A014206 24.9016 -(-2+2*x-2*x^2)/(3*x^2+1-3*x-x^3) ogf A014206 34.2397 -(2+x^2)/(x-1)/(x^2-x+1) lgdogf A014206 41.0876 -2*(1-x+x^2)/(x-1)^3 ogf A014206 11.574 20-20*x+20*x^2+(-4+24*x+10*x^3-24*x^2)*f(x)+(-9*x^2-3+9*x+3*x^3)*f(x)^2 ogf A014206 15.8029 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=2,a(1)=4,a(2)=8} ogf A014209 29.7234 (1+3*x^2-6*x)/(x-1)^3 ogf A014209 17.834 -(1+3*x^2-2*x^3)/(-1+3*x-3*x^2+x^3) ogf A014209 19.506 -(1-6*x+3*x^2)/(3*x^2+1-3*x-x^3) ogf A014209 17.834 -3*(-1-2*x+x^2)/(x-1)/(3*x^2-6*x+1) lgdogf A014209 6.24191 -5093+30558*x-15279*x^2+(-4597+12303*x+5093*x^3-13791*x^2)*f(x)+(496-1488*x+1488*x^2-496*x^3)*f(x)^2 ogf A014209 11.7772 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=-1,a(1)=3,a(2)=9} ogf A014217 21.3373 (1+x^3-x^2)/(x-1)/(x+1)/(x^2+x-1) ogf A014217 21.3373 -(-1+x^2-x^3)/(1-x-2*x^2+x^3+x^4) ogf A014217 10.5094 -(-1-2*x-x^2+6*x^3+x^4-2*x^5+x^6)/(x-1)/(x+1)/(x^2+x-1)/(x^3-x^2+1) lgdogf A014217 20.118 1+x^3-x^2+(-1+x+2*x^2-x^3-x^4)*f(x) ogf A014218 68.7132 1-x^10-x^18 ogf_with_Euler_Transform A014228 7.75591 {(1136*n+64*n^3+480*n^2+840)*a(n+1)+(-n^3-12*n^2-47*n-60)*a(n+2),a(0)=2,a(1)=10} ogf A014230 69.5122 1-x^12-x^16 ogf_with_Euler_Transform A014231 8.85404 {(1136*n+64*n^3+480*n^2+840)*a(n+1)+(-n^3-12*n^2-47*n-60)*a(n+2),a(0)=1,a(1)=5} ogf A014236 12.3468 -(1+4*x+8*x^3-14*x^2)/(x-1)/(2*x-1)/(2*x^2-1) lgdogf A014236 16.8365 -(2*x-2*x^2)/(-1+2*x+2*x^2-4*x^3) ogf A014236 21.3694 -2*(x-1)/(2*x-1)/(2*x^2-1) ogf A014236 8.96136 4*x-4*x^2+(-2+6*x-8*x^3+2*x^2)*f(x)+(2*x^2-1+2*x-4*x^3)*f(x)^2 ogf A014236 10.1019 {-a(n+3)+2*a(n+2)+2*a(n+1)-4*a(n),a(0)=0,a(1)=2,a(2)=2} ogf A014247 7.05647 (x+1)*(x^6-x^5+x^4-x^3+x^2-x+1)*(x^16-x^15+x^14-x^13+x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1) ogf A014255 19.6621 -(-1-2*x-3*x^2)/(-2*x^2+1-x+x^4-x^5+2*x^3) ogf A014255 27.527 -(1+2*x+3*x^2)/(x+1)^2/(x-1)^3 ogf A014255 17.2044 -(3+13*x+9*x^3+11*x^2)/(x-1)/(x+1)/(3*x^2+2*x+1) lgdogf A014255 5.57979 {(-4516-2925*n-449*n^2)*a(n+1)+(-15585-6824*n-667*n^2)*a(n+2)+(-423+911*n+449*n^2)*a(n+3)+(4374*n+6824+667*n^2)*a(n+4),a(0)=1,a(1)=3,a(2)=8,a(3)=12} ogf A014256 69.5122 1-x^12-x^18 ogf_with_Euler_Transform A014262 68.7132 1-x^10-x^22 ogf_with_Euler_Transform A014279 1.40365 -x^2+(2*x-2*x^2)*f(x)+(-1+2*x-x^2)*f(x)^2 ogf A014281 1.19637 -x^3+(-3*x^3+3*x^2)*f(x)+(-3*x-3*x^3+6*x^2)*f(x)^2+(1-3*x+3*x^2-x^3)*f(x)^3 ogf A014283 25.2225 (-3+5*x)/(x^2+x-1)/(x-1)^3 ogf A014283 14.9042 -(-3*x^2+5*x^3)/(-1+4*x-5*x^2-x^5+x^3+2*x^4) ogf A014283 8.62874 -(38*x^15-3*x^2-128*x^13+150*x^14+5*x^3-64*x^16)/(1-4*x+5*x^2+x^5-x^3-2*x^4) ogf A014283 14.2562 -(7-16*x+20*x^3-5*x^2)/(x-1)/(5*x-3)/(x^2+x-1) lgdogf A014283 5.00599 {(-n^2-2*n+3)*a(n+1)+(-2*n-1)*a(n+2)+(2*n^2+2*n-7)*a(n+3)+(-n^2+4)*a(n+4),a(0)=0,a(1)=0,a(2)=-3,a(3)=-7,a(4)=-13,a(5)=-20,a(6)=-28} ogf A014286 15.6 -(-3-3*x+3*x^4-x^3+6*x^2)/(x-1)/(1+x^2)/(x^2+x-1) lgdogf A014286 21.84 -(-x-x^3)/(1-3*x-x^4+x^2+3*x^3-x^5) ogf A014286 29.4 -(x^2+1)/(x-1)/(x^2+x-1)^2 ogf A014286 7.21132 {(12+7*n+n^2)*a(n+1)+(-4-n)*a(n+2)+(-14-11*n-2*n^2)*a(n+3)+(6+5*n+n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=3,a(3)=9} ogf A014288 7.73648 {(2*n+n^2)*a(n)+(-8*n-6-2*n^2)*a(n+1)+(8+7*n+n^2)*a(n+2)+(-2-n)*a(n+3),a(0)=0,a(1)=1,a(2)=2} ogf A014291 23.6597 (2*x-1)*(x-1)/(x^2+1-2*x+x^4) ogf A014291 21.4416 -(-3*x+1+2*x^2)/(-x^2-1+2*x-x^4) ogf A014291 11.4355 -(x^2-x-1)*(4*x^3-5*x^2+3*x-1)/(x-1)/(2*x-1)/(x^4+x^2-2*x+1) lgdogf A014291 11.6294 3-9*x+6*x^2+(-2+3*x-3*x^4-x^2)*f(x)+(-1+2*x-x^2-x^4)*f(x)^2 ogf A014292 27.2977 -x^2+(1-2*x+x^2+x^4)*f(x) ogf A014292 32.4973 -x^2/(-x^2-1+2*x-x^4) ogf A014292 40.1437 1/(x^2+1-2*x+x^4) ogf A014292 11.7663 {a(n+4)-2*a(n+3)+a(n+2)+a(n),a(0)=2,a(1)=2,a(2)=2,a(3)=-2} lgdogf A014295 7.44011 (x+1)*(x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1)*(x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1) ogf A014297 44.1509 -2/(2*x-1)^3 egf A014297 8.97984 -4+(4-12*x-16*x^3+24*x^2)*f(x)+(-1+8*x^3-12*x^2+6*x)*f(x)^2 egf A014297 48.1646 -6/(-1+2*x) lgdegf A014297 24.0823 2/(1-6*x+12*x^2-8*x^3) egf A014297 16.0549 x/(1+2*x)^(1/2)/(1+(1+2*x)^(1/2)) revegf A014297 13.5849 {(-2*n-8)*a(n+1)+a(n+2),a(0)=2,a(1)=12} ogf A014298 26.9301 -1+f(x)-2*x*f(x)^3 egf A014298 13.8497 1/54+2/3*x-1/54*(-(12*x-1)^3)^(1/2) revegf A014298 14.6891 hypergeom([1/3,2/3],[3/2],27/2*x) egf A014298 8.81347 {(27*n^2+81*n+60)*a(n+1)+(-2*n-5)*a(n+2),a(0)=1,a(1)=2} ogf A014300 19.2807 1+(-1+4*x)*f(x)+(4*x^3-2*x+7*x^2)*f(x)^2 ogf A014300 11.865 1/8*((9*x^2+2*x+1)^(1/2)+3*(9*x^2+2*x+1)^(1/2)*x-4*x-7*x^2-1)/x^2 revogf A014300 6.21957 {(-30-22*n-4*n^2)*a(n+1)+(20-4*n-3*n^2)*a(n+2)+(140+71*n+9*n^2)*a(n+3)+(-18*n-40-2*n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=7,a(3)=24} ogf A014301 16.1926 x+(-1+3*x+4*x^2)*f(x)+(4*x^3-2*x+7*x^2)*f(x)^2 ogf A014301 5.77411 {(20+18*n+4*n^2)*a(n+1)+(-184-89*n-9*n^2)*a(n+2)+(-388-218*n-30*n^2)*a(n+3)+(120+8*n^2+64*n)*a(n+4),a(0)=0,a(1)=1,a(2)=3,a(3)=11} ogf A014304 27.1114 -ln(2-2*x+x^2)+ln(2) revegf A014305 3.20103 (1-x+x^2)*(x^18+x^17-x^15-x^14+x^12+x^11-x^9+x^7+x^6-x^4-x^3+x^2+2*x+1) ogf A014308 69.5122 1-x^12-x^22 ogf_with_Euler_Transform A014309 18.5134 (1-8*x-5*x^3+10*x^2+x^4)/(x-1)^5 ogf A014309 8.84222 -(-1+2*x-9*x^4+2*x^5-10*x^2+15*x^3)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A014309 10.2143 -(-3-12*x+x^4-6*x^3+15*x^2)/(x-1)/(x^4-5*x^3+10*x^2-8*x+1) lgdogf A014309 10.3935 -(1-8*x+x^4+10*x^2-5*x^3)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A014318 13.9345 -1+(1-2*x)*f(x)+(-4*x^3-x+4*x^2)*f(x)^2 ogf A014318 7.99186 {(8*n+20)*a(n+1)+(-6*n-18)*a(n+2)+(n+4)*a(n+3),a(0)=1,a(1)=3,a(2)=8} ogf A014330 7.46005 {(-128*n-32*n^2-128)*a(n+1)+(12*n^2+76*n+116)*a(n+2)+(-n^2-9*n-20)*a(n+3),a(0)=1,a(1)=2,a(2)=6} ogf A014332 71.1102 1-x^16-x^18 ogf_with_Euler_Transform A014334 15.3791 -(-3-4*x+12*x^2)/(x-1)/(4*x^2+2*x-1) lgdogf A014334 17.8596 2*x^2+(-1+3*x+2*x^2-4*x^3)*f(x) ogf A014334 22.1459 2*x^2/(1-3*x-2*x^2+4*x^3) ogf A014334 26.3642 2/(x-1)/(4*x^2+2*x-1) ogf A014334 10.2527 {a(n+3)-3*a(n+2)-2*a(n+1)+4*a(n),a(0)=0,a(1)=0,a(2)=2} ogf A014335 15.2003 -(-3-4*x+12*x^2)/(x-1)/(4*x^2+2*x-1) lgdogf A014335 26.0576 1/(x-1)/(4*x^2+2*x-1) ogf A014335 18.8693 x^2+(-1+3*x+2*x^2-4*x^3)*f(x) ogf A014335 23.7917 x^2/(1-3*x-2*x^2+4*x^3) ogf A014335 10.1335 {a(n+3)-3*a(n+2)-2*a(n+1)+4*a(n),a(0)=0,a(1)=0,a(2)=1} ogf A014336 20.7166 -6/(x^2-3*x+1)/(9*x^2+3*x-1) ogf A014336 16.1129 6*x^3+(-1+6*x-x^2-24*x^3+9*x^4)*f(x) ogf A014336 19.3355 6*x^3/(1-6*x+x^2+24*x^3-9*x^4) ogf A014337 19.0369 -1/(x^2-3*x+1)/(9*x^2+3*x-1) ogf A014337 11.1049 -2*(3-x+18*x^3-36*x^2)/(1+x^2-3*x)/(9*x^2+3*x-1) lgdogf A014337 15.6775 x^3+(-1+6*x-x^2-24*x^3+9*x^4)*f(x) ogf A014337 19.0369 x^3/(1-6*x+x^2+24*x^3-9*x^4) ogf A014340 7.90666 -10*(1-3*x+16*x^4+48*x^3-21*x^2)/(2*x-1)/(16*x^2+4*x-1)/(x^2+4*x-1) lgdogf A014340 10.5949 -24*x^4+(1-10*x+15*x^2+70*x^3-120*x^4-32*x^5)*f(x) ogf A014340 11.5162 -24*x^4/(-1+10*x-15*x^2-70*x^3+120*x^4+32*x^5) ogf A014340 13.9407 -24/(2*x-1)/(16*x^2+4*x-1)/(x^2+4*x-1) ogf A014341 13.8679 -1/(2*x-1)/(16*x^2+4*x-1)/(x^2+4*x-1) ogf A014341 7.6584 -10*(1-3*x+16*x^4+48*x^3-21*x^2)/(2*x-1)/(16*x^2+4*x-1)/(x^2+4*x-1) lgdogf A014341 10.9173 -x^4+(1-10*x+15*x^2+70*x^3-120*x^4-32*x^5)*f(x) ogf A014341 11.9329 -x^4/(-1+10*x-15*x^2-70*x^3+120*x^4+32*x^5) ogf A014372 3.76286 1-2*x+x^5+(-3+6*x-2*x^5)*f(x)+(-6*x+x^5+3)*f(x)^2+(2*x-1)*f(x)^3 ogf A014374 9.51413 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A014375 13.5806 1-2*f(x)+f(x)^2 ogf A014376 13.7715 1-2*f(x)+f(x)^2 ogf A014377 3.21132 1+x^4+(-2-x^4)*f(x)+f(x)^2 ogf A014378 12.0884 1-2*f(x)+f(x)^2 ogf A014380 17.169 -(x^28+x^46-1)/(x-1)/(x^46-x^21-x^14-x^7-1) ogf A014381 4.6874 1-2*f(x)+f(x)^2 ogf A014382 12.3322 1-2*f(x)+f(x)^2 ogf A014384 3.51555 1-2*f(x)+f(x)^2 ogf A014384 2.10933 x^5*(6+91*x+64302368*x^2) lgdogf A014386 14.1599 (-1-x^10+x^29+x^23+x^39)/(x-1)/(x^39+x^26+x^13+x^10+1) ogf A014390 22.7638 -(-1-6*x-43*x^2)/(x^2+1-x-x^3) ogf A014390 23.5487 -(1+6*x+43*x^2)/(x-1)/(x^2+1) ogf A014390 11.3819 -(7+84*x+43*x^4+12*x^3-46*x^2)/(-1+x)/(x^2+1)/(43*x^2+6*x+1) lgdogf A014390 8.43102 299+1794*x+12857*x^2+(-304+269*x+299*x^3-514*x^2)*f(x)+(5*x^2+5-5*x-5*x^3)*f(x)^2 ogf A014390 13.937 {a(n+3)-a(n+2)+a(n+1)-a(n),a(0)=1,a(1)=7,a(2)=49} ogf A014391 20.2145 -(-1-7*x+3*x^2-5*x^3)/(x^2+1-x-x^3) ogf A014391 20.809 -(1+7*x+5*x^3-3*x^2)/(x-1)/(x^2+1) ogf A014391 11.5985 -2*(4-4*x+x^4+2*x^3+7*x^2)/(-1+x)/(1+x^2)/(5*x^3-3*x^2+7*x+1) lgdogf A014391 9.5609 15+105*x+75*x^3-45*x^2+(-14+22*x+20*x^3-18*x^2)*f(x)+(-1-x^2+x^3+x)*f(x)^2 ogf A014391 12.4124 {a(n+4)-a(n+3)+a(n+2)-a(n+1),a(0)=1,a(1)=8,a(2)=4,a(3)=2} ogf A014392 6.93702 -(-1-7*x-84*x^4-56*x^2+3*x^10+36*x^8+52*x^3+28*x^5-8*x^7-12*x^9-75*x^11+24*x^6)/(x^10+1-x-x^11) ogf A014392 5.88408 -(1+7*x-52*x^3+12*x^9+75*x^11-3*x^10-36*x^8+56*x^2+84*x^4-28*x^5-24*x^6+8*x^7)/(x-1)/(x^2+1)/(x^8-x^6+x^4-x^2+1) ogf A014393 9.23993 -(-1-9*x-81*x^2-29*x^3-61*x^4-49*x^5-41*x^6-69*x^7-21*x^8-89*x^9)/(1-x^10) ogf A014393 6.10495 -(1+9*x+81*x^2+29*x^3+61*x^4+49*x^5+41*x^6+69*x^7+21*x^8+89*x^9)/(x-1)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1) ogf A014400 71.1102 1-x^16-x^22 ogf_with_Euler_Transform A014401 8.64542 {(4*n^2+28*n+40)*a(n+1)-a(n+2),a(0)=48,a(1)=768} ogf A014407 1.71489 -1-8*x+16*x^3-4*x^4-12*x^2+(2+4*x+16*x^3-4*x^4-18*x^2)*f(x)+(-6*x^2-1+4*x-x^4+4*x^3)*f(x)^2 ogf A014409 11.213 -(-2*x-x^6-3*x^4-x^3-4*x^2-x^5)/(1-2*x+2*x^6-2*x^2-6*x^5+6*x^3+2*x^7-x^8) ogf A014409 19.4893 -(2+4*x+3*x^3+x^2+x^4+x^5)/(x+1)^3/(x-1)^5 ogf A014409 10.2319 -(8+26*x+39*x^2+16*x^3+22*x^4+6*x^5+3*x^6)/(x-1)/(x+1)/(x^5+x^4+3*x^3+x^2+4*x+2) lgdogf A014412 14.7045 (-1-x^8+x^31+x^21+x^39)/(x-1)/(x^39+x^26+x^13+x^8+1) ogf A014419 8.67171 -(x+x^6+2*x^4+x^3+3*x^10+2*x^2+3*x^5+2*x^7+x^8+2*x^9+2*x^12+x^13+5*x^14+x^11)/(-1+x+x^14-x^15) ogf A014431 25.3526 1+2*x+(-1-x)*f(x)+x*f(x)^2 ogf A014431 18.3102 1/4*x-1/4+1/4*(-(1+7*x)*(x-1))^(1/2) revogf A014431 6.27779 {(-21*n-21*n^2)*a(n)+(-43*n-30-13*n^2)*a(n+1)+(-6+n+n^2)*a(n+2)+(7*n+12+n^2)*a(n+3),a(0)=1,a(1)=2,a(2)=2} ogf A014432 26.3154 1+3*x+(-1-x)*f(x)+x*f(x)^2 ogf A014432 18.4919 1/6*x-1/6+1/6*(-(11*x+1)*(x-1))^(1/2) revogf A014432 6.45473 {(55*n+55*n^2)*a(n)+(69*n+48+21*n^2)*a(n+1)+(-9*n-3*n^2)*a(n+2)+(-7*n-12-n^2)*a(n+3),a(0)=1,a(1)=3,a(2)=3} ogf A014433 30.5499 1+4*x+(-1-x)*f(x)+x*f(x)^2 ogf A014433 21.4675 1/8*x-1/8+1/8*(-(1+15*x)*(x-1))^(1/2) revogf A014433 7.15583 {(-105*n-105*n^2)*a(n)+(-95*n-66-29*n^2)*a(n+1)+(6+17*n+5*n^2)*a(n+2)+(7*n+12+n^2)*a(n+3),a(0)=1,a(1)=4,a(2)=4} ogf A014434 22.5514 1+5*x+(-1-x)*f(x)+x*f(x)^2 ogf A014434 14.6584 1/10*x-1/10+1/10*(-(19*x+1)*(x-1))^(1/2) revogf A014434 5.18882 {(171*n+171*n^2)*a(n)+(121*n+84+37*n^2)*a(n+1)+(-12-25*n-7*n^2)*a(n+2)+(-7*n-12-n^2)*a(n+3),a(0)=1,a(1)=5,a(2)=5} ogf A014435 23.7574 1+6*x+(-1-x)*f(x)+x*f(x)^2 ogf A014435 15.4423 1/12*x-1/12+1/12*(-(23*x+1)*(x-1))^(1/2) revogf A014435 5.41835 {(253*n+253*n^2)*a(n)+(147*n+102+45*n^2)*a(n+1)+(-18-33*n-9*n^2)*a(n+2)+(-7*n-12-n^2)*a(n+3),a(0)=1,a(1)=6,a(2)=6} ogf A014437 23.5431 -(1+x+x^3-x^2)/(-1+x^4+4*x^2) ogf A014437 23.5431 -(1+x-x^2+x^3)/(-1+x^4+4*x^2) ogf A014437 10.668 -(x+1)*(x^5-3*x^4+2*x^3+2*x^2+5*x+1)/(x^3-x^2+x+1)/(x^4+4*x^2-1) lgdogf A014437 8.53438 -9-9*x-9*x^3+9*x^2+(25+16*x+16*x^3-9*x^4-52*x^2)*f(x)+(-16+16*x^4+64*x^2)*f(x)^2 ogf A014444 20.7516 -(-1+x-x^3+x^4-x^5+x^7-x^8)/(1-x^29) ogf A014444 20.7516 -(1+x+x^3+x^4+x^5+x^7+x^8)/(-1+x^29) ogf A014445 21.2929 (-1-2*x+(1+4*x+5*x^2)^(1/2))/x revogf A014445 31.9394 -2*(x+2)/(x^2-1+4*x) lgdogf A014445 30.4185 -2*x+(1-4*x-x^2)*f(x) ogf A014445 37.5758 -2*x/(-1+4*x+x^2) ogf A014445 45.6277 -2/(x^2+4*x-1) ogf A014445 17.2645 {-a(n+2)+4*a(n+1)+a(n),a(0)=0,a(1)=2} ogf A014446 7.14781 -(-1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10+x^23+x^24+x^25+x^26+x^27+x^28+x^29)/(1-x^11+x^19-x^34+x^38) ogf A014446 66.9295 1-x^18-x^22 ogf_with_Euler_Transform A014447 20.3958 (-1-3*x+x^3-3*x^2)/(-1+x^4+4*x^2) ogf A014447 20.3958 -(-1-3*x-3*x^2+x^3)/(1-x^4-4*x^2) ogf A014447 9.75452 -(x+1)*(x^5-7*x^4-6*x^3+2*x^2-11*x-3)/(x^3-3*x^2-3*x-1)/(x^4+4*x^2-1) lgdogf A014447 7.56249 -99-297*x+99*x^3-297*x^2+(19-240*x+80*x^3-99*x^4-636*x^2)*f(x)+(80-80*x^4-320*x^2)*f(x)^2 ogf A014448 20.1717 (-1-2*x+(1+5*x^2)^(1/2))/(x-4) revogf A014448 28.8166 -(2-4*x)/(-1+4*x+x^2) ogf A014448 17.7985 -2*(-1-x+x^2)/(-1+2*x)/(x^2+4*x-1) lgdogf A014448 10.0858 -276+552*x+(308-892*x-138*x^2)*f(x)+(85*x^2-85+340*x)*f(x)^2 ogf A014448 28.8166 2*(2*x-1)/(x^2+4*x-1) ogf A014448 16.3554 {-a(n+2)+4*a(n+1)+a(n),a(0)=2,a(1)=4} ogf A014455 30.4253 -(-4-3*x^4+x^3)/(x^4+1+x+x^5) ogf_with_Euler_Transform A014474 20.7516 -(1+x+x^3+x^4+x^5+x^7+x^8)/(-1+x^31) ogf A014474 20.7516 -(1-x+x^3-x^4+x^5-x^7+x^8)/(-1+x^31) ogf A014477 19.0987 -(-1-2*x)/(12*x^2+1-6*x-8*x^3) ogf A014477 31.8311 -(2*x+1)/(2*x-1)^3 ogf A014477 6.74071 -321-642*x+(557-1454*x-2568*x^3+3852*x^2)*f(x)+(-236+1888*x^3+1416*x-2832*x^2)*f(x)^2 ogf A014477 23.8734 -8*(x+1)/(2*x-1)/(2*x+1) lgdogf A014477 10.2314 {a(n+3)-6*a(n+2)+12*a(n+1)-8*a(n),a(0)=1,a(1)=8,a(2)=36} ogf A014478 18.9299 -(-x^14-x^60+1)/(x^8-1+x-x^7-x^61+x^60) ogf A014478 22.3717 -(x^14+x^60-1)/(x-1)/(x^60-x^7-1) ogf A014478 18.9299 -(x^14-x^60-1)/(-x^8+1-x+x^7-x^61+x^60) ogf A014479 17.377 -(-1-2*x)/(12*x^2+1-6*x-8*x^3) egf A014479 28.9617 -(2*x+1)/(2*x-1)^3 egf A014479 6.13307 -321-642*x+(557-1454*x-2568*x^3+3852*x^2)*f(x)+(-236+1888*x^3+1416*x-2832*x^2)*f(x)^2 egf A014479 21.7213 -8*(1+x)/(2*x-1)/(1+2*x) lgdegf A014479 22.6657 4*x/(1+(1+8*x)^(1/2))^2 revegf A014479 10.0252 {(-18-12*n-2*n^2)*a(n+1)+(n+2)*a(n+2),a(0)=1,a(1)=8} ogf A014480 40.2095 (2*x+1)/(2*x-1)^2 ogf A014480 29.7201 -(1+2*x)/(-4*x^2-1+4*x) ogf A014480 18.4746 -1/4*(-1-4*x+(1+16*x)^(1/2))/(-1+2*x) revogf A014480 26.2908 -2*(3+2*x)/(2*x-1)/(2*x+1) lgdogf A014480 27.3425 1+2*x+(-4*x^2-1+4*x)*f(x) ogf A014480 17.5272 {-a(n+2)+4*a(n+1)-4*a(n),a(0)=1,a(1)=6} ogf A014481 33.4943 (2*x+1)/(2*x-1)^2 egf A014481 24.7566 -(1+2*x)/(-4*x^2-1+4*x) egf A014481 21.9001 -2*(3+2*x)/(2*x-1)/(2*x+1) lgdegf A014481 22.7761 1+2*x+(-4*x^2-1+4*x)*f(x) egf A014481 6.94394 {(-8-8*n-2*n^2)*a(n+1)+(-24-13*n-2*n^2)*a(n+2)+(n+3)*a(n+3),a(0)=1,a(1)=6,a(2)=40} ogf A014483 30.986 (2*x+1)/(2*x-1)^4 ogf A014483 13.8622 -(1+2*x)/(-24*x^2-1+8*x+32*x^3-16*x^4) ogf A014483 20.2601 -2*(5+6*x)/(2*x-1)/(1+2*x) lgdogf A014483 4.38969 -7423-14846*x+(2175-69880*x-237536*x^3+118768*x^4+178152*x^2)*f(x)+(5248-167936*x^3-41984*x+125952*x^2+83968*x^4)*f(x)^2 ogf A014483 8.23066 {(-n-3)*a(n+3)+10*a(n+2)+(16+4*n)*a(n+1),a(0)=1,a(1)=10,a(2)=56} ogf A014484 28.0521 (2*x+1)/(2*x-1)^4 egf A014484 12.5496 -(1+2*x)/(-24*x^2-1+8*x+32*x^3-16*x^4) egf A014484 18.3417 -2*(5+6*x)/(2*x-1)/(1+2*x) lgdegf A014484 3.97405 -7423-14846*x+(2175-69880*x-237536*x^3+118768*x^4+178152*x^2)*f(x)+(5248-167936*x^3-41984*x+125952*x^2+83968*x^4)*f(x)^2 egf A014484 5.54518 {(-16-12*n-2*n^2)*a(n+1)+(40+19*n+2*n^2)*a(n+2)+(-n-3)*a(n+3),a(0)=1,a(1)=10,a(2)=112} ogf A014485 7.89111 (-1-x^14+x^6-x^34+x^40)/(x-1)/(x+1)/(x^2+1)/(x^4+1)/(x^28+x^26+x^20+x^18-x^14+x^10-x^6+x^2+1) ogf A014488 8.91197 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A014493 16.091 -(-1-2*x-10*x^2-x^4-2*x^3)/(-2*x^2+1-x+x^4+2*x^3-x^5) ogf A014493 20.8005 -(1+2*x+2*x^3+10*x^2+x^4)/(x+1)^2/(x-1)^3 ogf A014493 12.1831 -(3+27*x+x^5+5*x^4+36*x^3+24*x^2)/(x-1)/(x+1)/(x^4+2*x^3+10*x^2+2*x+1) lgdogf A014494 16.6945 -(5+23*x+9*x^3+11*x^2)/(x-1)/(x+1)/(3*x^2+2*x+3) lgdogf A014494 17.8075 -(6*x+4*x^2+6*x^3)/(-1+x+2*x^2+x^5-2*x^3-x^4) ogf A014494 25.0418 -2*(3+2*x+3*x^2)/(x+1)^2/(x-1)^3 ogf A014494 5.48862 {(2949+1907*n+308*n^2)*a(n+1)+(7509+3405*n+356*n^2)*a(n+2)+(393-627*n-308*n^2)*a(n+3)+(-2883-2029*n-356*n^2)*a(n+4),a(0)=0,a(1)=6,a(2)=10,a(3)=28} ogf A014495 13.7683 x^2+(-1+2*x-2*x^3+x^2)*f(x)+(-x+4*x^2-5*x^3+2*x^4)*f(x)^2 ogf A014495 6.70761 {(-4*n^2-20*n-24)*a(n+1)+(4*n^2+18*n+18)*a(n+2)+(n^2+9*n+16)*a(n+3)+(-n^2-10-7*n)*a(n+4),a(0)=0,a(1)=0,a(2)=1,a(3)=2} ogf A014497 6.95157 -1-14152320*x^5+(3+28304640*x^5)*f(x)+(-14152320*x^5-3)*f(x)^2+f(x)^3 ogf A014504 17.6824 -(-1+x^3-x^9+x^12-x^15+x^21-x^24)/(1-x^33) ogf A014504 17.6824 -(1+x^3+x^9+x^12+x^15+x^21+x^24)/(-1+x^33) ogf A014506 18.9299 -(-x^14-x^64+1)/(x^8-1+x-x^7-x^65+x^64) ogf A014506 22.3717 -(x^14+x^64-1)/(x-1)/(x^64-x^7-1) ogf A014506 18.9299 -(x^14-x^64-1)/(-x^8+1-x+x^7-x^65+x^64) ogf A014508 5.5282 {(n^2+7*n+12)*a(n+1)+(-n-4)*a(n+2)+(-n^2-7*n-10)*a(n+3)+(n+2)*a(n+4),a(0)=0,a(1)=0,a(2)=2,a(3)=8} ogf A014523 16.1794 (x^2-3*x+1)/(9*x^2+1-7*x+x^4-7*x^3) ogf A014523 15.3049 -(-1+3*x-x^2)/(9*x^2+1-7*x+x^4-7*x^3) ogf A014523 7.75727 -(-4+16*x+2*x^5-41*x^2+46*x^3-16*x^4)/(x^2-3*x+1)/(x^4-7*x^3+9*x^2-7*x+1) lgdogf A014523 4.60391 -281+843*x-281*x^2+(-22337+65887*x-1967*x^3+281*x^4-20089*x^2)*f(x)+(22618*x^4+203562*x^2+22618-158326*x-158326*x^3)*f(x)^2 ogf A014524 18.4771 (x+1)/(9*x^2+1-7*x+x^4-7*x^3) ogf A014524 16.2374 -(-x-x^2)/(9*x^2+1-7*x+x^4-7*x^3) ogf A014524 9.56849 -(x-4)*(3*x^3+2*x^2-4*x+2)/(x+1)/(x^4-7*x^3+9*x^2-7*x+1) lgdogf A014524 4.32125 -8126*x-8126*x^2+(8126-157657*x-56882*x^3+8126*x^4-27641*x^2)*f(x)+(100775-705425*x+100775*x^4+906975*x^2-705425*x^3)*f(x)^2 ogf A014528 10.729 -(-1-x+x^19+2*x^8-3*x^2-x^7-2*x^18+x^21)/(x^2+x+1)/(x-1)^2 ogf A014528 11.5237 -(1+x+x^7-2*x^8-x^21-x^19+2*x^18+3*x^2)/(-1+x+x^3-x^4) ogf A014531 6.79951 {(-60-27*n-3*n^2)*a(n+1)+(-45-19*n-2*n^2)*a(n+2)+(10*n+21+n^2)*a(n+3),a(0)=1,a(1)=3,a(2)=10} ogf A014532 7.15365 {(-90-33*n-3*n^2)*a(n+1)+(-66-23*n-2*n^2)*a(n+2)+(12*n+27+n^2)*a(n+3),a(0)=1,a(1)=4,a(2)=15} ogf A014533 6.68004 {(-126-39*n-3*n^2)*a(n+1)+(-91-27*n-2*n^2)*a(n+2)+(14*n+33+n^2)*a(n+3),a(0)=1,a(1)=5,a(2)=21} ogf A014544 11.1824 -(-1-6*x+2*x^3-x^11+x^10+3*x^8+3*x^4-3*x^5+3*x^6-3*x^7-x^15+x^16+x^14)/(x-1)^2 ogf A014544 10.6369 -(1+6*x+3*x^7-3*x^8-x^10+3*x^5-3*x^4-x^14+x^15-x^16-2*x^3+x^11-3*x^6)/(-x^2-1+2*x) ogf A014551 40.8315 (x-2)/(x+1)/(2*x-1) ogf A014551 22.1657 -(-1-8*x+2*x^2)/(x-2)/(2*x-1)/(1+x) lgdogf A014551 43.1 -(2-x)/(2*x^2-1+x) ogf A014551 12.93 -214+107*x+(215-161*x-214*x^2)*f(x)+(108*x^2-54+54*x)*f(x)^2 ogf A014551 20.9675 {-a(n+2)+a(n+1)+2*a(n),a(0)=2,a(1)=1} ogf A014553 7.66082 (-4-2*x-14*x^13+13*x^14+6*x^7-9*x^8+8*x^9-6*x^5-2*x^6-2*x^3+3*x^4-2*x^2)/(x-1)/(x^14+x^9+x^7+x^6+x^4+x^3+x^2+3*x+1) lgdogf A014553 20.4882 -(1+3*x+x^3+x^9+x^2+x^4+x^6+x^7+x^14)/(x-1) ogf A014553 20.0226 -(1+3*x+x^7+x^9+x^4+x^14+x^3+x^2+x^6)/(-1+x) ogf A014557 18.8755 -2*(1+2*x+x^2+4*x^3)/(x-1)/(x+1)/(x^2+1) lgdogf A014557 18.4151 2*x^6/(1-2*x+2*x^3-2*x^4+2*x^5-2*x^7+x^8) ogf A014557 30.2008 2/(x^2+1)/(x+1)^2/(x-1)^4 ogf A014560 11.7427 -(-1+x^9+x^38-x^29-x^28)/(1+x^10-x-x^9-x^39+x^19-x^20+x^38) ogf A014560 13.5847 -(-1-x^10+x^19+x^29+x^39)/(1-x+x^10-x^11+x^29-x^30) ogf A014562 23.8765 -(-x^7+1-x^72)/(x^72-1+x-x^73) ogf A014562 24.6998 -(x^7-1-x^72)/(x^72+1-x-x^73) ogf A014564 20.6295 -(-1+x-x^3+x^4-x^5+x^7-x^8)/(1-x^37) ogf A014564 20.6295 -(1+x+x^3+x^4+x^5+x^7+x^8)/(-1+x^37) ogf A014581 8.8406 -(x^18-x^26+x^28+x^6-1+x^38+x^2-x^4+x^44)/(-x^38+1+x^42+x^44-x^20-x^8-x^18+x^34-x^22) ogf A014590 12.4124 (2*x+3*x^2+4*x^3+5*x^4+6*x^5+1)/(x^2+1+x+x^4+x^3+x^6+x^5) lgdogf A014590 141.501 1-x^6 ogf_with_Euler_Transform A014590 30.7612 x^6+x^5+x^4+x^3+x^2+x+1 ogf A014590 9.96488 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=0} ogf A014590 12.1984 {a(n+7),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=-1} ogf_with_Euler_Transform A014591 23.5928 -(-1-x^5+x^2)/(-x^6+1-x-x^2+x^4+x^5) ogf A014591 11.1755 -(1+4*x^6+2*x^7+2*x+2*x^5+2*x^3+x^8+4*x^2)/(x-1)/(1+x)/(x^2+x+1)/(x^5-x^2+1) lgdogf A014591 23.5928 -(1+x^5-x^2)/(x+1)/(x^2+x+1)/(x-1)^3 ogf A014592 14.8205 -(-x^33+1-x^42)/(x^12-1+x-x^11+x^42-x^22+x^23-x^43) ogf A014592 14.8205 -(x^33-1-x^42)/(-x^12+1-x+x^11+x^42+x^22-x^23-x^43) ogf A014594 17.4732 -(-1+x^3-x^9+x^12-x^15+x^21-x^24)/(1-x^39) ogf A014594 17.4732 -(-1-x^3-x^9-x^12-x^15-x^21-x^24)/(1-x^39) ogf A014598 11.5598 -(-1+x^7-x^26+x^38-x^31)/(-x^39+1-x-x^7+x^8+x^19-x^20+x^38) ogf A014598 6.68656 -(-1-x^3-x^4-x^12-x^13-x^14-x^15-x^16-x^17-x^18-x-x^2+x^31+x^32+x^33+x^34+x^35)/(1-x^24+x^31-x^5+x^12) ogf A014601 42.7397 (3+x)/(x+1)/(x-1)^2 ogf A014601 32.4821 -(3*x+x^2)/(-1+x+x^2-x^3) ogf A014601 25.3767 -2*(2+5*x+x^2)/(x-1)/(x+3)/(x+1) lgdogf A014601 10.4109 -885*x-295*x^2+(295-487*x+295*x^3-359*x^2)*f(x)+(64-64*x-64*x^2+64*x^3)*f(x)^2 ogf A014601 16.5725 {-a(n+3)+a(n+2)+a(n+1)-a(n),a(0)=0,a(1)=3,a(2)=4} ogf A014606 8.8141 {(-9*n^3-45*n^2-74*n-40)*a(n+1)+2*a(n+2),a(0)=1,a(1)=1} ogf A014606 10.3144 {(9*n^2+27*n+20)*a(n+1)-2*a(n+2),a(0)=1,a(1)=1} egf A014610 15.0642 -(-3-2*x-x^3-2*x^2)/(-x^2+1-x-x^4-x^3) ogf A014610 15.9011 -(3+2*x+x^3+2*x^2)/(x^2-1+x+x^4+x^3) ogf A014610 7.63255 -(5+10*x+x^6+4*x^5+7*x^4+14*x^3+12*x^2)/(x^3+2*x^2+2*x+3)/(x^4+x^3+x^2+x-1) lgdogf A014610 6.98099 -21-14*x-7*x^3-14*x^2+(16-x-4*x^3-7*x^4-x^2)*f(x)+(3*x^2-3+3*x+3*x^4+3*x^3)*f(x)^2 ogf A014616 37.143 (-2+x^2)/(x+1)/(x-1)^3 ogf A014616 30.2647 -(2-x^2)/(-1+2*x-2*x^3+x^4) ogf A014616 21.5038 -2*(x+2)*(x^2-x-1)/(x-1)/(x+1)/(x^2-2) lgdogf A014616 9.72793 -380+190*x^2+(236-380*x+380*x^3-190*x^4-23*x^2)*f(x)+(-23-46*x^3+23*x^4+46*x)*f(x)^2 ogf A014616 6.14396 {(303+116*n+5*n^2)*a(n+1)+(1338+426*n+33*n^2)*a(n+2)+(163-40*n-5*n^2)*a(n+3)+(-350*n-872-33*n^2)*a(n+4),a(0)=2,a(1)=4,a(2)=7,a(3)=10} ogf A014618 16.527 -(1+x+x^3+x^4+x^6+x^8+x^9+x^11+x^12)/(-1+x^29) ogf A014618 16.527 -(1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12)/(-1+x^29) ogf A014620 7.01499 (13+182*x^13-169*x^12-338*x^25+351*x^26-47*x^34+468*x^39-507*x^38)/(x-1)/(39*x^39+47*x^34-13*x^26-13*x^13-13) lgdogf A014620 14.7045 -(-1+x^34+x^39)/(-x^14+1-x+x^13+x^26-x^27-x^34+x^35) ogf A014620 15.2927 -(1+x^34-x^39)/(x^14-1+x-x^13-x^26+x^27-x^34+x^35) ogf A014625 22.9335 -(-1+x^4-x^8-x^40)/(1+x^12-x^28) ogf A014625 22.9335 -(1-x^4+x^8+x^40)/(-1-x^12+x^28) ogf A014626 33.9788 -(1-3*x+3*x^2)/(x-1)^5 ogf A014626 21.9863 -(2-6*x+9*x^2)/(x-1)/(3*x^2-3*x+1) lgdogf A014626 15.2558 -(x+3*x^3-3*x^2)/(-1+5*x-10*x^2+x^5+10*x^3-5*x^4) ogf A014626 8.21466 {(n+3)*a(n+4)+(-10-4*n)*a(n+3)+(6*n+12)*a(n+2)+(-9-3*n)*a(n+1),a(0)=0,a(1)=1,a(2)=2,a(3)=3} ogf A014628 12.4807 -(-3+7*x-x^4+5*x^3-10*x^2)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A014628 21.9358 -(3-7*x-5*x^3+10*x^2+x^4)/(x-1)^5 ogf A014628 12.9264 -(8-8*x+x^4-6*x^3+15*x^2)/(x-1)/(x^4-5*x^3+10*x^2-7*x+3) lgdogf A014629 27.8416 (-4+5*x+x^3-4*x^2)/(x-1)^5 ogf A014629 15.4017 -(-15+12*x+2*x^3-9*x^2)/(x-1)/(x^3-4*x^2+5*x-4) lgdogf A014629 13.1615 -(4*x-x^4+4*x^3-5*x^2)/(-1+5*x-10*x^2+x^5+10*x^3-5*x^4) ogf A014629 5.02695 {(60+44*n+7*n^2)*a(n+1)+(36-18*n-9*n^2)*a(n+2)+(-20-6*n+2*n^2)*a(n+3),a(0)=0,a(1)=4,a(2)=15,a(3)=39,a(4)=84,a(5)=160,a(6)=279,a(7)=455,a(8)=704} ogf A014632 18.5021 -(1+4*x+8*x^3+28*x^2+7*x^4)/(x+1)^2/(x-1)^3 ogf A014632 10.4683 -(5+65*x+7*x^5+23*x^4+120*x^3+68*x^2)/(x-1)/(x+1)/(7*x^4+8*x^3+28*x^2+4*x+1) lgdogf A014633 13.0196 -(-12-10*x-2*x^3-24*x^2)/(-2*x^2+1-x+x^4-x^5+2*x^3) ogf A014633 10.8852 -(11+59*x+37*x^3+35*x^2+2*x^4)/(x-1)/(x+1)/(x^3+12*x^2+5*x+6) lgdogf A014633 17.9459 -2*(6+5*x+x^3+12*x^2)/(x+1)^2/(x-1)^3 ogf A014633 4.48648 {(2298+1333*n+189*n^2)*a(n+1)+(8062+3147*n+291*n^2)*a(n+2)+(364-475*n-189*n^2)*a(n+3)+(-2085*n-3684-291*n^2)*a(n+4),a(0)=12,a(1)=22,a(2)=70,a(3)=92} ogf A014634 23.5955 -(-1-12*x-3*x^2)/(3*x^2+1-3*x-x^3) ogf A014634 34.8804 -(1+12*x+3*x^2)/(x-1)^3 ogf A014634 22.2847 -3*(5+10*x+x^2)/(x-1)/(3*x^2+12*x+1) lgdogf A014634 7.78882 -8609-103308*x-25827*x^2+(9793-11619*x-8609*x^3+29379*x^2)*f(x)+(-3552*x^2-1184+3552*x+1184*x^3)*f(x)^2 ogf A014634 14.8564 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=15,a(2)=45} ogf A014635 24.7155 -(6*x+10*x^2)/(-1+3*x-3*x^2+x^3) ogf A014635 43.9387 -2*(5*x+3)/(x-1)^3 ogf A014635 32.954 -2*(7+5*x)/(5*x+3)/(x-1) lgdogf A014635 8.2385 44814*x+74690*x^2+(-7469+13767*x+7469*x^3-36807*x^2)*f(x)+(1440-4320*x+4320*x^2-1440*x^3)*f(x)^2 ogf A014635 14.9226 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=6,a(2)=28} ogf A014637 17.4687 -(1+6*x+14*x^3+46*x^2+13*x^4)/(x+1)^2/(x-1)^3 ogf A014637 9.70482 -(7+103*x+13*x^5+41*x^4+204*x^3+112*x^2)/(x-1)/(x+1)/(13*x^4+14*x^3+46*x^2+6*x+1) lgdogf A014638 6.91179 (x^12+x^11+x+x^13+1+x^5+x^6+x^7+x^36)/(-x^14+1-x^19-x^2+x^5+x^28-x^31+x^34-x^8+x^11+x^17+x^22-x^25) ogf A014640 12.9744 -(17+95*x+4*x^4+65*x^3+59*x^2)/(x-1)/(x+1)/(2*x^3+21*x^2+8*x+9) lgdogf A014640 20.9586 -2*(9+8*x+2*x^3+21*x^2)/(x+1)^2/(x-1)^3 ogf A014640 5.27345 {(-5914-4907*n-975*n^2)*a(n+1)+(-22646-11221*n-1265*n^2)*a(n+2)+(-2704+717*n+975*n^2)*a(n+3)+(7968+6451*n+1265*n^2)*a(n+4),a(0)=0,a(1)=18,a(2)=34,a(3)=112} ogf A014641 23.7841 -(-1-18*x-5*x^2)/(3*x^2+1-3*x-x^3) ogf A014641 35.159 -(1+18*x+5*x^2)/(x-1)^3 ogf A014641 21.8556 -(21+46*x+5*x^2)/(x-1)/(5*x^2+18*x+1) lgdogf A014641 6.91161 -115157-2072826*x-575785*x^2+(125957-151071*x-115157*x^3+399471*x^2)*f(x)+(-32400*x^2-10800+32400*x+10800*x^3)*f(x)^2 ogf A014641 14.9751 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=1,a(1)=21,a(2)=65} ogf A014642 13.9181 -(-8*x+808*x^18-16*x^2-392*x^19-416*x^17)/(3*x^2+1-3*x-x^3) ogf A014642 37.3259 -(5+4*x)/(2*x+1)/(x-1) lgdogf A014642 45.6205 -8*(2*x+1)/(x-1)^3 ogf A014642 10.1379 1664*x+3328*x^2+(-208+408*x+208*x^3-1056*x^2)*f(x)+(27-81*x+81*x^2-27*x^3)*f(x)^2 ogf A014642 15.4938 {a(n+3)-3*a(n+2)+3*a(n+1)-a(n),a(0)=0,a(1)=8,a(2)=40} ogf A014653 12.875 (-x^2+1+x^36-x^38+x^40)/(-x^14+1+x^28-x^4+x^36+x^18-x^32) ogf A014658 18.4353 -(-x^22-x^48+1)/(x^12-1+x-x^11-x^49+x^48) ogf A014658 22.2307 -(x^22+x^48-1)/(x-1)/(x^48-x^11-1) ogf A014658 18.4353 -(x^22-x^48-1)/(-x^12+1-x+x^11-x^49+x^48) ogf A014660 16.527 -(-1-x-x^3-x^4-x^6-x^8-x^9-x^11-x^12)/(1-x^31) ogf A014660 16.527 -(1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12)/(-1+x^31) ogf A014669 10.1547 -(x^36-x^28+x^16-x^8+1)*(x^8+1)/(-1+x^2-x^4-x^10+x^12-x^14-x^22-x^32+x^34) ogf A014670 8.40588 -(1-x+x^2)*(x^6-x^3+1)*(x^6-x^5+x^4-x^3+x^2-x+1)/(x^4+x^3+x^2+x+1)/(x^2+x+1)/(x^4+1)/(x^2+1)^2/(x-1)^5 ogf A014672 6.91127 (1-x+x^17-x^22+x^3+x^20+x^30-x^5+x^6-x^39-x^31+x^40+x^36-x^35+x^33-x^18+x^23)/(-x^21+1+x^30+x^4-x^17+x^8-x^13) ogf A014676 16.6448 (-1-x^6+x^23+x^29+x^35)/(x-1)/(x^29+x^6+1) ogf A014676 14.5642 -(-1-x^6+x^23+x^29+x^35)/(1-x+x^6-x^7+x^29-x^30) ogf A014676 14.5642 -(1-x^35-x^6-x^23+x^29)/(-1-x^7+x+x^6-x^30+x^29) ogf A014679 9.73067 -(-1+2*x-x^4+2*x^3-3*x^2)/(2*x^2+1-2*x+2*x^6+3*x^4-3*x^3-x^7-2*x^5) ogf A014679 17.1567 -(1-x+x^2)^2/(x^2+1)/(x^2+x+1)/(x-1)^3 ogf A014679 9.8781 -x*(2+3*x^5-3*x^4+8*x^3+x^2+7*x)/(x-1)/(1+x^2)/(x^2+x+1)/(x^2-x+1) lgdogf A014679 38.3503 x+3*x^2+x^3-2*x^5 ogf_with_Euler_Transform A014679 5.1335 {16*a(n+3)-4*a(n+3)*n^2+27*a(n+2)*n-9*a(n+2)*n^2-16*a(n+1)+12*a(n+1)*n-2*a(n+1)*n^2,a(0)=0,a(1)=1,a(2)=3,a(3)=1,a(4)=0,a(5)=-2} ogf_with_Euler_Transform A014680 18.4353 -(-x^22-x^50+1)/(x^12-1+x-x^11-x^51+x^50) ogf A014680 6.6889 -(1-x^2+x^4)*(x^46+x^44-x^40-x^38+x^34+x^32-x^28-x^26+x^22+x^20+x^18-x^14-x^12+x^8+x^6-x^2-1)/(x-1)/(x^50-x^11-1) ogf A014680 18.4353 -(x^22-x^50-1)/(-x^12+1-x+x^11-x^51+x^50) ogf A014681 36.7588 (2-x+x^2)/(x+1)/(x-1)^2 ogf A014681 22.2487 -(1+7*x+x^3-x^2)/(x-1)/(1+x)/(x^2-x+2) lgdogf A014681 29.1535 -(2*x+x^3-x^2)/(-1+x+x^2-x^3) ogf A014681 9.49946 890*x+445*x^3-445*x^2+(-445+1413*x+39*x^3-39*x^2)*f(x)+(484*x^2-484+484*x-484*x^3)*f(x)^2 ogf A014681 14.5767 {-a(n+4)+a(n+3)+a(n+2)-a(n+1),a(0)=0,a(1)=2,a(2)=1,a(3)=4} ogf A014682 33.6481 (2+x+x^2)/(x-1)^2/(x+1)^2 ogf A014682 29.007 -(-2*x-x^3-x^2)/(1+x^4-2*x^2) ogf A014682 19.5629 -(1+10*x+2*x^3+3*x^2)/(x-1)/(1+x)/(x^2+x+2) lgdogf A014682 8.08849 -7618*x-3809*x^3-3809*x^2+(3809+2368*x+1184*x^3+3809*x^4-6434*x^2)*f(x)+(-1184-1184*x^4+2368*x^2)*f(x)^2 ogf A014682 5.32407 {(21536+17198*n+3215*n^2)*a(n+1)+(53065+29077*n+3921*n^2)*a(n+2)+(-7861-10768*n-3215*n^2)*a(n+3)+(-28416-21235*n-3921*n^2)*a(n+4),a(0)=0,a(1)=2,a(2)=1,a(3)=5} ogf A014695 38.9071 -(-1-x-x^2)/(x^2+1-x-x^3) ogf A014695 23.159 -(2+x^4+2*x^3+x^2)/(x-1)/(x^2+1)/(x^2+x+1) lgdogf A014695 40.5282 -(x^2+x+1)/(x-1)/(x^2+1) ogf A014695 88.4252 2-x-x^2+x^3 ogf_with_Euler_Transform A014695 15.1981 6+6*x+6*x^2+(-11+x+6*x^3-11*x^2)*f(x)+(5*x^2+5-5*x-5*x^3)*f(x)^2 ogf A014695 24.9405 {-a(n+4),a(0)=2,a(1)=-1,a(2)=-1,a(3)=1} ogf_with_Euler_Transform A014695 20.2641 {a(n+3)-a(n+2)+a(n+1)-a(n),a(0)=1,a(1)=2,a(2)=2} ogf A014696 21.4098 (1+x+x^3+5*x^2+x^4)/(x+1)^4/(x-1)^6 ogf A014696 9.13834 -(1+x+x^4+x^3+5*x^2)/(3*x^8-1+2*x-2*x^6+3*x^2-8*x^3-x^10-2*x^4+12*x^5-8*x^7+2*x^9) ogf A014696 11.1842 -(3+22*x+6*x^5+46*x^3+9*x^4+22*x^2)/(x-1)/(x+1)/(x^4+x^3+5*x^2+x+1) lgdogf A014697 8.4009 1/(x-1)^10/(x+1)^8*(1+2*x+15*x^2+24*x^3+21*x^4+24*x^5+15*x^6+2*x^7+x^8) ogf A014698 14.9928 -(-x^39+1-x^40)/(x^14-1+x-x^13+x^40-x^26+x^27-x^41) ogf A014698 14.9928 -(x^39-1-x^40)/(-x^14+1-x+x^13+x^40+x^26-x^27-x^41) ogf A014712 13.0303 -(1-x+x^20-x^38+x^37)/(-x^2-1+2*x+x^39-x^19+x^20-x^38) ogf A014717 3.22218 -(-9+14*x+x^2)/(x+1)/(x^2-3*x+1) ogf A014717 1.90944 {-a(n+3)+2*a(n+2)+2*a(n+1)-a(n),a(0)=9,a(1)=4,a(2)=25} ogf A014722 14.1137 -(-1+x^8-x^31+x^23+x^39)/(1-x-x^8+x^9-x^31+x^32) ogf A014728 5.82758 -(1+20*x+28*x^5+204*x^3+x^8+4*x^7+238*x^4+80*x^2)/(x-1)/(1+x^2)/(x^2+4*x+1)/(x^2-4*x-1)/(x^2+4*x-1) lgdogf A014728 11.7741 -(1+x-x^5-x^4+8*x^3-8*x^2)/(-1+17*x^4+17*x^2-x^6) ogf A014728 11.0948 -(x^2+4*x+1)*(x-1)^3/(x^2+1)/(x^2+4*x-1)/(x^2-4*x-1) ogf A014729 15.8831 -(-4*x+4*x^2)/(1-17*x-17*x^2+x^3) ogf A014729 19.4127 -4*(x-1)/(x+1)/(x^2-18*x+1) ogf A014729 8.45393 -4*x+4*x^2+(1-33*x+x^3-x^2)*f(x)+(-68*x^2+4-68*x+4*x^3)*f(x)^2 ogf A014729 9.52989 {a(n+3)-17*a(n+2)-17*a(n+1)+a(n),a(0)=0,a(1)=4,a(2)=64} ogf A014731 13.1136 -(-4+52*x+16*x^2)/(1-17*x-17*x^2+x^3) ogf A014731 4.07734 -121948+1585324*x+487792*x^2+(128327-1790199*x+30487*x^3-909639*x^2)*f(x)+(-24460+415820*x+415820*x^2-24460*x^3)*f(x)^2 ogf A014731 7.46467 -2*(2+13*x+2*x^4+13*x^3-78*x^2)/(x+1)/(4*x^2+13*x-1)/(x^2-18*x+1) lgdogf A014731 13.1136 -4*(-1+13*x+4*x^2)/(x+1)/(x^2-18*x+1) ogf A014731 8.36557 {-a(n+3)+17*a(n+2)+17*a(n+1)-a(n),a(0)=4,a(1)=16,a(2)=324} ogf A014736 8.73281 -(1+8*x+184*x^3+x^8+212*x^2+726*x^4+184*x^5+212*x^6+8*x^7)/(x+1)^4/(x-1)^5 ogf A014736 5.98359 -(1+8*x+184*x^5+212*x^6+8*x^7+726*x^4+184*x^3+x^8+212*x^2)/(4*x^2-1+x-x^8-6*x^4+x^9-4*x^3+4*x^6+6*x^5-4*x^7) ogf A014737 13.1049 (1-x^20-x^36+x^40+x^32)/(1+x^4-x^20-x^24-x^28+x^48+x^44) ogf A014738 6.63234 -(-36-64*x-64*x^5-36*x^6-540*x^4-256*x^3-540*x^2)/(-4*x^2+1-x-x^9+6*x^4+4*x^3+x^8-4*x^6-6*x^5+4*x^7) ogf A014738 5.76725 -(25+367*x+27*x^7+455*x^2+1549*x^3+599*x^4+745*x^5+73*x^6)/(x-1)/(x+1)/(9*x^6+16*x^5+135*x^4+64*x^3+135*x^2+16*x+9) lgdogf A014738 10.5275 -4*(9+16*x+64*x^3+135*x^2+135*x^4+16*x^5+9*x^6)/(x+1)^4/(x-1)^5 ogf A014739 32.6553 (x^2+1)/(x-1)/(x^2+x-1) ogf A014739 17.4668 -(-2-2*x+x^4+5*x^2)/(x-1)/(x^2+1)/(x^2+x-1) lgdogf A014739 35.7653 -(1+x^2)/(-1+2*x-x^3) ogf A014739 11.5549 92+92*x^2+(-107+184*x-92*x^3-15*x^2)*f(x)+(15*x^3+15-30*x)*f(x)^2 ogf A014739 17.0698 {-a(n+3)+2*a(n+2)-a(n),a(0)=1,a(1)=2,a(2)=5} ogf A014740 13.723 (1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^42)/(1-x^8+x^17-x^25+x^34) ogf A014742 30.8829 (x^2+1)/(x+1)/(x^2-3*x+1) ogf A014742 17.1572 -(-2-6*x+x^4+5*x^2)/(x+1)/(1+x^2)/(1+x^2-3*x) lgdogf A014742 28.5953 -(1+x^2)/(-1+2*x+2*x^2-x^3) ogf A014742 10.7232 36+36*x^2+(23+72*x-36*x^3+131*x^2)*f(x)+(118*x^2-59*x^3-59+118*x)*f(x)^2 ogf A014742 14.8475 {a(n+3)-2*a(n+2)-2*a(n+1)+a(n),a(0)=1,a(1)=2,a(2)=7} ogf A014743 23.1938 -(-1-x)/(-x^2+1-x-x^4-x^5) ogf A014743 11.1674 -(2+2*x+4*x^5+8*x^4+4*x^3+x^2)/(x+1)/(x^5+x^4+x^2+x-1) lgdogf A014743 25.1266 -(x+1)/(x^2-1+x+x^4+x^5) ogf A014746 18.4353 -(-x^22-x^56+1)/(x^12-1+x-x^11-x^57+x^56) ogf A014746 22.2307 -(x^22+x^56-1)/(x-1)/(x^56-x^11-1) ogf A014746 18.4353 -(x^22-x^56-1)/(-x^12+1-x+x^11-x^57+x^56) ogf A014751 17.4732 (x^28+x^46-1)/(x+1)/(x^46+x^21-x^14+x^7-1) ogf A014757 16.3359 -(1+x^12+x^22+x^34+x^46)/(x^2+1)/(x^34-x^12-1) ogf A014763 14.0785 -(1+x^10+x^29+x^23+x^39)/(x+1)/(x^39-x^26+x^13-x^10-1) ogf A014769 9.04957 -(1+24*x+1280*x^3+49*x^8+1196*x^2+6294*x^4+1976*x^5+2828*x^6+176*x^7)/(x+1)^4/(x-1)^5 ogf A014770 5.71668 -(-144-340*x-908*x^5-3840*x^2-672*x^6-5712*x^4-4*x^7-2204*x^3)/(-4*x^2+1-x+x^8+6*x^4-x^9+4*x^3-4*x^6-6*x^5+4*x^7) ogf A014770 8.8491 -4*(36+85*x+551*x^3+960*x^2+1428*x^4+227*x^5+168*x^6+x^7)/(x+1)^4/(x-1)^5 ogf A014771 9.42343 -(-1-220*x-910*x^2-9*x^4-396*x^3)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A014771 15.3131 -(1+220*x+396*x^3+910*x^2+9*x^4)/(x-1)^5 ogf A014771 8.27734 -3*(75+900*x+1306*x^2+276*x^3+3*x^4)/(x-1)/(9*x^4+396*x^3+910*x^2+220*x+1) lgdogf A014772 10.3173 -(-36-604*x-796*x^2-100*x^3)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A014772 10.3173 -2*(98+501*x+336*x^2+25*x^3)/(-1+x)/(25*x^3+199*x^2+151*x+9) lgdogf A014772 17.6868 -4*(9+151*x+25*x^3+199*x^2)/(x-1)^5 ogf A014772 4.61969 {(351495+230145*n+37660*n^2)*a(n+1)+(-748780-337040*n-64576*n^2)*a(n+2)+(149871*n+207369+26916*n^2)*a(n+3),a(0)=36,a(1)=784,a(2)=4356} ogf A014773 5.03284 -(-1-48*x-169*x^8-5648*x^5-2972*x^2-8396*x^6-17262*x^4-560*x^7-3344*x^3)/(-4*x^2+1-x+x^8+6*x^4-x^9+4*x^3-4*x^6-6*x^5+4*x^7) ogf A014773 7.11539 -(1+48*x+3344*x^3+169*x^8+2972*x^2+17262*x^4+5648*x^5+8396*x^6+560*x^7)/(x+1)^4/(x-1)^5 ogf A014775 22.4084 (-2-2*x-x^2)*f(x)-2*f(x)^2 lgdegf A014775 48.5514 -1-x-1/2*x^2 lgdegf A014775 25.3312 exp(-1/6*x*(x^2+3*x+6)) egf A014775 6.93592 {(-5*n-n^2-6)*a(n+1)+(-2*n-6)*a(n+2)-2*a(n+4)-2*a(n+3),a(0)=1,a(1)=-1,a(2)=0,a(3)=1} ogf A014776 18.6496 -(-x^26-x^46+1)/(x^14-1+x-x^13-x^47+x^46) ogf A014776 7.42363 -(1-x^2+x^4)*(x^42+x^40-x^36-x^34+x^30+x^28-x^24+x^20+x^18-x^14-x^12+x^8+x^6-x^2-1)/(x-1)/(x^46-x^13-1) ogf A014776 18.6496 -(x^26-x^46-1)/(-x^14+1-x+x^13-x^47+x^46) ogf A014786 16.3359 -(-1+x-x^3+x^4-x^6+x^8-x^9+x^11-x^12)/(1-x^37) ogf A014786 16.3359 -(1+x+x^3+x^4+x^6+x^8+x^9+x^11+x^12)/(-1+x^37) ogf A014787 55.981 -12/(-1-x) ogf_with_Euler_Transform A014787 25.4459 {-a(n+1)-a(n),a(0)=12} ogf_with_Euler_Transform A014789 7.91001 -(x^28+x^14-x^18+1-x^34-x^36-x^38-x^4-x^6+x^12+x^52)/(x^44-1+x^2+x^40-x^26+x^48+x^30-x^32+x^34) ogf A014790 24.2404 -(-x^11+1-x^60)/(x^60-1+x-x^61) ogf A014790 25.0484 -(x^11-1-x^60)/(x^60+1-x-x^61) ogf A014792 4.20471 -(289+5983*x+1579*x^7+8*x^8+8711*x^2+35453*x^3+16519*x^4+24185*x^5+3273*x^6)/(x-1)/(x+1)/(4*x^7+525*x^6+680*x^5+4071*x^4+1508*x^3+2523*x^2+208*x+81) lgdogf A014792 5.14295 -(324*x+16*x^8+16284*x^5+832*x^2+10092*x^3+6032*x^4+2720*x^6+2100*x^7)/(-1+x-x^8+4*x^2+x^9-4*x^3-6*x^4+6*x^5+4*x^6-4*x^7) ogf A014792 7.97817 -4*(81+208*x+1508*x^3+2523*x^2+4071*x^4+680*x^5+525*x^6+4*x^7)/(x+1)^4/(x-1)^5 ogf A014793 9.53116 -(-1-436*x-2030*x^2-964*x^3-25*x^4)/(10*x^2+1-5*x+5*x^4-10*x^3-x^5) ogf A014793 15.2045 -(1+436*x+964*x^3+2030*x^2+25*x^4)/(x-1)^5 ogf A014793 8.18702 -(441+5804*x+25*x^4+2028*x^3+8982*x^2)/(x-1)/(25*x^4+964*x^3+2030*x^2+436*x+1) lgdogf A014794 6.62018 32*(-2-40*x-8*x^3-31250*x^9-15625*x^11+31250*x^10+3125*x^12+15625*x^8-58*x^2-3125*x^7)/(x-1)^5 ogf A014795 6.05966 -(-1-1218*x-1218*x^5-18671*x^2-42140*x^3-18671*x^4-x^6)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A014795 9.87139 -(1+1218*x+42140*x^3+18671*x^2+18671*x^4+1218*x^5+x^6)/(x-1)^7 ogf A014799 5.32574 -(-1-5618*x-21042*x^5-124671*x^2-369404*x^3-216463*x^4-81*x^6)/(21*x^2+1-7*x+35*x^4-35*x^3+7*x^6-21*x^5-x^7) ogf A014799 8.33594 -(1+5618*x+369404*x^3+124671*x^2+216463*x^4+21042*x^5+81*x^6)/(x-1)^7 ogf A014799 4.29239 -3*(1875+94350*x+577189*x^2+781156*x^3+251533*x^4+14190*x^5+27*x^6)/(x-1)/(81*x^6+21042*x^5+216463*x^4+369404*x^3+124671*x^2+5618*x+1) lgdogf A014802 18.6496 -(-x^26-x^48+1)/(x^14-1+x-x^13-x^49+x^48) ogf A014802 22.4892 -(x^26+x^48-1)/(x-1)/(x^48-x^13-1) ogf A014802 18.6496 -(x^26-x^48-1)/(-x^14+1-x+x^13-x^49+x^48) ogf A014805 54.721 -16/(-1-x) ogf_with_Euler_Transform A014805 24.8732 {-a(n+1)-a(n),a(0)=16} ogf_with_Euler_Transform A014806 57.8405 -20/(-1-x) ogf_with_Euler_Transform A014806 26.2911 {-a(n+1)-a(n),a(0)=20} ogf_with_Euler_Transform A014808 8.69125 (x^3+x^11+x^10+1+x^9+x^2+x^38+x^12+x)/(-x^21+1-x^30+x^34+x^17-x^4+x^9-x^13+x^26+x^43-x^39) ogf A014809 50.2346 -24/(-1-x) ogf_with_Euler_Transform A014809 22.8339 {-a(n+1)-a(n),a(0)=24} ogf_with_Euler_Transform A014812 23.9568 -(-x^11+1-x^62)/(x^62-1+x-x^63) ogf A014812 24.7554 -(x^11-1-x^62)/(x^62+1-x-x^63) ogf A014815 14.62 -(1+x^8+x^31+x^21+x^39)/(x+1)/(x^39-x^26+x^13-x^8-1) ogf A014820 11.2446 -(-1-3*x-x^3-3*x^2)/(10*x^2+1-5*x+5*x^4-x^5-10*x^3) ogf A014820 35.8423 -(x+1)^3/(x-1)^5 ogf A014820 28.6738 -2*(4+x)/(x-1)/(x+1) lgdogf A014820 114.695 8-3*x ogf_with_Euler_Transform A014820 9.71994 {(-n-3)*a(n+3)+8*a(n+2)+(n+3)*a(n+1),a(0)=1,a(1)=8,a(2)=33} ogf A014820 24.9338 {a(n+2),a(0)=8,a(1)=-3} ogf_with_Euler_Transform A014821 11.1193 (1-x^4+x^8)*(x^36+x^32-x^24+x^16+x^12-x^4-1)/(x^2+1)/(x^44+x^14-1) ogf A014821 17.0668 -(x^28+x^44-1)/(-x^16+1+x^2-x^14-x^46-x^44) ogf A014821 17.0668 -(x^28-x^44-1)/(-x^16+1-x^2+x^14-x^46+x^44) ogf A014824 26.0133 -1/(10*x-1)/(x-1)^2 ogf A014824 19.0097 -6*(-2+5*x)/(10*x-1)/(x-1) lgdogf A014824 7.6039 x+(-1+24*x+10*x^3-21*x^2)*f(x)+(-252*x^2-12+144*x+120*x^3)*f(x)^2 ogf A014824 20.5939 x/(1-12*x+21*x^2-10*x^3) ogf A014824 8.52161 {a(n+3)-12*a(n+2)+21*a(n+1)-10*a(n),a(0)=0,a(1)=1,a(2)=12} ogf A014825 30.3952 -1/(4*x-1)/(x-1)^2 ogf A014825 6.43664 -1040+(3619-6240*x-4160*x^3+9360*x^2)*f(x)+(-2579+15474*x-23211*x^2+10316*x^3)*f(x)^2 ogf A014825 26.0531 1/(1-6*x+9*x^2-4*x^3) ogf A014825 9.94753 {a(n+3)-6*a(n+2)+9*a(n+1)-4*a(n),a(0)=1,a(1)=6,a(2)=27} ogf A014826 8.50539 -(-x^4-x^10-x^11-x^14-1-x^12-x^13-x^2-x^3+x^38-x)/(-x^15+1-x^24+x^29-x^34-x^5+x^10+x^19+x^39) ogf A014827 22.9608 -(-7+15*x)/(5*x-1)/(x-1) lgdogf A014827 29.0031 -1/(-1+5*x)/(x-1)^2 ogf A014827 5.92536 -7325+(29786-51275*x-36625*x^3+80575*x^2)*f(x)+(-247071*x^2+112305*x^3-22461+157227*x)*f(x)^2 ogf A014827 25.0481 1/(1-7*x+11*x^2-5*x^3) ogf A014827 9.84032 {a(n+3)-7*a(n+2)+11*a(n+1)-5*a(n),a(0)=1,a(1)=7,a(2)=38} ogf A014829 29.9573 -1/(6*x-1)/(x-1)^2 ogf A014829 5.61699 -14796+(68917-118368*x-88776*x^3+192348*x^2)*f(x)+(-703573*x^2+324726*x^3-54121+432968*x)*f(x)^2 ogf A014829 21.5693 -2*(-4+9*x)/(6*x-1)/(x-1) lgdogf A014829 24.5105 1/(1-8*x+13*x^2-6*x^3) ogf A014829 9.62913 {a(n+3)-8*a(n+2)+13*a(n+1)-6*a(n),a(0)=1,a(1)=8,a(2)=51} ogf A014830 28.4629 -1/(7*x-1)/(x-1)^2 ogf A014830 5.56883 -2989+(15698-26901*x-20923*x^3+44835*x^2)*f(x)+(-190635*x^2+88963*x^3-12709+114381*x)*f(x)^2 ogf A014830 20.4933 -3*(-3+7*x)/(7*x-1)/(x-1) lgdogf A014830 23.2878 1/(1-9*x+15*x^2-7*x^3) ogf A014830 9.1488 {a(n+3)-9*a(n+2)+15*a(n+1)-7*a(n),a(0)=1,a(1)=9,a(2)=66} ogf A014831 37.7182 -1/(8*x-1)/(x-1)^2 ogf A014831 26.1126 -2*(-5+12*x)/(8*x-1)/(x-1) lgdogf A014831 7.22264 -6464+(37799-64640*x-51712*x^3+109888*x^2)*f(x)+(-532695*x^2+250680*x^3-31335+313350*x)*f(x)^2 ogf A014831 29.5186 1/(1-10*x+17*x^2-8*x^3) ogf A014831 11.7057 {a(n+3)-10*a(n+2)+17*a(n+1)-8*a(n),a(0)=1,a(1)=10,a(2)=83} ogf A014832 20.0014 -(-11+27*x)/(9*x-1)/(x-1) lgdogf A014832 27.7797 -1/(9*x-1)/(x-1)^2 ogf A014832 4.8547 -71685+(461962-788535*x-645165*x^3+1362015*x^2)*f(x)+(-7415263*x^2+3512493*x^3-390277+4293047*x)*f(x)^2 ogf A014832 21.7406 1/(1-11*x+19*x^2-9*x^3) ogf A014832 8.47515 {a(n+3)-11*a(n+2)+19*a(n+1)-9*a(n),a(0)=1,a(1)=11,a(2)=102} ogf A014833 16.9088 -(-1+4*x+x^3-5*x^2)/(2*x-1)/(x-1)^3 ogf A014833 13.1513 -(1-4*x-x^3+5*x^2)/(-9*x^2-1+5*x-2*x^4+7*x^3) ogf A014833 9.86348 -(1-6*x+2*x^4-16*x^3+16*x^2)/(x-1)/(2*x-1)/(x^3-5*x^2+4*x-1) lgdogf A014833 7.21718 -1+4*x+x^3-5*x^2+(2-9*x-8*x^3+2*x^4+14*x^2)*f(x)+(-9*x^2-1+5*x-2*x^4+7*x^3)*f(x)^2 ogf A014833 4.41648 {(336+272*n+52*n^2)*a(n+1)+(-552-478*n-100*n^2)*a(n+2)+(360+301*n+59*n^2)*a(n+3)+(-65*n-84-11*n^2)*a(n+4),a(0)=1,a(1)=1,a(2)=1,a(3)=2} ogf A014834 6.57188 -(-x^5+x^15+1-x^25+x^30-x^40+x^45)/(x-1)/(x^4+x^3+x^2+x+1)/(x^20+x^15+x^10+x^5+1)/(x^4+1)/(x^16-x^12+x^8-x^4+1) ogf A014844 20.6894 (1-3*x+x^3+2*x^2)/(2*x-1)/(x-1)^3 ogf A014844 15.1722 -(-1+3*x-x^3-2*x^2)/(9*x^2+1-5*x+2*x^4-7*x^3) ogf A014844 10.8373 -(-2+10*x+12*x^3+2*x^4-19*x^2)/(-1+x)/(2*x-1)/(x^3+2*x^2-3*x+1) lgdogf A014844 7.50276 3-9*x+3*x^3+6*x^2+(-14+48*x+10*x^3-6*x^4-49*x^2)*f(x)+(11-55*x+99*x^2-77*x^3+22*x^4)*f(x)^2 ogf A014844 5.41866 {(-60-50*n-10*n^2)*a(n+1)+(90+87*n+19*n^2)*a(n+2)+(-62-55*n-11*n^2)*a(n+3)+(12*n+16+2*n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=3,a(3)=5} ogf A014845 9.39314 -(-x^8+x^18+x^10+x^6+1-x^20+x^38+x^22)/(x^28-1-x^2-x^6-x^18+x^34-x^12+x^40+x^22) ogf A014846 14.9178 -(4*x-1)*(x^2-4*x+2)/(x-1)/(2*x-1)/(x^2-3*x+1) lgdogf A014846 10.242 -(x+12*x^5+x^3+2*x^4-20*x^6-3*x^2+8*x^7)/(-1+5*x-9*x^2+7*x^3-2*x^4) ogf A014846 17.1554 -(x-3*x^2+x^3)/(1-5*x+9*x^2-7*x^3+2*x^4) ogf A014846 24.5077 -(x^2-3*x+1)/(2*x-1)/(x-1)^3 ogf A014846 6.79422 -31*x-31*x^3+93*x^2+(-31+120*x+182*x^3-62*x^4-174*x^2)*f(x)+(-35+175*x-315*x^2+245*x^3-70*x^4)*f(x)^2 ogf A014846 4.66814 {(-1648-1272*n-224*n^2)*a(n+1)+(2486*n+3044+482*n^2)*a(n+2)+(-1659*n-1998-331*n^2)*a(n+3)+(444+367*n+73*n^2)*a(n+4),a(0)=0,a(1)=-1,a(2)=-2,a(3)=-2} ogf A014848 31.3034 -(2*x^2+x+1)/(x+1)/(x-1)^3 ogf A014848 18.0864 -(3+10*x+4*x^3+7*x^2)/(x-1)/(x+1)/(2*x^2+x+1) lgdogf A014848 24.6633 -(x+2*x^3+x^2)/(-1+2*x+x^4-2*x^3) ogf A014848 7.20256 8191*x+16382*x^3+8191*x^2+(-8191+12190*x-24766*x^3+8191*x^4-4192*x^2)*f(x)+(4192-8384*x-4192*x^4+8384*x^3)*f(x)^2 ogf A014848 5.42593 {(3410+3843*n+1069*n^2)*a(n+1)+(15784+9672*n+1053*n^2)*a(n+2)+(5567+401*n-1069*n^2)*a(n+3)+(-6807-5428*n-1053*n^2)*a(n+4),a(0)=0,a(1)=1,a(2)=3,a(3)=8} ogf A014849 10.1927 (1+x^4-x^12-x^16-x^20+x^28+x^32)/(x^4+1)/(x^24-x^20+x^16-x^12+x^8-x^4+1) ogf A014849 17.0668 -(-1-x^20-x^4+x^32-x^12-x^16+x^28)/(1-x^28) ogf A014849 17.0668 -(1+x^32+x^28+x^4-x^12-x^16-x^20)/(-1-x^28) ogf A014856 26.2039 (1+x^55+x^66)/(1-x^11+x^55) ogf A014856 24.3968 -(1+x^55+x^66)/(-1+x^11-x^55) ogf A014856 20.809 11*x^10*(1+7*x^55)/(1-x^11+7*x^55) lgdogf A014877 20.9678 (x^28+x^48-1)/(x^2+1)/(x^48+x^14-1) ogf A014877 17.0668 -(x^28+x^48-1)/(-x^16+1+x^2-x^14-x^50-x^48) ogf A014877 17.0668 -(x^28-x^48-1)/(-x^16+1-x^2+x^14-x^50+x^48) ogf A014878 23.1063 -(-x^11+1-x^68)/(x^68-1+x-x^69) ogf A014878 23.8765 -(x^11-1-x^68)/(x^68+1-x-x^69) ogf A014879 20.8736 -(-1-x+x^3+x^4+x^5-x^7-x^8)/(1+x^29) ogf A014879 20.8736 -(1+x+x^3+x^4+x^5+x^7+x^8)/(-1+x^29) ogf A014881 23.5555 -(-13+33*x)/(11*x-1)/(x-1) lgdogf A014881 32.2339 -1/(11*x-1)/(x-1)^2 ogf A014881 5.51751 -157421+(1202642-2046473*x-1731631*x^3+3620683*x^2)*f(x)+(-24040083*x^2+11497431*x^3-1045221+13587873*x)*f(x)^2 ogf A014881 25.5185 1/(1-13*x+23*x^2-11*x^3) ogf A014881 10.2074 {a(n+3)-13*a(n+2)+23*a(n+1)-11*a(n),a(0)=1,a(1)=13,a(2)=146} ogf A014882 33.3187 -1/(12*x-1)/(x-1)^2 ogf A014882 23.4465 -2*(-7+18*x)/(12*x-1)/(x-1) lgdogf A014882 5.70319 -221616+(1825657-3102624*x-2659392*x^3+5540400*x^2)*f(x)+(-40101025*x^2+19248492*x^3-1604041+22456574*x)*f(x)^2 ogf A014882 26.3773 1/(1-14*x+25*x^2-12*x^3) ogf A014882 10.5509 {a(n+3)-14*a(n+2)+25*a(n+1)-12*a(n),a(0)=1,a(1)=14,a(2)=171} ogf A014888 5.30062 (761729+x+61813*x^2)/(x^2+x+1)/(x-1)^2 ogf A014888 5.5951 -(761729+x+61813*x^2)/(-1+x+x^3-x^4) ogf A014889 11.3532 (761664+55835*x+7*x^3+x^2+x^4+2101*x^5+3934*x^6)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A014889 14.5462 -(761664+55835*x+2101*x^5+7*x^3+3934*x^6+x^4+x^2)/(-1+x+x^7-x^8) ogf A014892 7.85584 (42768+2153*x+x^3+x^2+x^4+x^5+1731*x^6)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x-1)^2 ogf A014892 10.4268 -(42768+2153*x+x^5+x^3+1731*x^6+x^4+x^2)/(-1+x+x^7-x^8) ogf A014893 7.31 -(x^6+x^18-x^20+1-x^16-x^28-x^2+x^14+x^26+x^34-x^36+x^30+x^40)/(-x^6-1-x^30+x^4+x^22+x^34-x^8-x^14+x^40) ogf A014895 3.49985 (2787+x+x^3+5*x^2+146*x^4+185*x^5)/(x^2-x+1)/(x^2+x+1)/(x+1)/(x-1)^2 ogf A014896 34.0935 -1/(13*x-1)/(x-1)^2 ogf A014896 5.94291 -101231+(894526-1518465*x-1316003*x^3+2733237*x^2)*f(x)+(-21418965*x^2+10312835*x^3-793295+11899425*x)*f(x)^2 ogf A014896 26.9907 1/(1-15*x+27*x^2-13*x^3) ogf A014896 10.7963 {a(n+3)-15*a(n+2)+27*a(n+1)-13*a(n),a(0)=1,a(1)=15,a(2)=198} ogf A014897 34.8684 -1/(14*x-1)/(x-1)^2 ogf A014897 24.537 -2*(-8+21*x)/(14*x-1)/(x-1) lgdogf A014897 5.91517 -406700+(3837317-6507200*x-5693800*x^3+11794300*x^2)*f(x)+(-99487893*x^2+48028638*x^3-3430617+54889872*x)*f(x)^2 ogf A014897 27.6041 1/(1-16*x+29*x^2-14*x^3) ogf A014897 11.0417 {a(n+3)-16*a(n+2)+29*a(n+1)-14*a(n),a(0)=1,a(1)=16,a(2)=227} ogf A014898 27.5865 -1/(15*x-1)/(x-1)^2 ogf A014898 4.85318 -76275+(765358-1296675*x-1144125*x^3+2364525*x^2)*f(x)+(-21361573*x^2+10336245*x^3-689083+11714411*x)*f(x)^2 ogf A014898 21.8393 1/(1-17*x+31*x^2-15*x^3) ogf A014898 8.73573 {a(n+3)-17*a(n+2)+31*a(n+1)-15*a(n),a(0)=1,a(1)=17,a(2)=258} ogf A014899 33.1637 -1/(16*x-1)/(x-1)^2 ogf A014899 23.3374 -6*(-3+8*x)/(-1+16*x)/(x-1) lgdogf A014899 26.2546 1/(1-18*x+33*x^2-16*x^3) ogf A014899 9.694 x+(-1+36*x+16*x^3-33*x^2)*f(x)+(-594*x^2-18+324*x+288*x^3)*f(x)^2 ogf A014899 10.864 {a(n+3)-18*a(n+2)+33*a(n+1)-16*a(n),a(0)=0,a(1)=1,a(2)=18} ogf A014900 23.9011 -(-19+51*x)/(17*x-1)/(x-1) lgdogf A014900 32.7068 -1/(17*x-1)/(x-1)^2 ogf A014900 5.31136 -875381+(9832682-16632239*x-14881477*x^3+30638335*x^2)*f(x)+(-313505535*x^2+152274117*x^3-8957301+170188719*x)*f(x)^2 ogf A014900 25.8929 1/(1-19*x+35*x^2-17*x^3) ogf A014900 10.3572 {a(n+3)-19*a(n+2)+35*a(n+1)-17*a(n),a(0)=1,a(1)=19,a(2)=326} ogf A014901 29.3759 -1/(18*x-1)/(x-1)^2 ogf A014901 4.65119 -1097388+(12984013-21947760*x-19752984*x^3+40603356*x^2)*f(x)+(-439805125*x^2+213959250*x^3-11886625+237732500*x)*f(x)^2 ogf A014901 19.9337 -2*(-10+27*x)/(18*x-1)/(x-1) lgdogf A014901 23.2559 1/(1-20*x+37*x^2-18*x^3) ogf A014901 9.30237 {a(n+3)-20*a(n+2)+37*a(n+1)-18*a(n),a(0)=1,a(1)=20,a(2)=363} ogf A014903 33.7717 -1/(19*x-1)/(x-1)^2 ogf A014903 5.62862 -453055+(5631974-9514155*x-8608045*x^3+17669145*x^2)*f(x)+(-201977841*x^2+98399461*x^3-5178919+108757299*x)*f(x)^2 ogf A014903 26.7359 1/(1-21*x+39*x^2-19*x^3) ogf A014903 10.6944 {a(n+3)-21*a(n+2)+39*a(n+1)-19*a(n),a(0)=1,a(1)=21,a(2)=402} ogf A014904 34.3802 -1/(20*x-1)/(x-1)^2 ogf A014904 5.44353 -1665200+(21698441-36634400*x-33304000*x^3+68273200*x^2)*f(x)+(-821362881*x^2+400664820*x^3-20033241+440731302*x)*f(x)^2 ogf A014904 23.3294 -2*(-11+30*x)/(20*x-1)/(x-1) lgdogf A014904 27.2177 1/(1-22*x+41*x^2-20*x^3) ogf A014904 10.8871 {a(n+3)-22*a(n+2)+41*a(n+1)-20*a(n),a(0)=1,a(1)=22,a(2)=443} ogf A014905 19.4081 -(-23+63*x)/(21*x-1)/(x-1) lgdogf A014905 26.5585 -1/(21*x-1)/(x-1)^2 ogf A014905 4.17034 -2020221+(27535642-46465083*x-42424641*x^3+86869503*x^2)*f(x)+(-1097163103*x^2+535823841*x^3-25515421+586854683*x)*f(x)^2 ogf A014905 21.0255 1/(1-23*x+43*x^2-21*x^3) ogf A014905 8.41019 {a(n+3)-23*a(n+2)+43*a(n+1)-21*a(n),a(0)=1,a(1)=23,a(2)=486} ogf A014907 27.1422 -1/(22*x-1)/(x-1)^2 ogf A014907 4.64596 -115676+(1646017-2776224*x-2544872*x^3+5205420*x^2)*f(x)+(-68865345*x^2+33667502*x^3-1530341+36728184*x)*f(x)^2 ogf A014907 19.1001 -6*(-4+11*x)/(22*x-1)/(x-1) lgdogf A014907 21.4876 1/(1-24*x+45*x^2-22*x^3) ogf A014907 8.59503 {a(n+3)-24*a(n+2)+45*a(n+1)-22*a(n),a(0)=1,a(1)=24,a(2)=531} ogf A014908 13.9655 -(1+x^31-x^33-x^29-x^2)/(-1+x+x^2-x^3+x^31-x^32) ogf A014909 20.048 -(-25+69*x)/(23*x-1)/(x-1) lgdogf A014909 27.434 -1/(23*x-1)/(x-1)^2 ogf A014909 4.23778 -2897333+(42964898-72433325*x-66638659*x^3+136174651*x^2)*f(x)+(-1883175555*x^2+921553995*x^3-40067565+1001689125*x)*f(x)^2 ogf A014909 21.7186 1/(1-25*x+47*x^2-23*x^3) ogf A014909 8.68745 {a(n+3)-25*a(n+2)+47*a(n+1)-23*a(n),a(0)=1,a(1)=25,a(2)=578} ogf A014910 8.94452 -(-306*x^17+289*x^16-544*x^34+578*x^33+53*x^36-17)/(x-1)/(53*x^36+34*x^34-17*x^17-17) lgdogf A014910 18.5435 -(-x^34-x^36+1)/(x^18-1+x-x^17-x^37+x^36) ogf A014910 22.3613 -(x^34+x^36-1)/(x-1)/(x^36-x^17-1) ogf A014910 18.5435 -(x^34-x^36-1)/(-x^18+1-x+x^17-x^37+x^36) ogf A014913 27.58 -1/(24*x-1)/(x-1)^2 ogf A014913 18.0696 -2*(-13+36*x)/(24*x-1)/(-1+x) lgdogf A014913 4.22596 -3430080+(52921777-89182080*x-82321920*x^3+168073920*x^2)*f(x)+(-2425093153*x^2+1187800728*x^3-49491697+1286784122*x)*f(x)^2 ogf A014913 21.8341 1/(1-26*x+49*x^2-24*x^3) ogf A014913 8.73366 {a(n+3)-26*a(n+2)+49*a(n+1)-24*a(n),a(0)=1,a(1)=26,a(2)=627} ogf A014914 28.1637 -1/(25*x-1)/(x-1)^2 ogf A014914 4.77777 -149375+(2394238-4033125*x-3734375*x^3+7618125*x^2)*f(x)+(-114488013*x^2+56121575*x^3-2244863+60611301*x)*f(x)^2 ogf A014914 19.8189 -3*(-9+25*x)/(25*x-1)/(x-1) lgdogf A014914 22.2962 1/(1-27*x+51*x^2-25*x^3) ogf A014914 8.9185 {a(n+3)-27*a(n+2)+51*a(n+1)-25*a(n),a(0)=1,a(1)=27,a(2)=678} ogf A014915 26.9443 -(-7+9*x)/(3*x-1)/(x-1) lgdogf A014915 34.4289 -1/(x-1)/(3*x-1)^2 ogf A014915 8.26293 -61+(242-427*x-549*x^3+915*x^2)*f(x)+(-2715*x^2+1629*x^3-181+1267*x)*f(x)^2 ogf A014915 28.1691 1/(1-7*x+15*x^2-9*x^3) ogf A014915 11.0664 {a(n+3)-7*a(n+2)+15*a(n+1)-9*a(n),a(0)=1,a(1)=7,a(2)=34} ogf A014916 33.3145 -1/(x-1)/(4*x-1)^2 ogf A014916 8.10354 -20+(121-180*x-320*x^3+480*x^2)*f(x)+(-2424*x^2+1616*x^3-101+909*x)*f(x)^2 ogf A014916 23.0639 -3*(-3+4*x)/(-1+4*x)/(x-1) lgdogf A014916 26.0723 1/(1-9*x+24*x^2-16*x^3) ogf A014916 10.5204 {a(n+3)-9*a(n+2)+24*a(n+1)-16*a(n),a(0)=1,a(1)=9,a(2)=57} ogf A014917 21.8089 -(-11+15*x)/(5*x-1)/(x-1) lgdogf A014917 28.6959 -1/(x-1)/(-1+5*x)^2 ogf A014917 6.19571 -625+(5506-6875*x-15625*x^3+21875*x^2)*f(x)+(-170835*x^2+122025*x^3-4881+53691*x)*f(x)^2 ogf A014917 22.7176 1/(1-11*x+35*x^2-25*x^3) ogf A014917 9.24107 {a(n+3)-11*a(n+2)+35*a(n+1)-25*a(n),a(0)=1,a(1)=11,a(2)=86} ogf A014918 22.6984 -(-13+18*x)/(6*x-1)/(-1+x) lgdogf A014918 32.7866 -1/(x-1)/(6*x-1)^2 ogf A014918 7.19706 -83+(1016-1079*x-2988*x^3+3984*x^2)*f(x)+(-44784*x^2+33588*x^3-933+12129*x)*f(x)^2 ogf A014918 24.59 1/(1-13*x+48*x^2-36*x^3) ogf A014918 9.83598 {a(n+3)-13*a(n+2)+48*a(n+1)-36*a(n),a(0)=1,a(1)=13,a(2)=121} ogf A014920 29.5994 -1/(x-1)/(-1+7*x)^2 ogf A014920 22.4955 -3*(-5+7*x)/(7*x-1)/(x-1) lgdogf A014920 6.31897 -497+(8122-7455*x-24353*x^3+31311*x^2)*f(x)+(-7625+114375*x-480375*x^2+373625*x^3)*f(x)^2 ogf A014920 23.4328 1/(1-15*x+63*x^2-49*x^3) ogf A014920 9.37313 {a(n+3)-15*a(n+2)+63*a(n+1)-49*a(n),a(0)=1,a(1)=15,a(2)=162} ogf A014921 21.1575 -(-17+24*x)/(8*x-1)/(x-1) lgdogf A014921 27.8388 -1/(x-1)/(-1+8*x)^2 ogf A014921 6.07974 -152+(3209-2584*x-9728*x^3+12160*x^2)*f(x)+(-244560*x^2+195648*x^3-3057+51969*x)*f(x)^2 ogf A014921 22.0391 1/(1-17*x+80*x^2-64*x^3) ogf A014921 8.81563 {a(n+3)-17*a(n+2)+80*a(n+1)-64*a(n),a(0)=1,a(1)=17,a(2)=209} ogf A014922 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A014922 17.6877 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10 ogf A014922 117.918 1-x^10 ogf_with_Euler_Transform A014922 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A014922 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A014923 19.1525 -(-19+27*x)/(9*x-1)/(x-1) lgdogf A014923 25.2007 -1/(x-1)/(-1+9*x)^2 ogf A014923 5.09375 -975+(25886-18525*x-78975*x^3+96525*x^2)*f(x)+(-2466189*x^2+2017791*x^3-24911+473309*x)*f(x)^2 ogf A014923 19.9505 1/(1-19*x+99*x^2-81*x^3) ogf A014923 7.98021 {a(n+3)-19*a(n+2)+99*a(n+1)-81*a(n),a(0)=1,a(1)=19,a(2)=262} ogf A014925 25.0739 -1/(x-1)/(-1+10*x)^2 ogf A014925 5.39224 -325+(10613-6825*x-32500*x^3+39000*x^2)*f(x)+(-1234560*x^2+1028800*x^3-10288+216048*x)*f(x)^2 ogf A014925 19.2876 1/(1-21*x+120*x^2-100*x^3) ogf A014925 8.08836 {a(n+3)-21*a(n+2)+120*a(n+1)-100*a(n),a(0)=1,a(1)=21,a(2)=321} ogf A014926 16.6355 -(-23+33*x)/(11*x-1)/(-1+x) lgdogf A014926 23.64 -1/(x-1)/(11*x-1)^2 ogf A014926 4.36077 -5071+(199942-116633*x-613591*x^3+725153*x^2)*f(x)+(-27866553*x^2+23579391*x^3-194871+4482033*x)*f(x)^2 ogf A014926 17.2754 1/(1-23*x+143*x^2-121*x^3) ogf A014926 7.24451 {a(n+3)-23*a(n+2)+143*a(n+1)-121*a(n),a(0)=1,a(1)=23,a(2)=386} ogf A014927 17.8086 -(-25+36*x)/(12*x-1)/(x-1) lgdogf A014927 24.3696 -1/(x-1)/(12*x-1)^2 ogf A014927 4.72472 -1076+(50431-26900*x-154944*x^3+180768*x^2)*f(x)+(-8291640*x^2+7107120*x^3-49355+1233875*x)*f(x)^2 ogf A014927 17.8086 1/(1-25*x+168*x^2-144*x^3) ogf A014927 7.46811 {a(n+3)-25*a(n+2)+168*a(n+1)-144*a(n),a(0)=1,a(1)=25,a(2)=457} ogf A014928 24.8074 -1/(x-1)/(13*x-1)^2 ogf A014928 5.06818 -299+(16438-8073*x-50531*x^3+58305*x^2)*f(x)+(-3147105*x^2+2727491*x^3-16139+435753*x)*f(x)^2 ogf A014928 17.457 -3*(-9+13*x)/(13*x-1)/(x-1) lgdogf A014928 18.1285 1/(1-27*x+195*x^2-169*x^3) ogf A014928 7.60226 {a(n+3)-27*a(n+2)+195*a(n+1)-169*a(n),a(0)=1,a(1)=27,a(2)=534} ogf A014929 27.2927 -(-29+42*x)/(14*x-1)/(x-1) lgdogf A014929 37.3479 -1/(x-1)/(14*x-1)^2 ogf A014929 6.95696 -2485+(158422-72065*x-487060*x^3+556640*x^2)*f(x)+(-34929888*x^2+30563652*x^3-155937+4522173*x)*f(x)^2 ogf A014929 27.2927 1/(1-29*x+224*x^2-196*x^3) ogf A014929 11.4453 {a(n+3)-29*a(n+2)+224*a(n+1)-196*a(n),a(0)=1,a(1)=29,a(2)=617} ogf A014930 18.9816 -(-31+45*x)/(15*x-1)/(x-1) lgdogf A014930 25.9748 -1/(x-1)/(15*x-1)^2 ogf A014930 5.03593 -575+(42086-17825*x-129375*x^3+146625*x^2)*f(x)+(-10585305*x^2+9339975*x^3-41511+1286841*x)*f(x)^2 ogf A014930 18.9816 1/(1-31*x+255*x^2-225*x^3) ogf A014930 7.96002 {a(n+3)-31*a(n+2)+255*a(n+1)-225*a(n),a(0)=1,a(1)=31,a(2)=706} ogf A014931 26.5585 -1/(x-1)/(16*x-1)^2 ogf A014931 4.94717 -2416+(201257-79728*x-618496*x^3+695808*x^2)*f(x)+(-57266208*x^2+50903296*x^3-198841+6561753*x)*f(x)^2 ogf A014931 18.0218 -3*(-11+16*x)/(16*x-1)/(x-1) lgdogf A014931 19.4081 1/(1-33*x+288*x^2-256*x^3) ogf A014931 8.13889 {a(n+3)-33*a(n+2)+288*a(n+1)-256*a(n),a(0)=1,a(1)=33,a(2)=801} ogf A014932 24.2404 -(-x^13+1-x^58)/(x^58-1+x-x^59) ogf A014932 25.0484 -(x^13-1-x^58)/(x^58+1-x-x^59) ogf A014934 19.6214 -(-35+51*x)/(17*x-1)/(x-1) lgdogf A014934 26.8503 -1/(x-1)/(17*x-1)^2 ogf A014934 4.59601 -17221+(1620106-602735*x-4976869*x^3+5562383*x^2)*f(x)+(-517731855*x^2+463233765*x^3-1602885+56100975*x)*f(x)^2 ogf A014934 19.6214 1/(1-35*x+323*x^2-289*x^3) ogf A014934 8.22833 {a(n+3)-35*a(n+2)+323*a(n+1)-289*a(n),a(0)=1,a(1)=35,a(2)=902} ogf A014935 19.4081 -(-37+54*x)/(18*x-1)/(-1+x) lgdogf A014935 27.58 -1/(x-1)/(18*x-1)^2 ogf A014935 5.13745 -1689+(178223-62493*x-547236*x^3+608040*x^2)*f(x)+(-63552240*x^2+57197016*x^3-176534+6531758*x)*f(x)^2 ogf A014935 20.1546 1/(1-37*x+360*x^2-324*x^3) ogf A014935 8.31777 {a(n+3)-37*a(n+2)+360*a(n+1)-324*a(n),a(0)=1,a(1)=37,a(2)=1009} ogf A014936 27.8718 -1/(x-1)/(19*x-1)^2 ogf A014936 18.913 -3*(-13+19*x)/(19*x-1)/(x-1) lgdogf A014936 4.90338 -7885+(927506-307515*x-2846485*x^3+3146115*x^2)*f(x)+(-366928779*x^2+331983181*x^3-919621+35865219*x)*f(x)^2 ogf A014936 20.3679 1/(1-39*x+399*x^2-361*x^3) ogf A014936 8.40579 {a(n+3)-39*a(n+2)+399*a(n+1)-361*a(n),a(0)=1,a(1)=39,a(2)=1122} ogf A014937 20.6878 -(-41+60*x)/(20*x-1)/(x-1) lgdogf A014937 28.3096 -1/(x-1)/(20*x-1)^2 ogf A014937 4.84579 -13700+(1786553-561700*x-5480000*x^3+6028000*x^2)*f(x)+(-780055320*x^2+709141200*x^3-1772853+72686973*x)*f(x)^2 ogf A014937 20.6878 1/(1-41*x+440*x^2-400*x^3) ogf A014937 8.53782 {a(n+3)-41*a(n+2)+440*a(n+1)-400*a(n),a(0)=1,a(1)=41,a(2)=1241} ogf A014938 20.2296 -(-43+63*x)/(21*x-1)/(-1+x) lgdogf A014938 28.7474 -1/(x-1)/(21*x-1)^2 ogf A014938 4.92072 -10507+(1511414-451801*x-4633587*x^3+5074881*x^2)*f(x)+(-724938081*x^2+661899987*x^3-1500907+64539001*x)*f(x)^2 ogf A014938 21.0077 1/(1-43*x+483*x^2-441*x^3) ogf A014938 8.66984 {a(n+3)-43*a(n+2)+483*a(n+1)-441*a(n),a(0)=1,a(1)=43,a(2)=1366} ogf A014939 20.8736 -(-1-x+x^3+x^4+x^5-x^7-x^8)/(1+x^31) ogf A014939 20.8736 -(1+x+x^3+x^4+x^5+x^7+x^8)/(-1+x^31) ogf A014940 28.8933 -1/(x-1)/(22*x-1)^2 ogf A014940 5.71847 -143+(22588-6435*x-69212*x^3+75504*x^2)*f(x)+(-11850960*x^2+10863380*x^3-22445+1010025*x)*f(x)^2 ogf A014940 19.6062 -3*(-15+22*x)/(22*x-1)/(x-1) lgdogf A014940 21.1143 1/(1-45*x+528*x^2-484*x^3) ogf A014940 8.71385 {a(n+3)-45*a(n+2)+528*a(n+1)-484*a(n),a(0)=1,a(1)=45,a(2)=1497} ogf A014941 21.4343 -(-47+69*x)/(23*x-1)/(x-1) lgdogf A014941 29.3311 -1/(x-1)/(23*x-1)^2 ogf A014941 4.76317 -40963+(7075726-1925261*x-21669427*x^3+23553725*x^2)*f(x)+(-4044988725*x^2+3721389627*x^3-7034763+330633861*x)*f(x)^2 ogf A014941 21.4343 1/(1-47*x+575*x^2-529*x^3) ogf A014941 8.84588 {a(n+3)-47*a(n+2)+575*a(n+1)-529*a(n),a(0)=1,a(1)=47,a(2)=1634} ogf A014942 21.6475 -(-49+72*x)/(24*x-1)/(x-1) lgdogf A014942 29.6229 -1/(x-1)/(24*x-1)^2 ogf A014942 5.11669 -7720+(1452733-378280*x-4446720*x^3+4817280*x^2)*f(x)+(-901688112*x^2+832327488*x^3-1445013+70805637*x)*f(x)^2 ogf A014942 21.6475 1/(1-49*x+624*x^2-576*x^3) ogf A014942 8.9339 {a(n+3)-49*a(n+2)+624*a(n+1)-576*a(n),a(0)=1,a(1)=49,a(2)=1777} ogf A014943 25.7977 -1/(x-1)/(25*x-1)^2 ogf A014943 4.22549 -17375+(3549502-886125*x-10859375*x^3+11728125*x^2)*f(x)+(-2384185725*x^2+2207579375*x^3-3532127+180138477*x)*f(x)^2 ogf A014943 17.5056 -3*(-17+25*x)/(25*x-1)/(x-1) lgdogf A014943 18.8522 1/(1-51*x+675*x^2-625*x^3) ogf A014943 7.78027 {a(n+3)-51*a(n+2)+675*a(n+1)-625*a(n),a(0)=1,a(1)=51,a(2)=1926} ogf A014947 22.9335 (x^14+x^60-1)/(x+1)/(x^60+x^7-1) ogf A014947 18.8173 -(x^14+x^60-1)/(-x^8+1+x-x^7-x^61-x^60) ogf A014947 18.8173 -(x^14-x^60-1)/(-x^8+1-x+x^7-x^61+x^60) ogf A014958 23.9568 -(-x^13+1-x^60)/(x^60-1+x-x^61) ogf A014958 24.7554 -(x^13-1-x^60)/(x^60+1-x-x^61) ogf A014961 21.4553 -(-x^28-1+x^40)/(-x^40+1+x^4-x^44) ogf A014961 22.7962 -(x^28-1-x^40)/(x^40+1-x^4-x^44) ogf A014961 6.18202 -4*x^3*(-7-17*x^20+83*x^24-9*x^28+68*x^32-85*x^36+119*x^40)/(-7-7*x^4-17*x^20+17*x^24-24*x^28+10*x^32-17*x^36+34*x^40) lgdogf A014969 25.7883 -(-8+4*x-8*x^2)/(1-x^4) ogf_with_Euler_Transform A014970 23.3047 -(-12+6*x-12*x^2)/(1-x^4) ogf_with_Euler_Transform A014972 26.2661 -(-16+8*x-16*x^2)/(1-x^4) ogf_with_Euler_Transform A014977 22.6984 -(x^6+x^3+1)*(x^7-x^4-x^2-1) ogf_with_Euler_Transform A014979 12.9002 -(-x-15*x^2)/(1-195*x+195*x^2-x^3) ogf A014979 15.1244 -(1+15*x)/(x-1)/(x^2-194*x+1) ogf A014979 7.97466 -6*(35-65*x+5*x^3-487*x^2)/(x-1)/(15*x+1)/(x^2-194*x+1) lgdogf A014979 7.56218 {a(n+3)-195*a(n+2)+195*a(n+1)-a(n),a(0)=0,a(1)=1,a(2)=210} ogf A014983 45.6095 -1/(3*x+1)/(x-1) ogf A014983 29.1901 -2*(-1+3*x)/(3*x+1)/(x-1) lgdogf A014983 42.9266 -x/(-1+2*x+3*x^2) ogf A014983 20.8501 1/6/x*(-1+2*x+(1-4*x+16*x^2)^(1/2)) revogf A014983 34.7501 x+(-1-2*x+3*x^2)*f(x) ogf A014983 48.6501 x/(1+2*x-3*x^2) ogf A014983 19.204 {a(n+2)+2*a(n+1)-3*a(n),a(0)=0,a(1)=1} ogf A014985 26.5835 -(-3+8*x)/(4*x+1)/(x-1) lgdogf A014985 35.9659 -1/(-1+3*x+4*x^2) ogf A014985 38.2138 -1/(4*x+1)/(x-1) ogf A014985 12.478 -8+(25+24*x-32*x^2)*f(x)+(-17-51*x+68*x^2)*f(x)^2 ogf A014985 40.7614 1/(1+3*x-4*x^2) ogf A014985 17.4692 1/8/x*(-1+3*x+(1-6*x+25*x^2)^(1/2)) revogf A014985 15.6775 {a(n+2)+3*a(n+1)-4*a(n),a(0)=1,a(1)=-3} ogf A014986 33.4897 -1/(-1+4*x+5*x^2) ogf A014986 35.5828 -1/(5*x+1)/(x-1) ogf A014986 22.773 -2*(-2+5*x)/(5*x+1)/(x-1) lgdogf A014986 11.6189 -5+(18+20*x-25*x^2)*f(x)+(-13-52*x+65*x^2)*f(x)^2 ogf A014986 37.955 1/(1+4*x-5*x^2) ogf A014986 16.2664 1/10/x*(4*x-1+(36*x^2-8*x+1)^(1/2)) revogf A014986 14.5981 {a(n+2)+4*a(n+1)-5*a(n),a(0)=1,a(1)=-4} ogf A014987 25.7516 -(-5+12*x)/(6*x+1)/(x-1) lgdogf A014987 36.3552 -1/(-1+5*x+6*x^2) ogf A014987 38.6273 -1/(6*x+1)/(x-1) ogf A014987 11.8853 -12+(49+60*x-72*x^2)*f(x)+(-37-185*x+222*x^2)*f(x)^2 ogf A014987 41.2025 1/(1+5*x-6*x^2) ogf A014987 16.7037 1/12/x*(-1+5*x+(1-10*x+49*x^2)^(1/2)) revogf A014987 15.8471 {a(n+2)+5*a(n+1)-6*a(n),a(0)=1,a(1)=-5} ogf A014988 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A014988 17.6877 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10 ogf A014988 117.918 1-x^10 ogf_with_Euler_Transform A014988 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A014988 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A014989 35.0677 -1/(-1+6*x+7*x^2) ogf A014989 37.2594 -1/(7*x+1)/(x-1) ogf A014989 23.846 -2*(-3+7*x)/(7*x+1)/(x-1) lgdogf A014989 11.6892 -7+(32+42*x-49*x^2)*f(x)+(-25-150*x+175*x^2)*f(x)^2 ogf A014989 39.7434 1/(1+6*x-7*x^2) ogf A014989 16.5597 1/14/x*(6*x-1+(64*x^2-12*x+1)^(1/2)) revogf A014989 15.2859 {a(n+2)+6*a(n+1)-7*a(n),a(0)=1,a(1)=-6} ogf A014990 22.3777 -(-7+16*x)/(8*x+1)/(-1+x) lgdogf A014990 32.9084 -1/(-1+7*x+8*x^2) ogf A014990 34.9652 -1/(8*x+1)/(x-1) ogf A014990 10.3601 -16+(81+112*x-128*x^2)*f(x)+(-65-455*x+520*x^2)*f(x)^2 ogf A014990 37.2962 1/(1+7*x-8*x^2) ogf A014990 15.1201 1/16/x*(-1+7*x+(1-14*x+81*x^2)^(1/2)) revogf A014990 14.3447 {a(n+2)+7*a(n+1)-8*a(n),a(0)=1,a(1)=-7} ogf A014991 30.6039 -1/(-1+8*x+9*x^2) ogf A014991 32.5167 -1/(9*x+1)/(x-1) ogf A014991 20.8107 -2*(-4+9*x)/(9*x+1)/(x-1) lgdogf A014991 10.2013 -9+(50+72*x-81*x^2)*f(x)+(-41-328*x+369*x^2)*f(x)^2 ogf A014991 34.6844 1/(1+8*x-9*x^2) ogf A014991 14.0613 1/18/x*(8*x-1+(100*x^2-16*x+1)^(1/2)) revogf A014991 13.3402 {a(n+2)+8*a(n+1)-9*a(n),a(0)=1,a(1)=-8} ogf A014992 20.8107 -(-9+20*x)/(10*x+1)/(x-1) lgdogf A014992 28.9037 -1/(-1+9*x+10*x^2) ogf A014992 30.6039 -1/(10*x+1)/(x-1) ogf A014992 9.12748 -20+(121+180*x-200*x^2)*f(x)+(-101-909*x+1010*x^2)*f(x)^2 ogf A014992 32.5167 1/(1+9*x-10*x^2) ogf A014992 14.0613 1/20/x*(9*x-1+(121*x^2-18*x+1)^(1/2)) revogf A014992 13.0067 {a(n+2)+9*a(n+1)-10*a(n),a(0)=1,a(1)=-9} ogf A014993 26.3936 -1/(-1+10*x+11*x^2) ogf A014993 29.4987 -1/(11*x+1)/(x-1) ogf A014993 9.28663 -11+(72+110*x-121*x^2)*f(x)+(-61-610*x+671*x^2)*f(x)^2 ogf A014993 29.4987 1/(1+10*x-11*x^2) ogf A014993 12.8584 1/22/x*(-1+10*x+(1-20*x+144*x^2)^(1/2)) revogf A014993 11.94 {a(n+2)+10*a(n+1)-11*a(n),a(0)=1,a(1)=-10} ogf A014994 19.6145 -(-11+24*x)/(12*x+1)/(x-1) lgdogf A014994 26.8409 -1/(-1+11*x+12*x^2) ogf A014994 29.9987 -1/(12*x+1)/(x-1) ogf A014994 8.79272 -24+(169+264*x-288*x^2)*f(x)+(-145-1595*x+1740*x^2)*f(x)^2 ogf A014994 29.9987 1/(1+11*x-12*x^2) ogf A014994 13.0764 1/24/x*(-1+11*x+(1-22*x+169*x^2)^(1/2)) revogf A014994 12.1423 {a(n+2)+11*a(n+1)-12*a(n),a(0)=1,a(1)=-11} ogf A014997 11.3469 -(x^14-x^16-x^20+x^22-x^24+x^18+x^26+x^38+1)/(x^40-1-x^2-x^14+x^26) ogf A014999 17.7871 -(-1-x^3+x^9+x^12+x^15-x^21-x^24)/(1+x^33) ogf A014999 17.7871 -(1+x^3+x^9+x^12+x^15+x^21+x^24)/(-1+x^33) ogf A015000 27.4374 -1/(-1+12*x+13*x^2) ogf A015000 30.6653 -1/(13*x+1)/(x-1) ogf A015000 9.30912 -13+(98+156*x-169*x^2)*f(x)+(-85-1020*x+1105*x^2)*f(x)^2 ogf A015000 19.3078 -2*(-6+13*x)/(13*x+1)/(x-1) lgdogf A015000 30.6653 1/(1+12*x-13*x^2) ogf A015000 13.3669 1/26/x*(-1+12*x+(1-24*x+196*x^2)^(1/2)) revogf A015000 12.4122 {a(n+2)+12*a(n+1)-13*a(n),a(0)=1,a(1)=-12} ogf A015003 22.9335 (x^14+x^64-1)/(x+1)/(x^64+x^7-1) ogf A015003 18.8173 -(x^14+x^64-1)/(-x^8+1+x-x^7-x^65-x^64) ogf A015003 18.8173 -(x^14-x^64-1)/(-x^8+1-x+x^7-x^65+x^64) ogf A015012 18.5435 -(-x^34-x^42+1)/(x^18-1+x-x^17-x^43+x^42) ogf A015012 22.3613 -(x^34+x^42-1)/(x-1)/(x^42-x^17-1) ogf A015012 18.5435 -(x^34-x^42-1)/(-x^18+1-x+x^17-x^43+x^42) ogf A015016 9.26534 (19+380*x^19-361*x^18-53*x^34-722*x^37+684*x^38)/(x-1)/(38*x^38+53*x^34-19*x^19-19) lgdogf A015016 18.3101 -(-1+x^34+x^38)/(-x^20+1-x+x^19-x^34+x^35) ogf A015016 19.2256 -(1+x^34-x^38)/(x^20-1+x-x^19-x^34+x^35) ogf A015016 8.26907 -(x^4-x^2+1)*(x^34+x^32+x^30-x^26-x^24+x^20+x^18-x^14-x^12+x^8+x^6-x^2-1)/(x-1)/(x^34-x^19-1) ogf A015029 18.3281 -(1+x^2+x^6+x^8+x^10+x^14+x^16)/(-1+x^34) ogf A015029 18.3281 -(1+x^2-x^6-x^8-x^10+x^14+x^16)/(-1-x^34) ogf A015036 23.1063 -(-x^13+1-x^66)/(x^66-1+x-x^67) ogf A015036 23.8765 -(x^13-1-x^66)/(x^66+1-x-x^67) ogf A015045 21.4553 -(-x^14-1+x^60)/(-x^60+1+x^2-x^62) ogf A015045 22.7962 -(x^14-1-x^60)/(x^60+1-x^2-x^62) ogf A015046 18.5435 -(x^34-x^44-1)/(-x^18+1-x+x^17-x^45+x^44) ogf A015073 6.65215 (-x^28-1+x^48)/(x-1)/(x+1)/(x^2+1)/(x^16-x^8+1)/(x^2+x+1)/(x^2-x+1)/(x^4-x^2+1)/(x^8-x^4+1)/(x^8+1)/(x^4+1)^2 ogf A015073 21.326 -(-x^28-1+x^48)/(-x^48+1+x^4-x^52) ogf A015073 22.6589 -(x^28-1-x^48)/(x^48+1-x^4-x^52) ogf A015076 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015076 17.6877 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10 ogf A015076 117.918 1-x^10 ogf_with_Euler_Transform A015076 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015076 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015088 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015088 117.918 1-x^12 ogf_with_Euler_Transform A015088 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015088 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015101 6.64899 (1+x^12-x^4-x^16+x^10+x^22-x^14-x^26+x^28+x^30-x^34-x^36-x^6-x^42-x^44+x^48+x^50+x^20+x^52)/(-x^40+1-x^2+x^26+x^52) ogf A015111 13.3323 -(-1+x^9-x^28+x^38-x^29)/(1+x^10-x-x^9-x^39+x^19-x^20+x^38) ogf A015111 13.3323 -(1-x^9+x^29-x^38-x^28)/(-x^39-1-x+x^9+x^10+x^19+x^20-x^38) ogf A015114 7.83169 -(1+x^13+x^26-x^35+x^39-x^4-x^18)/(x-1)/(x^4+x^3+x^2+x+1)/(x^33+x^32+x^31-x^20-x^19-x^18+x^3+x^2+x+1) ogf A015115 23.3898 -(-x^7-1+x^72)/(-x^72+1+x-x^73) ogf A015115 25.0029 -(x^7-1-x^72)/(x^72+1-x-x^73) ogf A015119 20.8736 -(1+x+x^3+x^4+x^5+x^7+x^8)/(-1+x^37) ogf A015119 20.8736 -(1+x-x^3-x^4-x^5+x^7+x^8)/(-1-x^37) ogf A015120 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015120 17.6877 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10 ogf A015120 117.918 1-x^10 ogf_with_Euler_Transform A015120 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015120 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015128 49.6769 -(2+x)/(-1+x^2) ogf_with_Euler_Transform A015128 53.2253 -(x+2)/(x^2-1) ogf_with_Euler_Transform A015128 26.6126 {-a(n+2)+a(n),a(0)=2,a(1)=1} ogf_with_Euler_Transform A015130 24.4538 -(-x^19+1-x^40)/(x^40-1+x-x^41) ogf A015130 18.4895 -(x^38-x^40-1)/(-x^20+1-x+x^19-x^41+x^40) ogf A015142 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015142 17.6877 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10 ogf A015142 117.918 1-x^10 ogf_with_Euler_Transform A015142 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015142 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015148 24.8074 -(-x^17+1-x^50)/(x^50-1+x-x^51) ogf A015148 6.99117 -(x^17-1+x^50)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x^20+x^15+x^10+x^5+1)/(x^20-x^15+x^10-x^5+1)/(x-1)^2 ogf A015148 25.6343 -(x^17-1-x^50)/(x^50+1-x-x^51) ogf A015149 18.0065 -(1+x^2+x^6+x^8+x^10+x^14+x^16)/(-1+x^38) ogf A015149 18.0065 -(1+x^2-x^6-x^8-x^10+x^14+x^16)/(-1-x^38) ogf A015153 13.3403 (-x^4+x^16-x^20+1+x^32-x^36+x^40)/(x^16+1-x^8+x^32-x^24) ogf A015156 6.38423 -(-1-x^24+x^18-x^12+x^30+x^6+x^31)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^6+x^3+1)/(x^6-x^3+1)/(x^12-x^6+1)/(x-1)^2 ogf A015157 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A015157 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A015159 6.61082 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A015160 1.79546 1-2*x+1020*x^5+4*x^2+(-2+4*x-1020*x^5-8*x^2)*f(x)+(4*x^2+1-2*x)*f(x)^2 ogf A015161 17.17 1-2*f(x)+f(x)^2 egf A015164 2.23246 -1-102*x^4+(3+204*x^4)*f(x)+(-102*x^4-3)*f(x)^2+f(x)^3 ogf A015165 7.48379 1-3*f(x)+3*f(x)^2-f(x)^3 ogf A015166 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015166 117.918 1-x^12 ogf_with_Euler_Transform A015166 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015166 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015168 24.1727 -(-x^19+1-x^42)/(x^42-1+x-x^43) ogf A015171 12.4257 (-1+2*x-3*x^2+4*x^3-5*x^4+6*x^5)/(1-x+x^2-x^3+x^4-x^5+x^6) lgdogf A015171 55.4377 -1+x+x^6-x^13 ogf_with_Euler_Transform A015171 31.3343 x^6-x^5+x^4-x^3+x^2-x+1 ogf A015171 9.73905 {a(n+2)+a(n+1),a(0)=1,a(1)=-1,a(2)=1,a(3)=-1,a(4)=1,a(5)=-1,a(6)=1,a(7)=0} ogf A015175 14.451 -(-x^33-1+x^42)/(-x^12+1+x-x^11-x^42+x^22+x^23-x^43) ogf A015175 14.7343 -(x^33-1-x^42)/(-x^12+1-x+x^11+x^42+x^22-x^23-x^43) ogf A015179 17.5778 -(-1-x^3-x^9-x^12-x^15-x^21-x^24)/(1-x^39) ogf A015179 17.5778 -(1+x^3-x^9-x^12-x^15+x^21+x^24)/(-1-x^39) ogf A015186 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015186 17.6877 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10 ogf A015186 117.918 1-x^10 ogf_with_Euler_Transform A015186 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015186 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015187 13.5622 -(-1+x^7-x^31+x^38+x^26)/(x^39+1+x-x^7-x^8-x^19-x^20+x^38) ogf A015187 13.3323 -(-1-x^31+x^38+x^7-x^26)/(-x^39+1-x-x^7+x^8+x^19-x^20+x^38) ogf A015205 11.018 (x^4+1-x^18-x^2-x^14+x^16+x^38+x^12)/(x^6+1-x^20-x^26-x^32+x^12+x^40) ogf A015208 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015208 17.6877 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10 ogf A015208 117.918 1-x^10 ogf_with_Euler_Transform A015208 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015208 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015213 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A015213 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A015216 24.2404 -(-x^17+1-x^54)/(x^54-1+x-x^55) ogf A015216 7.66787 -(x^17-1+x^54)/(x+1)/(x^2+x+1)/(x^2-x+1)/(x^6+x^3+1)/(x^6-x^3+1)/(x^18+x^9+1)/(x^18-x^9+1)/(x-1)^2 ogf A015216 25.0484 -(x^17-1-x^54)/(x^54+1-x-x^55) ogf A015219 28.0326 (x+1)*(x^2+30*x+1)/(x-1)^4 ogf A015219 16.1966 -(1+31*x+x^3+31*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A015219 15.5074 -(35+155*x+x^3+65*x^2)/(x-1)/(1+x)/(x^2+30*x+1) lgdogf A015219 7.2163 {(-78-67*n-14*n^2)*a(n+1)+(273+140*n+28*n^2)*a(n+2)+(-73*n-93-14*n^2)*a(n+3),a(0)=1,a(1)=35,a(2)=165} ogf A015220 9.23751 -(4+6*x+4*x^6+24*x^3+10*x^4+6*x^5+10*x^2)/(x^9-1+x-3*x^4+3*x^7+3*x^3-3*x^6-x^10) ogf A015220 6.53983 -(5+15*x+8*x^8+17*x^7+35*x^6+104*x^5+72*x^4+64*x^3+64*x^2)/(x-1)/(x^2+x+1)/(2*x^6+3*x^5+5*x^4+12*x^3+5*x^2+3*x+2) lgdogf A015220 12.3167 2*(2+3*x+12*x^3+5*x^2+5*x^4+3*x^5+2*x^6)/(x^2+x+1)^3/(x-1)^4 ogf A015221 13.6073 (1+4*x+24*x^3+47*x^2+47*x^4+4*x^5+x^6)/(x+1)^3/(x-1)^4 ogf A015221 9.54277 -(1+4*x+x^6+24*x^3+47*x^4+4*x^5+47*x^2)/(3*x^2-1+x-3*x^4-3*x^3+x^6+3*x^5-x^7) ogf A015221 7.13391 -(5+105*x+9*x^6+143*x^2+447*x^3+163*x^4+x^7+151*x^5)/(x-1)/(x+1)/(x^6+4*x^5+47*x^4+24*x^3+47*x^2+4*x+1) lgdogf A015222 10.2312 -(14+16*x+16*x^3+14*x^4+68*x^2)/(3*x^2-1+x-3*x^4-3*x^3+x^6+3*x^5-x^7) ogf A015222 8.71547 -(15+125*x+21*x^5+206*x^3+39*x^4+106*x^2)/(-1+x)/(1+x)/(7*x^4+8*x^3+34*x^2+8*x+7) lgdogf A015222 16.0444 2*(7+8*x+8*x^3+34*x^2+7*x^4)/(x+1)^3/(x-1)^4 ogf A015223 22.5273 (1+71*x+9*x^3+111*x^2)/(x-1)^4 ogf A015223 14.0796 -(1+71*x+9*x^3+111*x^2)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A015223 12.9965 -3*(3*x+5)*(x^2+26*x+5)/(x-1)/(9*x^3+111*x^2+71*x+1) lgdogf A015223 5.49447 {(-27834-24741*n-5412*n^2)*a(n+1)+(59441+32148*n+8320*n^2)*a(n+2)+(-14919*n-18585-2908*n^2)*a(n+3),a(0)=1,a(1)=75,a(2)=405} ogf A015224 7.96641 -(-6*x-26*x^6-22*x^3-68*x^4-2*x^8-34*x^5-12*x^2-22*x^7)/(1-x+x^10-3*x^7-3*x^3+3*x^6+3*x^4-x^9) ogf A015224 5.67305 -(9+31*x+133*x^6+334*x^5+149*x^2+167*x^3+204*x^4+45*x^8+77*x^7+3*x^9)/(x-1)/(x^2+x+1)/(x^7+11*x^6+13*x^5+17*x^4+34*x^3+11*x^2+6*x+3) lgdogf A015224 11.0124 2*(3+6*x+34*x^3+11*x^2+17*x^4+13*x^5+11*x^6+x^7)/(x^2+x+1)^3/(x-1)^4 ogf A015225 12.4805 (1+6*x+48*x^3+85*x^2+103*x^4+10*x^5+3*x^6)/(x+1)^3/(x-1)^4 ogf A015225 8.93668 -(1+6*x+3*x^6+48*x^3+103*x^4+10*x^5+85*x^2)/(3*x^2-1+x-3*x^4-3*x^3+x^6+3*x^5-x^7) ogf A015225 6.58065 -(7+183*x+23*x^6+265*x^2+885*x^3+345*x^4+3*x^7+337*x^5)/(x-1)/(x+1)/(3*x^6+10*x^5+103*x^4+48*x^3+85*x^2+6*x+1) lgdogf A015226 10.1074 -(22+28*x+36*x^3+34*x^4+136*x^2)/(3*x^2-1+x-3*x^4-3*x^3+x^6+3*x^5-x^7) ogf A015226 8.42279 -(25+227*x+51*x^5+89*x^4+426*x^3+206*x^2)/(x-1)/(1+x)/(17*x^4+18*x^3+68*x^2+14*x+11) lgdogf A015226 14.7399 2*(11+14*x+18*x^3+68*x^2+17*x^4)/(x+1)^3/(x-1)^4 ogf A015227 16.6225 -(1+x+x^3+x^4+x^6+x^8+x^9+x^11+x^12)/(-1+x^29) ogf A015227 16.6225 -(1+x-x^3-x^4+x^6-x^8-x^9+x^11+x^12)/(-1-x^29) ogf A015231 6.91127 (-13-338*x^25+182*x^13+169*x^12-351*x^26+47*x^34+507*x^38+468*x^39)/(x+1)/(39*x^39-47*x^34+13*x^26-13*x^13+13) lgdogf A015231 15.2048 -(1+x^34-x^39)/(x^14-1+x-x^13-x^26+x^27-x^34+x^35) ogf A015231 15.2048 -(1-x^34+x^39)/(x^14-1-x+x^13-x^26-x^27+x^34+x^35) ogf A015234 14.7323 -(-15*x+8*x^2+19*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015234 26.5182 -(-15+8*x+19*x^2)/(x-1)^4 ogf A015234 8.39184 -(15*x+162*x^9-19*x^3-8*x^2+128*x^12-218*x^11-48*x^10)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A015234 15.7847 -2*(-26+31*x+19*x^2)/(x-1)/(19*x^2+8*x-15) lgdogf A015234 6.43646 {(-45-15*n)*a(n+4)+(98+23*n)*a(n+3)+(-51+11*n)*a(n+2)+(-38-19*n)*a(n+1),a(0)=0,a(1)=15,a(2)=52,a(3)=99} ogf A015237 27.3061 (1+8*x+3*x^2)/(x-1)^4 ogf A015237 13.986 -(-x-3*x^3-8*x^2)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015237 16.8655 -6*(2+5*x+x^2)/(x-1)/(3*x^2+8*x+1) lgdogf A015237 6.23291 {(n+3)*a(n+4)+(2+7*n)*a(n+3)+(-35-5*n)*a(n+2)+(-6-3*n)*a(n+1),a(0)=0,a(1)=1,a(2)=12,a(3)=45} ogf A015238 27.0889 (-1+8*x+5*x^2)/(x-1)^4 ogf A015238 14.1894 -(-x+8*x^2+5*x^3)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A015238 12.4157 -(x+17*x^3-8*x^4+2*x^5)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A015238 16.1069 -2*(2+17*x+5*x^2)/(x-1)/(5*x^2+8*x-1) lgdogf A015238 5.00802 2699*x-13495*x^3-21592*x^2+(2699-9876*x-15396*x^3+2699*x^4+8834*x^2)*f(x)+(5520*x^2+920-3680*x+920*x^4-3680*x^3)*f(x)^2 ogf A015238 6.40812 {(n+3)*a(n+4)+(-14-9*n)*a(n+3)+(37+3*n)*a(n+2)+(10+5*n)*a(n+1),a(0)=0,a(1)=-1,a(2)=4,a(3)=27} ogf A015238 6.40812 {(n+3)*a(n+4)+(-14-9*n)*a(n+3)+(37+3*n)*a(n+2)+(5*n+10)*a(n+1),a(0)=0,a(1)=-1,a(2)=4,a(3)=27} ogf A015240 27.0889 (-3+8*x+7*x^2)/(x-1)^4 ogf A015240 9.31179 -(-3*x-8*x^6-11*x^3-24*x^4+26*x^5+8*x^2)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015240 14.1894 -(3*x-8*x^2-7*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015240 15.683 -2*(-2+19*x+7*x^2)/(x-1)/(7*x^2+8*x-3) lgdogf A015240 6.20786 {(-9-3*n)*a(n+4)+(26+11*n)*a(n+3)+(-39-n)*a(n+2)+(-14-7*n)*a(n+1),a(0)=0,a(1)=-3,a(2)=-4,a(3)=9} ogf A015240 6.20786 {(-9-3*n)*a(n+4)+(26+11*n)*a(n+3)+(-39-n)*a(n+2)+(-7*n-14)*a(n+1),a(0)=0,a(1)=-3,a(2)=-4,a(3)=9} ogf A015242 26.9286 (-5+8*x+9*x^2)/(x-1)^4 ogf A015242 8.34406 -(5*x-48*x^6-9*x^3+32*x^4+22*x^5-8*x^2+18*x^7)/(-6*x^2-1+4*x-x^4+4*x^3) ogf A015242 14.1054 -(5*x-8*x^2-9*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015242 16.0116 -6*(-2+7*x+3*x^2)/(x-1)/(9*x^2+8*x-5) lgdogf A015242 4.42111 -72505*x+130509*x^3+116008*x^2+(-14501+37484*x+94940*x^3-14501*x^4-54174*x^2)*f(x)+(-24624*x^2-4104+16416*x-4104*x^4+16416*x^3)*f(x)^2 ogf A015242 5.98413 {(-15-5*n)*a(n+4)+(38+13*n)*a(n+3)+(-41+n)*a(n+2)+(-18-9*n)*a(n+1),a(0)=0,a(1)=-5,a(2)=-12,a(3)=-9} ogf A015242 5.98413 {(-15-5*n)*a(n+4)+(38+13*n)*a(n+3)+(-41+n)*a(n+2)+(-9*n-18)*a(n+1),a(0)=0,a(1)=-5,a(2)=-12,a(3)=-9} ogf A015243 26.0644 (-7+8*x+11*x^2)/(x-1)^4 ogf A015243 8.32613 -(-7*x-16*x^6+11*x^3-32*x^8-50*x^5+8*x^2+74*x^7)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015243 13.9414 -(7*x-8*x^2-11*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015243 4.87383 -14497*x+22781*x^3+16568*x^2+(-2071+3076*x+16468*x^3-2071*x^4-6474*x^2)*f(x)+(-4464*x^2-744+2976*x-744*x^4+2976*x^3)*f(x)^2 ogf A015243 14.6215 -2*(-10+23*x+11*x^2)/(x-1)/(11*x^2+8*x-7) lgdogf A015243 5.82021 {(-21-7*n)*a(n+4)+(50+15*n)*a(n+3)+(-43+3*n)*a(n+2)+(-11*n-22)*a(n+1),a(0)=0,a(1)=-7,a(2)=-20,a(3)=-27} ogf A015243 5.82021 {(-21-7*n)*a(n+4)+(50+15*n)*a(n+3)+(-43+3*n)*a(n+2)+(-22-11*n)*a(n+1),a(0)=0,a(1)=-7,a(2)=-20,a(3)=-27} ogf A015245 25.7578 (-9+8*x+13*x^2)/(x-1)^4 ogf A015245 8.22817 -(9*x+72*x^6-13*x^3+50*x^9-104*x^8-8*x^2+6*x^7)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A015245 13.7774 -(9*x-8*x^2-13*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015245 14.4495 -2*(-14+25*x+13*x^2)/(x-1)/(13*x^2+8*x-9) lgdogf A015245 5.75173 {(-27-9*n)*a(n+4)+(62+17*n)*a(n+3)+(-45+5*n)*a(n+2)+(-13*n-26)*a(n+1),a(0)=0,a(1)=-9,a(2)=-28,a(3)=-45} ogf A015245 5.75173 {(-27-9*n)*a(n+4)+(62+17*n)*a(n+3)+(-45+5*n)*a(n+2)+(-26-13*n)*a(n+1),a(0)=0,a(1)=-9,a(2)=-28,a(3)=-45} ogf A015246 24.8315 (-11+8*x+15*x^2)/(x-1)^4 ogf A015246 8.05344 -(-11*x+15*x^3+138*x^9+8*x^8+8*x^2-98*x^7-72*x^10)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015246 13.5444 -(11*x-8*x^2-15*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015246 15.2809 -6*(-6+9*x+5*x^2)/(x-1)/(15*x^2+8*x-11) lgdogf A015246 5.78597 {(33+11*n)*a(n+4)+(-74-19*n)*a(n+3)+(47-7*n)*a(n+2)+(30+15*n)*a(n+1),a(0)=0,a(1)=-11,a(2)=-36,a(3)=-63} ogf A015247 25.1253 (-13+8*x+17*x^2)/(x-1)^4 ogf A015247 7.83127 -(13*x-17*x^3-26*x^9+128*x^8-8*x^2+98*x^11-176*x^10)/(-1+4*x-6*x^2+4*x^3-x^4) ogf A015247 13.7047 -(13*x-8*x^2-17*x^3)/(1-4*x+6*x^2-4*x^3+x^4) ogf A015247 14.3573 -2*(-22+29*x+17*x^2)/(x-1)/(17*x^2+8*x-13) lgdogf A015247 5.85444 {(39+13*n)*a(n+4)+(-86-21*n)*a(n+3)+(49-9*n)*a(n+2)+(34+17*n)*a(n+1),a(0)=0,a(1)=-13,a(2)=-44,a(3)=-81} ogf A015249 7.6924 -104+(-197-312*x+832*x^3-624*x^2)*f(x)+(301-903*x-1806*x^2+2408*x^3)*f(x)^2 ogf A015249 14.4233 -3*(-1-4*x+8*x^2)/(x-1)/(1+2*x)/(-1+4*x) lgdogf A015249 27.4729 1/(1-3*x-6*x^2+8*x^3) ogf A015249 25.0839 1/(x-1)/(2*x+1)/(4*x-1) ogf A015249 10.4896 {a(n+3)-3*a(n+2)-6*a(n+1)+8*a(n),a(0)=1,a(1)=3,a(2)=15} ogf A015250 23.9568 -(-x^17+1-x^56)/(x^56-1+x-x^57) ogf A015250 24.7554 -(x^17-1-x^56)/(x^56+1-x-x^57) ogf A015251 12.6732 -(-7-42*x+81*x^2)/(x-1)/(3*x+1)/(9*x-1) lgdogf A015251 5.61651 -729+(-6382-5103*x+19683*x^3-15309*x^2)*f(x)+(7111-49777*x-149331*x^2+191997*x^3)*f(x)^2 ogf A015251 21.4893 1/(1-7*x-21*x^2+27*x^3) ogf A015251 20.5939 1/(x-1)/(3*x+1)/(-1+9*x) ogf A015251 8.67111 {a(n+3)-7*a(n+2)-21*a(n+1)+27*a(n),a(0)=1,a(1)=7,a(2)=70} ogf A015252 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015252 17.6877 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10 ogf A015252 117.918 1-x^10 ogf_with_Euler_Transform A015252 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015252 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015253 12.3212 -(-13-104*x+192*x^2)/(x-1)/(4*x+1)/(16*x-1) lgdogf A015253 20.3773 -1/(-1+13*x+52*x^2-64*x^3) ogf A015253 5.46196 -3008+(-65809-39104*x+192512*x^3-156416*x^2)*f(x)+(68817-894621*x-3578484*x^2+4404288*x^3)*f(x)^2 ogf A015253 22.0754 1/(x-1)/(4*x+1)/(16*x-1) ogf A015253 8.83017 {a(n+3)-13*a(n+2)-52*a(n+1)+64*a(n),a(0)=1,a(1)=13,a(2)=221} ogf A015254 12.0115 (-1+8*x^7+5*x^4-4*x^3-7*x^6+3*x^2)/(x^3+1-x+x^5-x^4+x^8-x^7) lgdogf A015254 48.046 -1+x^2+x^4-x^14 ogf_with_Euler_Transform A015254 31.3343 x^8-x^7+x^5-x^4+x^3-x+1 ogf A015254 6.92971 {-a(n+3)-a(n+2)-a(n+1),a(0)=1,a(1)=-1,a(2)=0,a(3)=1,a(4)=-1,a(5)=1,a(6)=0,a(7)=-1,a(8)=1,a(9)=0,a(10)=0} ogf A015255 18.814 -1/(-1+21*x+105*x^2-125*x^3) ogf A015255 11.9725 -3*(-7-70*x+125*x^2)/(-1+x)/(5*x+1)/(25*x-1) lgdogf A015255 5.06531 -9125+(-394526-191625*x+1140625*x^3-958125*x^2)*f(x)+(403651-8476671*x-42383355*x^2+50456375*x^3)*f(x)^2 ogf A015255 21.9497 1/(x-1)/(5*x+1)/(25*x-1) ogf A015255 8.49665 {a(n+3)-21*a(n+2)-105*a(n+1)+125*a(n),a(0)=1,a(1)=21,a(2)=546} ogf A015257 20.7944 -1/(-1+31*x+186*x^2-216*x^3) ogf A015257 5.65285 -3240+(-242419-100440*x+699840*x^3-602640*x^2)*f(x)+(245659-7615429*x-45692574*x^2+53062344*x^3)*f(x)^2 ogf A015257 24.2602 1/(x-1)/(36*x-1)/(6*x+1) ogf A015257 9.24197 {a(n+3)-31*a(n+2)-186*a(n+1)+216*a(n),a(0)=1,a(1)=31,a(2)=1147} ogf A015258 14.241 -(-43-602*x+1029*x^2)/(x-1)/(7*x+1)/(49*x-1) lgdogf A015258 22.3788 -1/(-1+43*x+301*x^2-343*x^3) ogf A015258 5.3556 -49049+(-5818702-2109107*x+16823807*x^3-14763749*x^2)*f(x)+(5867751-252313293*x-1766193051*x^2+2012638593*x^3)*f(x)^2 ogf A015258 26.1086 1/(x-1)/(7*x+1)/(49*x-1) ogf A015258 9.94612 {a(n+3)-43*a(n+2)-301*a(n+1)+343*a(n),a(0)=1,a(1)=43,a(2)=2150} ogf A015259 17.3424 -1/(-1+57*x+456*x^2-512*x^3) ogf A015259 10.7908 -3*(-19-304*x+512*x^2)/(x-1)/(8*x+1)/(64*x-1) lgdogf A015259 4.08056 -95744+(-16914497-5457408*x+49020928*x^3-43659264*x^2)*f(x)+(17010241-969583737*x-7756669896*x^2+8709243392*x^3)*f(x)^2 ogf A015259 20.2328 1/(x-1)/(8*x+1)/(64*x-1) ogf A015259 7.70773 {a(n+3)-57*a(n+2)-456*a(n+1)+512*a(n),a(0)=1,a(1)=57,a(2)=3705} ogf A015260 13.2995 -(-73-1314*x+2187*x^2)/(x-1)/(81*x-1)/(9*x+1) lgdogf A015260 21.3743 -1/(-1+73*x+657*x^2-729*x^3) ogf A015260 4.74983 -172773+(-43352254-12612429*x+125951517*x^3-113511861*x^2)*f(x)+(43525027-3177326971*x-28595942739*x^2+31729744683*x^3)*f(x)^2 ogf A015260 24.9366 1/(x-1)/(81*x-1)/(9*x+1) ogf A015260 9.49967 {a(n+3)-73*a(n+2)-657*a(n+1)+729*a(n),a(0)=1,a(1)=73,a(2)=5986} ogf A015261 9.22291 -(-91-1820*x+3000*x^2)/(x-1)/(10*x+1)/(100*x-1) lgdogf A015261 14.9475 -1/(-1+91*x+910*x^2-1000*x^3) ogf A015261 3.36028 -293000+(-100616101-26663000*x+293000000*x^3-266630000*x^2)*f(x)+(100909101-9182728191*x-91827281910*x^2+100909101000*x^3)*f(x)^2 ogf A015261 16.6722 1/(x-1)/(10*x+1)/(100*x-1) ogf A015261 6.77307 {a(n+3)-91*a(n+2)-910*a(n+1)+1000*a(n),a(0)=1,a(1)=91,a(2)=9191} ogf A015262 17.8775 -1/(-1+111*x+1221*x^2-1331*x^3) ogf A015262 11.3103 -3*(-37-814*x+1331*x^2)/(-1+x)/(11*x+1)/(121*x-1) lgdogf A015262 21.3155 1/(x-1)/(11*x+1)/(121*x-1) ogf A015262 8.15004 {a(n+3)-111*a(n+2)-1221*a(n+1)+1331*a(n),a(0)=1,a(1)=111,a(2)=13542} ogf A015264 9.78869 -(-133-3192*x+5184*x^2)/(-1+x)/(12*x+1)/(144*x-1) lgdogf A015264 15.4724 -1/(-1+133*x+1596*x^2-1728*x^3) ogf A015264 18.4479 1/(x-1)/(12*x+1)/(144*x-1) ogf A015264 7.05361 {a(n+3)-133*a(n+2)-1596*a(n+1)+1728*a(n),a(0)=1,a(1)=133,a(2)=19285} ogf A015265 12.2606 -(-157-4082*x+6591*x^2)/(x-1)/(13*x+1)/(169*x-1) lgdogf A015265 18.9842 -1/(-1+157*x+2041*x^2-2197*x^3) ogf A015265 4.49245 -155987+(-117017266-24489959*x+342703439*x^3-318369467*x^2)*f(x)+(117173253-18396200721*x-239150609373*x^2+257429636841*x^3)*f(x)^2 ogf A015265 22.635 1/(x-1)/(13*x+1)/(169*x-1) ogf A015265 8.65456 {a(n+3)-157*a(n+2)-2041*a(n+1)+2197*a(n),a(0)=1,a(1)=157,a(2)=26690} ogf A015266 9.8148 -(5-60*x-120*x^2+256*x^3)/(-1+x)/(2*x+1)/(8*x+1)/(-1+4*x) lgdogf A015266 17.4826 -1/(-1+5*x+30*x^2-40*x^3-64*x^4) ogf A015266 5.04003 -512+(-9501+2560*x-20480*x^3+32768*x^4-15360*x^2)*f(x)+(-300390*x^2-400520*x^3+10013+50065*x+640832*x^4)*f(x)^2 ogf A015266 18.6481 1/(1+5*x-30*x^2-40*x^3+64*x^4) ogf A015266 18.0466 1/(x-1)/(2*x+1)/(8*x+1)/(4*x-1) ogf A015268 15.5573 -1/(-1+20*x+210*x^2-540*x^3-729*x^4) ogf A015268 9.4926 -4*(5-105*x-405*x^2+729*x^3)/(x-1)/(27*x+1)/(3*x+1)/(9*x-1) lgdogf A015268 16.4724 1/(1+20*x-210*x^2-540*x^3+729*x^4) ogf A015268 16.9716 1/(x-1)/(27*x+1)/(3*x+1)/(-1+9*x) ogf A015270 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015270 117.918 1-x^12 ogf_with_Euler_Transform A015270 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015270 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015271 7.71418 -(51-1768*x-9792*x^2+16384*x^3)/(-1+x)/(64*x+1)/(1+4*x)/(-1+16*x) lgdogf A015271 13.1953 -1/(-1-51*x+884*x^2+3264*x^3-4096*x^4) ogf A015271 13.9284 1/(1-51*x-884*x^2+3264*x^3+4096*x^4) ogf A015271 15.1946 1/(x-1)/(64*x+1)/(4*x+1)/(16*x-1) ogf A015272 9.58465 -1/(-1-104*x+2730*x^2+13000*x^3-15625*x^4) ogf A015272 6.00829 -4*(26-1365*x+15625*x^3-9750*x^2)/(-1+x)/(5*x+1)/(25*x-1)/(125*x+1) lgdogf A015272 10.0639 1/(1-104*x-2730*x^2+13000*x^3+15625*x^4) ogf A015272 11.8399 1/(x-1)/(5*x+1)/(25*x-1)/(125*x+1) ogf A015273 6.33832 -(185-13764*x+186624*x^3-119880*x^2)/(x-1)/(216*x+1)/(36*x-1)/(6*x+1) lgdogf A015273 10.413 -1/(-1-185*x+6882*x^2+39960*x^3-46656*x^4) ogf A015273 10.9336 1/(1-185*x-6882*x^2+39960*x^3+46656*x^4) ogf A015273 12.8631 1/(x-1)/(216*x+1)/(36*x-1)/(6*x+1) ogf A015275 10.5471 -1/(-1-300*x+15050*x^2+102900*x^3-117649*x^4) ogf A015275 6.97967 -4*(75-7525*x-77175*x^2+117649*x^3)/(x-1)/(7*x+1)/(343*x+1)/(49*x-1) lgdogf A015275 11.0376 1/(1-300*x-15050*x^2+102900*x^3+117649*x^4) ogf A015275 13.9593 1/(x-1)/(7*x+1)/(343*x+1)/(49*x-1) ogf A015276 7.17074 -(455-59280*x-698880*x^2+1048576*x^3)/(x-1)/(512*x+1)/(8*x+1)/(64*x-1) lgdogf A015276 11.1545 -1/(-1-455*x+29640*x^2+232960*x^3-262144*x^4) ogf A015276 11.6733 1/(1-455*x-29640*x^2+232960*x^3+262144*x^4) ogf A015276 14.7633 1/(x-1)/(512*x+1)/(8*x+1)/(64*x-1) ogf A015277 9.43174 -1/(-1-656*x+53874*x^2+478224*x^3-531441*x^4) ogf A015277 9.87043 1/(1-656*x-53874*x^2+478224*x^3+531441*x^4) ogf A015277 12.4832 1/(x-1)/(81*x-1)/(9*x+1)/(729*x+1) ogf A015278 5.78693 -(909-183820*x+4000000*x^3-2727000*x^2)/(x-1)/(10*x+1)/(1000*x+1)/(100*x-1) lgdogf A015278 9.43522 -1/(-1-909*x+91910*x^2+909000*x^3-1000000*x^4) ogf A015278 9.86409 1/(1-909*x-91910*x^2+909000*x^3+1000000*x^4) ogf A015278 11.7303 1/(x-1)/(10*x+1)/(1000*x+1)/(100*x-1) ogf A015279 9.44479 -1/(-1-1220*x+148962*x^2+1623820*x^3-1771561*x^4) ogf A015279 6.0894 -4*(305-74481*x-1217865*x^2+1771561*x^3)/(x-1)/(11*x+1)/(121*x-1)/(1331*x+1) lgdogf A015279 9.8467 1/(1-1220*x-148962*x^2+1623820*x^3+1771561*x^4) ogf A015279 12.508 1/(x-1)/(11*x+1)/(121*x-1)/(1331*x+1) ogf A015281 7.75362 -1/(-1-1595*x+231420*x^2+2756160*x^3-2985984*x^4) ogf A015281 8.08356 1/(1-1595*x-231420*x^2+2756160*x^3+2985984*x^4) ogf A015281 10.2683 1/(x-1)/(12*x+1)/(1728*x+1)/(144*x-1) ogf A015282 24.8074 -(-x^19+1-x^48)/(x^48-1+x-x^49) ogf A015282 7.05531 -(x^19-1+x^48)/(x+1)/(x^2+1)/(x^16-x^8+1)/(x^8-x^4+1)/(x^2+x+1)/(x^2-x+1)/(x^4-x^2+1)/(x^8+1)/(x^4+1)/(x-1)^2 ogf A015282 25.6343 -(x^19-1-x^48)/(x^48+1-x-x^49) ogf A015284 9.23961 5*x^4*(-1+3*x^10-4*x^15+5*x^20-7*x^30+8*x^35)/(1-x^5+x^15-x^20+x^25-x^35+x^40) lgdogf A015286 7.98858 -1/(-1-2040*x+346970*x^2+4481880*x^3-4826809*x^4) ogf A015286 8.32852 1/(1-2040*x-346970*x^2+4481880*x^3+4826809*x^4) ogf A015286 10.5795 1/(x-1)/(2197*x+1)/(13*x+1)/(169*x-1) ogf A015287 6.79244 -(11+220*x-1320*x^2-2816*x^3+5120*x^4)/(x-1)/(-1+4*x)/(8*x+1)/(2*x+1)/(16*x-1) lgdogf A015287 12.9222 -1/(x-1)/(4*x-1)/(8*x+1)/(2*x+1)/(16*x-1) ogf A015287 12.3212 1/(1-11*x-110*x^2+440*x^3+704*x^4-1024*x^5) ogf A015288 5.09936 -(61+3660*x+295245*x^4-177876*x^3-49410*x^2)/(x-1)/(27*x+1)/(81*x-1)/(9*x-1)/(3*x+1) lgdogf A015288 9.96155 -1/(x-1)/(27*x+1)/(81*x-1)/(-1+9*x)/(3*x+1) ogf A015288 8.74177 1/(1-61*x-1830*x^2+16470*x^3+44469*x^4-59049*x^5) ogf A015289 9.93964 -1/(x-1)/(256*x-1)/(64*x+1)/(4*x+1)/(16*x-1) ogf A015289 7.95171 1/(1-205*x-13940*x^2+223040*x^3+839680*x^4-1048576*x^5) ogf A015290 8.53635 -(x^40-x^21+1)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x^2+x+1)/(x^8+1)/(x^16+1-x^8+x^32-x^24) ogf A015291 9.00545 -1/(x-1)/(5*x+1)/(25*x-1)/(625*x-1)/(125*x+1) ogf A015291 7.10956 1/(1-521*x-67730*x^2+1693250*x^3+8140625*x^4-9765625*x^5) ogf A015292 9.74798 -1/(x-1)/(216*x+1)/(36*x-1)/(1296*x-1)/(6*x+1) ogf A015292 7.35094 1/(1-1111*x-246642*x^2+8879112*x^3+51834816*x^4-60466176*x^5) ogf A015297 9.6092 4*x^3*(-1+2*x^4-3*x^8+4*x^12-5*x^16+6*x^20)/(1-x^4+x^8-x^12+x^16-x^20+x^24) lgdogf A015301 7.47902 -(1+x^6-x^16+x^22-x^24+x^30-x^32-x^8+x^34+x^38+x^14)/(x^40-1-x^2-x^6+x^34+x^10-x^14+x^18-x^22+x^26-x^30) ogf A015305 11.534 -1/(x-1)/(8*x+1)/(2*x+1)/(32*x+1)/(4*x-1)/(16*x-1) ogf A015305 5.76699 -3*(-7+308*x+65536*x^5-35840*x^4-19712*x^3+3080*x^2)/(x-1)/(8*x+1)/(2*x+1)/(32*x+1)/(4*x-1)/(16*x-1) lgdogf A015305 10.1175 1/(1+21*x-462*x^2-3080*x^3+14784*x^4+21504*x^5-32768*x^6) ogf A015305 10.1175 1/(1-21*x-462*x^2+3080*x^3+14784*x^4-21504*x^5-32768*x^6) ogf A015307 22.7712 (x^22+x^48-1)/(x+1)/(x^48+x^11-1) ogf A015307 18.3281 -(x^22+x^48-1)/(-x^12+1+x-x^11-x^49-x^48) ogf A015307 18.3281 -(x^22-x^48-1)/(-x^12+1-x+x^11-x^49+x^48) ogf A015311 16.6225 -(-1-x+x^3+x^4-x^6+x^8+x^9-x^11-x^12)/(1+x^31) ogf A015311 16.6225 -(-1-x-x^3-x^4-x^6-x^8-x^9-x^11-x^12)/(1-x^31) ogf A015314 9.6092 3*x^2*(-1+3*x^6-4*x^9+5*x^12-7*x^18+8*x^21)/(1-x^3+x^9-x^12+x^15-x^21+x^24) lgdogf A015322 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015322 117.918 1-x^12 ogf_with_Euler_Transform A015322 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015322 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015325 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A015325 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A015329 23.0709 -(-1+x^8+x^12-x^40)/(1-x^4-x^24) ogf A015329 9.58789 -(x-1)*(x+1)*(x^2+1)*(x^36+x^32+x^28+x^24+x^20+x^16+x^12-x^4-1)/(-1+x^4+x^24) ogf A015335 7.01499 (1+x-x^17-x^22-x^3+x^20+x^30+x^5+x^6+x^39+x^31+x^40+x^36+x^35-x^33-x^18-x^23)/(x^21+1+x^30+x^4+x^17+x^8+x^13) ogf A015342 11.1007 -(-x^24+x^19-1-x^7+x^36+x^12+x^38)/(x-1)/(x^36-x^31-x^24+x^19+x^12-x^7-1) ogf A015343 16.7538 -(-1-x^6-x^23-x^29-x^35)/(1+x+x^6+x^7-x^29-x^30) ogf A015343 19.1472 -(1+x^6+x^23+x^29+x^35)/(x+1)/(x^29-x^6-1) ogf A015343 16.7538 -(1-x^6-x^35-x^23+x^29)/(-1-x^7+x+x^6-x^30+x^29) ogf A015348 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015348 117.918 1-x^12 ogf_with_Euler_Transform A015348 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015348 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015351 6.70938 (x^4-x^2+1)*(x^46+x^44-x^40-x^38+x^34+x^32-x^28-x^26+x^22+x^20+x^18-x^14-x^12+x^8+x^6-x^2-1)/(x+1)/(x^50+x^11-1) ogf A015351 18.3281 -(x^22+x^50-1)/(-x^12+1+x-x^11-x^51-x^50) ogf A015351 18.3281 -(x^22-x^50-1)/(-x^12+1-x+x^11-x^51+x^50) ogf A015352 23.1063 -(-x^17+1-x^62)/(x^62-1+x-x^63) ogf A015352 23.8765 -(x^17-1-x^62)/(x^62+1-x-x^63) ogf A015358 24.2404 -(-x^19+1-x^52)/(x^52-1+x-x^53) ogf A015358 25.0484 -(x^19-1-x^52)/(x^52+1-x-x^53) ogf A015366 12.8486 -(-23+529*x^22+59*x^36-506*x^23)/(x-1)/(59*x^36+23*x^23-23) lgdogf A015366 24.4538 -(-x^23+1-x^36)/(x^36-1+x-x^37) ogf A015366 7.21969 -(x^23-1+x^36)/(x+1)/(x^2+1)/(x^2+x+1)/(x^2-x+1)/(x^4-x^2+1)/(x^6+x^3+1)/(x^6-x^3+1)/(x^12-x^6+1)/(x-1)^2 ogf A015366 25.2689 -(x^23-1-x^36)/(x^36+1-x-x^37) ogf A015372 11.1348 -(1+x^18+x^36-x^40+x^11)/(-1+x^12+x-x^11+x^19-x^29-x^18-x^36+x^37+x^30) ogf A015373 22.1015 -(-x^22-1+x^40)/(-x^40+1+x^2-x^42) ogf A015373 23.4828 -(x^22-1-x^40)/(x^40+1-x^2-x^42) ogf A015387 14.62 -(-x^39-1+x^40)/(-x^14+1+x-x^13-x^40+x^26+x^27-x^41) ogf A015387 14.9067 -(x^39-1-x^40)/(-x^14+1-x+x^13+x^40+x^26-x^27-x^41) ogf A015396 23.9568 -(-x^19+1-x^54)/(x^54-1+x-x^55) ogf A015396 7.57818 -(x^19-1+x^54)/(x+1)/(1+x^2+x)/(1-x+x^2)/(x^6+x^3+1)/(x^6-x^3+1)/(x^18+x^9+1)/(x^18-x^9+1)/(x-1)^2 ogf A015396 24.7554 -(x^19-1-x^54)/(x^54+1-x-x^55) ogf A015400 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015400 117.918 1-x^12 ogf_with_Euler_Transform A015400 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015400 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015404 9.6092 3*x^2*(-1+3*x^6-4*x^9+5*x^12-7*x^18+8*x^21)/(1-x^3+x^9-x^12+x^15-x^21+x^24) lgdogf A015406 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015406 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015406 117.918 1-x^10 ogf_with_Euler_Transform A015406 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015406 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015412 12.9602 -(-23+529*x^22+61*x^38-506*x^23)/(x-1)/(61*x^38+23*x^23-23) lgdogf A015412 24.6662 -(-x^23+1-x^38)/(x^38-1+x-x^39) ogf A015412 25.4885 -(x^23-1-x^38)/(x^38+1-x-x^39) ogf A015415 15.7321 -(-x+x^37+1-x^38-x^20)/(x^19-1-x^39+x^2-x^38+x^20) ogf A015415 14.5668 -(1-x+x^37-x^38+x^20)/(-x^2-1+2*x+x^39-x^19+x^20-x^38) ogf A015420 117.918 1-x^16 ogf_with_Euler_Transform A015420 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015426 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015426 117.918 1-x^12 ogf_with_Euler_Transform A015426 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015426 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015435 16.7538 -(-1-x^31+x^39+x^23+x^8)/(1-x-x^8+x^9-x^31+x^32) ogf A015435 16.7538 -(1+x^8+x^23+x^31+x^39)/(-1-x-x^8-x^9+x^31+x^32) ogf A015440 29.9764 -(1+10*x)/(5*x^2-1+x) lgdogf A015440 41.967 -1/(-1+x+5*x^2) ogf A015440 12.3432 -40+(81-40*x-200*x^2)*f(x)+(205*x^2-41+41*x)*f(x)^2 ogf A015440 18.5149 1/10/x*(-1-x+(21*x^2+2*x+1)^(1/2)) revogf A015440 17.0137 {-a(n+2)+a(n+1)+5*a(n),a(0)=1,a(1)=1} ogf A015441 31.6992 -(1+12*x)/(2*x+1)/(3*x-1) lgdogf A015441 44.0266 -1/(2*x+1)/(3*x-1) ogf A015441 52.832 -x/(-1+x+6*x^2) ogf A015441 23.3082 1/12/x*(-1-x+(25*x^2+2*x+1)^(1/2)) revogf A015441 19.812 x+(-1+2*x+6*x^2)*f(x)+(6*x^2-1+x)*f(x)^2 ogf A015441 21.4184 {-a(n+2)+a(n+1)+6*a(n),a(0)=0,a(1)=1} ogf A015442 30.9181 -(1+14*x)/(7*x^2-1+x) lgdogf A015442 43.2854 -1/(-1+x+7*x^2) ogf A015442 43.2854 -x/(-1+x+7*x^2) ogf A015442 19.0965 1/14/x*(-1-x+(29*x^2+2*x+1)^(1/2)) revogf A015442 16.232 x+(-1+2*x+7*x^2)*f(x)+(7*x^2-1+x)*f(x)^2 ogf A015442 17.5481 {-a(n+2)+a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015443 29.1232 -(1+16*x)/(8*x^2-1+x) lgdogf A015443 40.7725 -1/(-1+x+8*x^2) ogf A015443 43.6848 -1/(8*x^2-1+x) ogf A015443 11.7613 -88+(177-88*x-704*x^2)*f(x)+(712*x^2-89+89*x)*f(x)^2 ogf A015443 17.9879 1/16/x*(-1-x+(33*x^2+2*x+1)^(1/2)) revogf A015443 16.5294 {-a(n+2)+a(n+1)+8*a(n),a(0)=1,a(1)=1} ogf A015445 27.8458 -(1+18*x)/(9*x^2-1+x) lgdogf A015445 38.9841 -1/(-1+x+9*x^2) ogf A015445 10.4422 -108+(217-108*x-972*x^2)*f(x)+(981*x^2-109+109*x)*f(x)^2 ogf A015445 17.1989 1/18/x*(-1-x+(37*x^2+2*x+1)^(1/2)) revogf A015445 15.8044 {-a(n+2)+a(n+1)+9*a(n),a(0)=1,a(1)=1} ogf A015446 27.1579 -(1+20*x)/(10*x^2-1+x) lgdogf A015446 37.3421 -1/(-1+x+10*x^2) ogf A015446 10.3013 -130+(261-130*x-1300*x^2)*f(x)+(1310*x^2-131+131*x)*f(x)^2 ogf A015446 17.5727 1/20/x*(-1-x+(41*x^2+2*x+1)^(1/2)) revogf A015446 15.723 {-a(n+2)+a(n+1)+10*a(n),a(0)=1,a(1)=1} ogf A015447 27.8802 -(1+22*x)/(11*x^2-1+x) lgdogf A015447 38.3352 -1/(-1+x+11*x^2) ogf A015447 10.5752 -154+(309-154*x-1694*x^2)*f(x)+(1705*x^2-155+155*x)*f(x)^2 ogf A015447 18.0401 1/22/x*(-1-x+(45*x^2+2*x+1)^(1/2)) revogf A015447 16.1411 {-a(n+2)+a(n+1)+11*a(n),a(0)=1,a(1)=1} ogf A015448 42.499 (3*x-1)/(x^2-1+4*x) ogf A015448 40.374 -(1-3*x)/(x^2-1+4*x) ogf A015448 23.7494 -(3*x+1)*(x-1)/(3*x-1)/(x^2+4*x-1) lgdogf A015448 14.4193 -25+75*x+(51-178*x-25*x^2)*f(x)+(26*x^2-26+104*x)*f(x)^2 ogf A015448 20.187 1/2/(-3+x)*(-1-4*x+(1-4*x+20*x^2)^(1/2)) revogf A015448 21.8238 {-a(n+2)+4*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A015449 29.9343 (4*x-1)/(x^2-1+5*x) ogf A015449 15.7986 -(-1-2*x+4*x^2)/(-1+4*x)/(x^2+5*x-1) lgdogf A015449 28.4376 -(1-4*x)/(x^2-1+5*x) ogf A015449 9.97809 -36+144*x+(73-328*x-36*x^2)*f(x)+(37*x^2-37+185*x)*f(x)^2 ogf A015449 14.5834 1/2/(x-4)*(-1-5*x+(1-6*x+29*x^2)^(1/2)) revogf A015449 15.3717 {-a(n+2)+5*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A015450 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015450 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015450 117.918 1-x^10 ogf_with_Euler_Transform A015450 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015450 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015451 27.8574 (-1+5*x)/(x^2-1+6*x) ogf A015451 15.9185 -(-1-2*x+5*x^2)/(5*x-1)/(x^2+6*x-1) lgdogf A015451 27.8574 -(1-5*x)/(x^2-1+6*x) ogf A015451 9.77451 -49+245*x+(99-544*x-49*x^2)*f(x)+(50*x^2-50+300*x)*f(x)^2 ogf A015451 13.9287 1/2/(-5+x)*(-6*x-1+(40*x^2-8*x+1)^(1/2)) revogf A015451 15.058 {-a(n+2)+6*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A015453 31.2464 (6*x-1)/(x^2-1+7*x) ogf A015453 16.9623 -(-1-2*x+6*x^2)/(6*x-1)/(x^2+7*x-1) lgdogf A015453 29.6841 -(1-6*x)/(x^2-1+7*x) ogf A015453 10.2359 -64+384*x+(129-838*x-64*x^2)*f(x)+(65*x^2-65+455*x)*f(x)^2 ogf A015453 14.842 1/2/(x-6)*(-1-7*x+(1-10*x+53*x^2)^(1/2)) revogf A015453 16.0454 {-a(n+2)+7*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A015454 31.0541 (-1+7*x)/(x^2-1+8*x) ogf A015454 31.0541 -(1-7*x)/(x^2-1+8*x) ogf A015454 10.5268 -81+567*x+(163-1222*x-81*x^2)*f(x)+(82*x^2-82+656*x)*f(x)^2 ogf A015454 15.1483 1/2/(-7+x)*(-8*x-1+(68*x^2-12*x+1)^(1/2)) revogf A015454 16.786 {-a(n+2)+8*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A015455 25.6166 (-1+8*x)/(x^2-1+9*x) ogf A015455 25.6166 -(1-8*x)/(x^2-1+9*x) ogf A015455 13.8468 -(4*x+1)*(2*x-1)/(-1+8*x)/(x^2+9*x-1) lgdogf A015455 8.13226 -100+800*x+(201-1708*x-100*x^2)*f(x)+(101*x^2-101+909*x)*f(x)^2 ogf A015455 12.4959 1/2/(-8+x)*(-1-9*x+(1-14*x+85*x^2)^(1/2)) revogf A015455 13.8468 {-a(n+2)+9*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A015456 33.4897 (-1+9*x)/(x^2-1+10*x) ogf A015456 19.5357 -(-1-2*x+9*x^2)/(9*x-1)/(x^2+10*x-1) lgdogf A015456 33.4897 -(1-9*x)/(x^2-1+10*x) ogf A015456 10.8198 -121+1089*x+(243-2308*x-121*x^2)*f(x)+(122*x^2-122+1220*x)*f(x)^2 ogf A015456 16.3554 1/2/(-9+x)*(-1-10*x+(1-16*x+104*x^2)^(1/2)) revogf A015456 18.5075 {-a(n+2)+10*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A015457 31.9675 (-1+10*x)/(x^2-1+11*x) ogf A015457 18.5075 -(-1-2*x+10*x^2)/(10*x-1)/(x^2+11*x-1) lgdogf A015457 31.9675 -(1-10*x)/(x^2-1+11*x) ogf A015457 10.8198 -144+1440*x+(289-3034*x-144*x^2)*f(x)+(145*x^2-145+1595*x)*f(x)^2 ogf A015457 15.9837 1/2/(-10+x)*(-1-11*x+(1-18*x+125*x^2)^(1/2)) revogf A015457 18.5075 {-a(n+2)+11*a(n+1)+a(n),a(0)=1,a(1)=1} ogf A015466 8.85831 -(-1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15+x^31)/(1-x^16+x^32) ogf A015466 8.75878 -(961-1457*x^16-29791*x^30+28830*x^31+2209*x^32)/(x-1)/(2209*x^32-961*x^31-1457*x^16+961) lgdogf A015471 13.6459 (1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^42)/(1-x^8-x^17+x^25+x^34) ogf A015478 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015478 117.918 1-x^12 ogf_with_Euler_Transform A015478 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015478 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015483 22.7712 (x^22+x^56-1)/(x+1)/(x^56+x^11-1) ogf A015483 18.3281 -(x^22+x^56-1)/(-x^12+1+x-x^11-x^57-x^56) ogf A015483 18.3281 -(x^22-x^56-1)/(-x^12+1-x+x^11-x^57+x^56) ogf A015493 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A015493 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A015494 15.6672 (1-x^9+x^27)/(x^4+1)/(x^8-x^4+1)/(x^24-x^12+1) ogf A015494 31.3343 -(1+x^9+x^27)/(-1+x^36) ogf A015494 31.3343 -(1-x^9+x^27)/(-1-x^36) ogf A015500 6.83581 -(x^50-x^21+1)/(x-1)/(x^2+1)/(1+x^2+x)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x^8-x^6+x^4-x^2+1)/(x^40-x^30+x^20-x^10+1) ogf A015505 16.0493 (-x^4+1+x^16-x^20+x^8-x^12+x^40)/(x^40+1-x^24) ogf A015510 23.1063 -(-x^19+1-x^60)/(x^60-1+x-x^61) ogf A015510 23.8765 -(x^19-1-x^60)/(x^60+1-x-x^61) ogf A015516 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015516 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015516 117.918 1-x^10 ogf_with_Euler_Transform A015516 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015516 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015517 12.4629 (-x^26-1+x^32)/(x-1)/(x+1)/(x^4+1)/(x^16+1)/(x^8+1)/(x^2+1)^2 ogf A015517 22.36 -(-x^26-1+x^32)/(-x^32+1+x^2-x^34) ogf A015517 23.7575 -(x^26-1-x^32)/(x^32+1-x^2-x^34) ogf A015517 11.696 -2*x*(-13+169*x^24+156*x^26+29*x^32)/(1+x^2)/(29*x^32-13*x^26-13) lgdogf A015518 39.5501 -1/(x+1)/(3*x-1) ogf A015518 25.3121 -2*(1+3*x)/(x+1)/(-1+3*x) lgdogf A015518 30.1334 -x+(1-2*x-3*x^2)*f(x) ogf A015518 37.2236 -x/(-1+2*x+3*x^2) ogf A015518 18.08 1/6/x*(-2*x-1+(16*x^2+4*x+1)^(1/2)) revogf A015518 16.2257 {-a(n+2)+2*a(n+1)+3*a(n),a(0)=0,a(1)=1} ogf A015519 36.9224 -1/(-1+2*x+7*x^2) ogf A015519 26.1534 -2*(1+7*x)/(7*x^2-1+2*x) lgdogf A015519 29.8896 -x+(1-2*x-7*x^2)*f(x) ogf A015519 36.9224 -x/(-1+2*x+7*x^2) ogf A015519 17.4356 1/14/x*(-2*x-1+(32*x^2+4*x+1)^(1/2)) revogf A015519 16.0944 {-a(n+2)+2*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015520 31.5291 -1/(-1+2*x+11*x^2) ogf A015520 21.8278 -2*(1+11*x)/(11*x^2-1+2*x) lgdogf A015520 31.5291 -x/(-1+2*x+11*x^2) ogf A015520 15.7645 1/22/x*(-2*x-1+(48*x^2+4*x+1)^(1/2)) revogf A015520 12.8983 x+(-1+4*x+11*x^2)*f(x)+(22*x^2-2+4*x)*f(x)^2 ogf A015520 14.1881 {-a(n+2)+2*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015521 25.7008 -(3+8*x)/(x+1)/(-1+4*x) lgdogf A015521 36.9448 -1/(x+1)/(4*x-1) ogf A015521 28.1484 -x+(1-3*x-4*x^2)*f(x) ogf A015521 34.7716 -x/(-1+3*x+4*x^2) ogf A015521 16.8891 1/8/x*(-1-3*x+(1+6*x+25*x^2)^(1/2)) revogf A015521 15.1569 {-a(n+2)+3*a(n+1)+4*a(n),a(0)=0,a(1)=1} ogf A015522 117.918 1-x^16 ogf_with_Euler_Transform A015522 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015523 26.3916 -(3+10*x)/(5*x^2-1+3*x) lgdogf A015523 35.7063 -1/(-1+3*x+5*x^2) ogf A015523 28.9051 -x+(1-3*x-5*x^2)*f(x) ogf A015523 35.7063 -x/(-1+3*x+5*x^2) ogf A015523 16.8613 1/10/x*(-1-3*x+(1+6*x+29*x^2)^(1/2)) revogf A015523 15.5643 {-a(n+2)+3*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A015524 34.1215 -1/(-1+3*x+7*x^2) ogf A015524 27.6222 -x+(1-3*x-7*x^2)*f(x) ogf A015524 34.1215 -x/(-1+3*x+7*x^2) ogf A015524 16.1129 1/14/x*(-1-3*x+(1+6*x+37*x^2)^(1/2)) revogf A015524 14.8735 {-a(n+2)+3*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015525 34.1215 -1/(-1+3*x+8*x^2) ogf A015525 27.6222 -x+(1-3*x-8*x^2)*f(x) ogf A015525 34.1215 -x/(-1+3*x+8*x^2) ogf A015525 16.1129 1/16/x*(-1-3*x+(1+6*x+41*x^2)^(1/2)) revogf A015525 14.8735 {-a(n+2)+3*a(n+1)+8*a(n),a(0)=0,a(1)=1} ogf A015528 24.206 -(3+20*x)/(2*x+1)/(5*x-1) lgdogf A015528 31.85 -1/(2*x+1)/(-1+5*x) ogf A015528 27.5068 -x+(1-3*x-10*x^2)*f(x) ogf A015528 33.6194 -x/(-1+3*x+10*x^2) ogf A015528 16.8097 1/20/x*(-1-3*x+(1+6*x+49*x^2)^(1/2)) revogf A015528 15.1287 {-a(n+2)+3*a(n+1)+10*a(n),a(0)=0,a(1)=1} ogf A015529 28.0728 -(3+22*x)/(11*x^2-1+3*x) lgdogf A015529 37.4304 -1/(-1+3*x+11*x^2) ogf A015529 30.6248 -x+(1-3*x-11*x^2)*f(x) ogf A015529 37.4304 -x/(-1+3*x+11*x^2) ogf A015529 18.7152 1/22/x*(-1-3*x+(1+6*x+53*x^2)^(1/2)) revogf A015529 16.8437 {-a(n+2)+3*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015530 34.1215 -1/(-1+4*x+3*x^2) ogf A015530 27.6222 -x+(1-4*x-3*x^2)*f(x) ogf A015530 34.1215 -x/(-1+4*x+3*x^2) ogf A015530 16.5733 1/6/x*(-1-4*x+(1+8*x+28*x^2)^(1/2)) revogf A015530 14.8735 {-a(n+2)+4*a(n+1)+3*a(n),a(0)=0,a(1)=1} ogf A015531 32.5468 -1/(x+1)/(-1+5*x) ogf A015531 23.054 -2*(2+5*x)/(x+1)/(5*x-1) lgdogf A015531 26.3474 -x+(1-4*x-5*x^2)*f(x) ogf A015531 32.5468 -x/(-1+4*x+5*x^2) ogf A015531 15.3693 1/10/x*(-1-4*x+(1+8*x+36*x^2)^(1/2)) revogf A015531 14.1871 {-a(n+2)+4*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A015532 40.5669 -1/(-1+4*x+7*x^2) ogf A015532 28.7349 -2*(7*x+2)/(7*x^2-1+4*x) lgdogf A015532 32.8398 -x+(1-4*x-7*x^2)*f(x) ogf A015532 40.5669 -x/(-1+4*x+7*x^2) ogf A015532 19.1566 1/14/x*(-1-4*x+(1+8*x+44*x^2)^(1/2)) revogf A015532 17.683 {-a(n+2)+4*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015533 41.6885 -1/(-1+4*x+9*x^2) ogf A015533 29.5294 -2*(2+9*x)/(9*x^2-1+4*x) lgdogf A015533 33.7479 -x+(1-4*x-9*x^2)*f(x) ogf A015533 41.6885 -x/(-1+4*x+9*x^2) ogf A015533 19.6863 1/18/x*(-1-4*x+(1+8*x+52*x^2)^(1/2)) revogf A015533 18.1719 {-a(n+2)+4*a(n+1)+9*a(n),a(0)=0,a(1)=1} ogf A015534 29.5995 -1/(-1+4*x+11*x^2) ogf A015534 20.492 -2*(2+11*x)/(11*x^2-1+4*x) lgdogf A015534 24.2178 -x+(1-4*x-11*x^2)*f(x) ogf A015534 29.5995 -x/(-1+4*x+11*x^2) ogf A015534 14.7997 1/22/x*(-1-4*x+(1+8*x+60*x^2)^(1/2)) revogf A015534 13.3198 {-a(n+2)+4*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015535 31.925 -(5+4*x)/(2*x^2-1+5*x) lgdogf A015535 41.3147 -1/(-1+5*x+2*x^2) ogf A015535 33.4452 -x+(1-5*x-2*x^2)*f(x) ogf A015535 41.3147 -x/(-1+5*x+2*x^2) ogf A015535 19.5097 1/4/x*(-1-5*x+(1+10*x+33*x^2)^(1/2)) revogf A015535 18.0089 {-a(n+2)+5*a(n+1)+2*a(n),a(0)=0,a(1)=1} ogf A015536 32.2139 -(5+6*x)/(3*x^2-1+5*x) lgdogf A015536 41.6885 -1/(-1+5*x+3*x^2) ogf A015536 33.7479 -x+(1-5*x-3*x^2)*f(x) ogf A015536 41.6885 -x/(-1+5*x+3*x^2) ogf A015536 19.6863 1/6/x*(-1-5*x+(1+10*x+37*x^2)^(1/2)) revogf A015536 18.1719 {-a(n+2)+5*a(n+1)+3*a(n),a(0)=0,a(1)=1} ogf A015537 29.6446 -(5+8*x)/(4*x^2-1+5*x) lgdogf A015537 38.3636 -1/(-1+5*x+4*x^2) ogf A015537 31.0563 -x+(1-5*x-4*x^2)*f(x) ogf A015537 38.3636 -x/(-1+5*x+4*x^2) ogf A015537 18.1162 1/8/x*(-1-5*x+(1+10*x+41*x^2)^(1/2)) revogf A015537 16.7226 {-a(n+2)+5*a(n+1)+4*a(n),a(0)=0,a(1)=1} ogf A015538 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015538 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015538 117.918 1-x^10 ogf_with_Euler_Transform A015538 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015538 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015540 22.5802 -(5+12*x)/(x+1)/(-1+6*x) lgdogf A015540 33.8703 -1/(x+1)/(6*x-1) ogf A015540 25.8059 -x+(1-5*x-6*x^2)*f(x) ogf A015540 31.8779 -x/(-1+5*x+6*x^2) ogf A015540 14.6466 1/12/x*(-1-5*x+(1+10*x+49*x^2)^(1/2)) revogf A015540 13.8955 {-a(n+2)+5*a(n+1)+6*a(n),a(0)=0,a(1)=1} ogf A015541 29.31 -(5+14*x)/(7*x^2-1+5*x) lgdogf A015541 39.6547 -1/(-1+5*x+7*x^2) ogf A015541 32.1014 -x+(1-5*x-7*x^2)*f(x) ogf A015541 39.6547 -x/(-1+5*x+7*x^2) ogf A015541 18.2197 1/14/x*(-1-5*x+(1+10*x+53*x^2)^(1/2)) revogf A015541 17.2854 {-a(n+2)+5*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015543 7.45333 (x^4-x^2+1)*(x^42+x^40-x^36-x^34+x^30+x^28-x^24+x^20+x^18-x^14-x^12+x^8+x^6-x^2-1)/(x+1)/(x^46+x^13-1) ogf A015543 18.5424 -(x^26+x^46-1)/(-x^14+1+x-x^13-x^47-x^46) ogf A015543 18.5424 -(x^26-x^46-1)/(-x^14+1-x+x^13-x^47+x^46) ogf A015544 29.5827 -(5+16*x)/(8*x^2-1+5*x) lgdogf A015544 40.0236 -1/(-1+5*x+8*x^2) ogf A015544 32.4001 -x+(1-5*x-8*x^2)*f(x) ogf A015544 40.0236 -x/(-1+5*x+8*x^2) ogf A015544 18.3892 1/16/x*(-1-5*x+(1+10*x+57*x^2)^(1/2)) revogf A015544 17.4462 {-a(n+2)+5*a(n+1)+8*a(n),a(0)=0,a(1)=1} ogf A015545 29.8553 -(5+18*x)/(9*x^2-1+5*x) lgdogf A015545 40.3925 -1/(-1+5*x+9*x^2) ogf A015545 32.6987 -x+(1-5*x-9*x^2)*f(x) ogf A015545 40.3925 -x/(-1+5*x+9*x^2) ogf A015545 18.5587 1/18/x*(-1-5*x+(1+10*x+61*x^2)^(1/2)) revogf A015545 17.607 {-a(n+2)+5*a(n+1)+9*a(n),a(0)=0,a(1)=1} ogf A015546 13.2201 (29-53*x^24+812*x^29-841*x^28)/(x-1)/(29*x^29+53*x^24-29) lgdogf A015546 24.308 -(-1+x^24+x^29)/(1-x-x^24+x^25) ogf A015546 8.46682 -(-1+x^24+x^29)/(x+1)/(x^8-x^4+1)/(x^4-x^2+1)/(1+x^2+x)/(1-x+x^2)/(x^4+1)/(x^2+1)/(x-1)^2 ogf A015547 26.2738 -(5+22*x)/(11*x^2-1+5*x) lgdogf A015547 35.0318 -1/(-1+5*x+11*x^2) ogf A015547 28.6624 -x+(1-5*x-11*x^2)*f(x) ogf A015547 35.0318 -x/(-1+5*x+11*x^2) ogf A015547 17.0425 1/22/x*(-1-5*x+(1+10*x+69*x^2)^(1/2)) revogf A015547 15.7643 {-a(n+2)+5*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015548 26.5314 -(5+24*x)/(12*x^2-1+5*x) lgdogf A015548 35.3752 -1/(-1+5*x+12*x^2) ogf A015548 28.9434 -x+(1-5*x-12*x^2)*f(x) ogf A015548 35.3752 -x/(-1+5*x+12*x^2) ogf A015548 17.2096 1/24/x*(-1-5*x+(1+10*x+73*x^2)^(1/2)) revogf A015548 15.9189 {-a(n+2)+5*a(n+1)+12*a(n),a(0)=0,a(1)=1} ogf A015550 24.8074 -(-x^23+1-x^44)/(x^44-1+x-x^45) ogf A015550 25.6343 -(x^23-1-x^44)/(x^44+1-x-x^45) ogf A015551 33.6688 -1/(-1+6*x+5*x^2) ogf A015551 23.8487 -2*(3+5*x)/(5*x^2-1+6*x) lgdogf A015551 27.2557 -x+(1-6*x-5*x^2)*f(x) ogf A015551 33.6688 -x/(-1+6*x+5*x^2) ogf A015551 15.4695 1/10/x*(-6*x-1+(56*x^2+12*x+1)^(1/2)) revogf A015551 14.6761 {-a(n+2)+6*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A015552 34.2061 -1/(x+1)/(-1+7*x) ogf A015552 24.2293 -2*(3+7*x)/(x+1)/(7*x-1) lgdogf A015552 27.6906 -x+(1-6*x-7*x^2)*f(x) ogf A015552 34.2061 -x/(-1+6*x+7*x^2) ogf A015552 15.7163 1/14/x*(-6*x-1+(64*x^2+12*x+1)^(1/2)) revogf A015552 14.9103 {-a(n+2)+6*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015553 33.1514 -1/(-1+6*x+11*x^2) ogf A015553 22.951 -2*(3+11*x)/(11*x^2-1+6*x) lgdogf A015553 27.1239 -x+(1-6*x-11*x^2)*f(x) ogf A015553 33.1514 -x/(-1+6*x+11*x^2) ogf A015553 16.1277 1/22/x*(-6*x-1+(80*x^2+12*x+1)^(1/2)) revogf A015553 14.9181 {-a(n+2)+6*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015555 26.9855 -(7+4*x)/(2*x^2-1+7*x) lgdogf A015555 34.9224 -1/(-1+7*x+2*x^2) ogf A015555 28.2705 -x+(1-7*x-2*x^2)*f(x) ogf A015555 34.9224 -x/(-1+7*x+2*x^2) ogf A015555 16.4912 1/4/x*(-1-7*x+(1+14*x+57*x^2)^(1/2)) revogf A015555 15.2226 {-a(n+2)+7*a(n+1)+2*a(n),a(0)=0,a(1)=1} ogf A015556 48.8883 -1+x^6+x^12+x^16 ogf_with_Euler_Transform A015559 27.1239 -(7+6*x)/(3*x^2-1+7*x) lgdogf A015559 35.1015 -1/(-1+7*x+3*x^2) ogf A015559 28.4155 -x+(1-7*x-3*x^2)*f(x) ogf A015559 35.1015 -x/(-1+7*x+3*x^2) ogf A015559 16.5757 1/6/x*(-1-7*x+(1+14*x+61*x^2)^(1/2)) revogf A015559 15.3007 {-a(n+2)+7*a(n+1)+3*a(n),a(0)=0,a(1)=1} ogf A015561 27.2623 -(7+8*x)/(4*x^2-1+7*x) lgdogf A015561 35.2806 -1/(-1+7*x+4*x^2) ogf A015561 28.5605 -x+(1-7*x-4*x^2)*f(x) ogf A015561 35.2806 -x/(-1+7*x+4*x^2) ogf A015561 16.6603 1/8/x*(-1-7*x+(1+14*x+65*x^2)^(1/2)) revogf A015561 15.3787 {-a(n+2)+7*a(n+1)+4*a(n),a(0)=0,a(1)=1} ogf A015562 26.2093 -(7+10*x)/(5*x^2-1+7*x) lgdogf A015562 35.4597 -1/(-1+7*x+5*x^2) ogf A015562 28.7055 -x+(1-7*x-5*x^2)*f(x) ogf A015562 35.4597 -x/(-1+7*x+5*x^2) ogf A015562 16.2923 1/10/x*(-1-7*x+(1+14*x+69*x^2)^(1/2)) revogf A015562 15.4568 {-a(n+2)+7*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A015563 16.4314 -(-1-x+x^3+x^4-x^6+x^8+x^9-x^11-x^12)/(1+x^37) ogf A015563 16.4314 -(1+x+x^3+x^4+x^6+x^8+x^9+x^11+x^12)/(-1+x^37) ogf A015564 26.3417 -(7+12*x)/(6*x^2-1+7*x) lgdogf A015564 35.6388 -1/(-1+7*x+6*x^2) ogf A015564 28.8505 -x+(1-7*x-6*x^2)*f(x) ogf A015564 35.6388 -x/(-1+7*x+6*x^2) ogf A015564 16.3746 1/12/x*(-1-7*x+(1+14*x+73*x^2)^(1/2)) revogf A015564 15.5349 {-a(n+2)+7*a(n+1)+6*a(n),a(0)=0,a(1)=1} ogf A015565 26.7388 -(7+16*x)/(x+1)/(8*x-1) lgdogf A015565 36.1761 -1/(x+1)/(-1+8*x) ogf A015565 29.2854 -x+(1-7*x-8*x^2)*f(x) ogf A015565 36.1761 -x/(-1+7*x+8*x^2) ogf A015565 16.6214 1/16/x*(-1-7*x+(1+14*x+81*x^2)^(1/2)) revogf A015565 15.7691 {-a(n+2)+7*a(n+1)+8*a(n),a(0)=0,a(1)=1} ogf A015566 26.8712 -(7+18*x)/(9*x^2-1+7*x) lgdogf A015566 36.3552 -1/(-1+7*x+9*x^2) ogf A015566 29.4304 -x+(1-7*x-9*x^2)*f(x) ogf A015566 36.3552 -x/(-1+7*x+9*x^2) ogf A015566 16.7037 1/18/x*(-1-7*x+(1+14*x+85*x^2)^(1/2)) revogf A015566 15.8471 {-a(n+2)+7*a(n+1)+9*a(n),a(0)=0,a(1)=1} ogf A015568 34.5046 -1/(-1+7*x+10*x^2) ogf A015568 28.231 -x+(1-7*x-10*x^2)*f(x) ogf A015568 34.5046 -x/(-1+7*x+10*x^2) ogf A015568 16.786 1/20/x*(-1-7*x+(1+14*x+89*x^2)^(1/2)) revogf A015568 15.5271 {-a(n+2)+7*a(n+1)+10*a(n),a(0)=0,a(1)=1} ogf A015570 34.5046 -1/(-1+7*x+11*x^2) ogf A015570 28.231 -x+(1-7*x-11*x^2)*f(x) ogf A015570 34.5046 -x/(-1+7*x+11*x^2) ogf A015570 16.786 1/22/x*(-1-7*x+(1+14*x+93*x^2)^(1/2)) revogf A015570 15.5271 {-a(n+2)+7*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015571 23.4828 -(-x^11-1+x^60)/(-x^60+1+x-x^61) ogf A015571 25.0484 -(x^11-1-x^60)/(x^60+1-x-x^61) ogf A015572 26.0053 -(7+24*x)/(12*x^2-1+7*x) lgdogf A015572 34.6737 -1/(-1+7*x+12*x^2) ogf A015572 28.3694 -x+(1-7*x-12*x^2)*f(x) ogf A015572 34.6737 -x/(-1+7*x+12*x^2) ogf A015572 16.8683 1/24/x*(-1-7*x+(1+14*x+97*x^2)^(1/2)) revogf A015572 15.6032 {-a(n+2)+7*a(n+1)+12*a(n),a(0)=0,a(1)=1} ogf A015574 36.7133 -1/(-1+8*x+3*x^2) ogf A015574 26.0053 -2*(4+3*x)/(3*x^2-1+8*x) lgdogf A015574 29.7203 -x+(1-8*x-3*x^2)*f(x) ogf A015574 36.7133 -x/(-1+8*x+3*x^2) ogf A015574 17.3368 1/6/x*(-8*x-1+(76*x^2+16*x+1)^(1/2)) revogf A015574 16.0032 {-a(n+2)+8*a(n+1)+3*a(n),a(0)=0,a(1)=1} ogf A015575 37.0715 -1/(-1+8*x+5*x^2) ogf A015575 26.259 -2*(4+5*x)/(5*x^2-1+8*x) lgdogf A015575 30.0103 -x+(1-8*x-5*x^2)*f(x) ogf A015575 37.0715 -x/(-1+8*x+5*x^2) ogf A015575 17.0329 1/10/x*(-8*x-1+(84*x^2+16*x+1)^(1/2)) revogf A015575 16.1594 {-a(n+2)+8*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A015576 37.6088 -1/(-1+8*x+7*x^2) ogf A015576 26.6395 -2*(4+7*x)/(7*x^2-1+8*x) lgdogf A015576 30.4452 -x+(1-8*x-7*x^2)*f(x) ogf A015576 37.6088 -x/(-1+8*x+7*x^2) ogf A015576 17.2797 1/14/x*(-8*x-1+(92*x^2+16*x+1)^(1/2)) revogf A015576 16.3936 {-a(n+2)+8*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015577 42.3654 -1/(x+1)/(-1+9*x) ogf A015577 30.0088 -2*(4+9*x)/(x+1)/(9*x-1) lgdogf A015577 34.2958 -x+(1-8*x-9*x^2)*f(x) ogf A015577 42.3654 -x/(-1+8*x+9*x^2) ogf A015577 18.953 1/18/x*(-8*x-1+(100*x^2+16*x+1)^(1/2)) revogf A015577 18.467 {-a(n+2)+8*a(n+1)+9*a(n),a(0)=0,a(1)=1} ogf A015578 35.8577 -1/(-1+8*x+11*x^2) ogf A015578 24.8245 -2*(4+11*x)/(11*x^2-1+8*x) lgdogf A015578 29.3381 -x+(1-8*x-11*x^2)*f(x) ogf A015578 35.8577 -x/(-1+8*x+11*x^2) ogf A015578 16.9852 1/22/x*(-8*x-1+(108*x^2+16*x+1)^(1/2)) revogf A015578 16.136 {-a(n+2)+8*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015579 32.7369 -(9+4*x)/(2*x^2-1+9*x) lgdogf A015579 42.3654 -1/(-1+9*x+2*x^2) ogf A015579 34.2958 -x+(1-9*x-2*x^2)*f(x) ogf A015579 42.3654 -x/(-1+9*x+2*x^2) ogf A015579 20.0059 1/4/x*(-1-9*x+(1+18*x+89*x^2)^(1/2)) revogf A015579 18.467 {-a(n+2)+9*a(n+1)+2*a(n),a(0)=0,a(1)=1} ogf A015580 32.7369 -(9+8*x)/(4*x^2-1+9*x) lgdogf A015580 42.3654 -1/(-1+9*x+4*x^2) ogf A015580 34.2958 -x+(1-9*x-4*x^2)*f(x) ogf A015580 42.3654 -x/(-1+9*x+4*x^2) ogf A015580 20.0059 1/8/x*(-1-9*x+(1+18*x+97*x^2)^(1/2)) revogf A015580 18.467 {-a(n+2)+9*a(n+1)+4*a(n),a(0)=0,a(1)=1} ogf A015581 31.3136 -(9+10*x)/(5*x^2-1+9*x) lgdogf A015581 42.3654 -1/(-1+9*x+5*x^2) ogf A015581 34.2958 -x+(1-9*x-5*x^2)*f(x) ogf A015581 42.3654 -x/(-1+9*x+5*x^2) ogf A015581 18.953 1/10/x*(-1-9*x+(1+18*x+101*x^2)^(1/2)) revogf A015581 18.467 {-a(n+2)+9*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A015582 13.8727 -1/(x-1)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x) ogf A015582 12.1984 -11*x^10/(-1+x)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015582 70.7506 1/(1-x^11) ogf A015582 176.877 x^10 ogf_with_Euler_Transform A015582 8.13226 {-a(n+1),a(0)=0,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=1} ogf_with_Euler_Transform A015583 31.3136 -(9+14*x)/(7*x^2-1+9*x) lgdogf A015583 42.3654 -1/(-1+9*x+7*x^2) ogf A015583 34.2958 -x+(1-9*x-7*x^2)*f(x) ogf A015583 42.3654 -x/(-1+9*x+7*x^2) ogf A015583 18.953 1/14/x*(-1-9*x+(1+18*x+109*x^2)^(1/2)) revogf A015583 18.467 {-a(n+2)+9*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015584 31.3136 -(9+16*x)/(8*x^2-1+9*x) lgdogf A015584 42.3654 -1/(-1+9*x+8*x^2) ogf A015584 34.2958 -x+(1-9*x-8*x^2)*f(x) ogf A015584 42.3654 -x/(-1+9*x+8*x^2) ogf A015584 18.953 1/16/x*(-1-9*x+(1+18*x+113*x^2)^(1/2)) revogf A015584 18.467 {-a(n+2)+9*a(n+1)+8*a(n),a(0)=0,a(1)=1} ogf A015585 30.0088 -(9+20*x)/(x+1)/(10*x-1) lgdogf A015585 40.0118 -1/(x+1)/(-1+10*x) ogf A015585 32.7369 -x+(1-9*x-10*x^2)*f(x) ogf A015585 40.0118 -x/(-1+9*x+10*x^2) ogf A015585 18.953 1/20/x*(-1-9*x+(1+18*x+121*x^2)^(1/2)) revogf A015585 18.0053 {-a(n+2)+9*a(n+1)+10*a(n),a(0)=0,a(1)=1} ogf A015586 8.84383 1+x+x^3+x^4+x^5+x^6+x^8+x^9+x^2+x^7+x^10+x^11+x^12+x^13+x^14+x^15+x^17+x^18+x^16 ogf A015586 117.918 1-x^18 ogf_with_Euler_Transform A015587 27.9081 -(9+22*x)/(11*x^2-1+9*x) lgdogf A015587 37.2108 -1/(-1+9*x+11*x^2) ogf A015587 30.4452 -x+(1-9*x-11*x^2)*f(x) ogf A015587 37.2108 -x/(-1+9*x+11*x^2) ogf A015587 17.6262 1/22/x*(-1-9*x+(1+18*x+125*x^2)^(1/2)) revogf A015587 16.7449 {-a(n+2)+9*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015588 39.0713 -1/(-1+10*x+3*x^2) ogf A015588 28.1314 -2*(3*x+5)/(3*x^2-1+10*x) lgdogf A015588 31.9675 -x+(1-10*x-3*x^2)*f(x) ogf A015588 39.0713 -x/(-1+10*x+3*x^2) ogf A015588 18.5075 1/6/x*(-1-10*x+(1+20*x+112*x^2)^(1/2)) revogf A015588 17.5821 {-a(n+2)+10*a(n+1)+3*a(n),a(0)=0,a(1)=1} ogf A015589 39.0713 -1/(-1+10*x+7*x^2) ogf A015589 28.1314 -2*(5+7*x)/(7*x^2-1+10*x) lgdogf A015589 31.9675 -x+(1-10*x-7*x^2)*f(x) ogf A015589 39.0713 -x/(-1+10*x+7*x^2) ogf A015589 18.0329 1/14/x*(-1-10*x+(1+20*x+128*x^2)^(1/2)) revogf A015589 17.5821 {-a(n+2)+10*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015591 39.0713 -1/(-1+10*x+9*x^2) ogf A015591 28.1314 -2*(5+9*x)/(9*x^2-1+10*x) lgdogf A015591 31.9675 -x+(1-10*x-9*x^2)*f(x) ogf A015591 39.0713 -x/(-1+10*x+9*x^2) ogf A015591 18.0329 1/18/x*(-1-10*x+(1+20*x+136*x^2)^(1/2)) revogf A015591 17.5821 {-a(n+2)+10*a(n+1)+9*a(n),a(0)=0,a(1)=1} ogf A015592 29.0737 -1/(x+1)/(11*x-1) ogf A015592 19.0097 -2*(5+11*x)/(x+1)/(11*x-1) lgdogf A015592 21.4893 -x+(1-10*x-11*x^2)*f(x) ogf A015592 26.0133 -x/(-1+10*x+11*x^2) ogf A015592 12.6732 1/22/x*(-1-10*x+(1+20*x+144*x^2)^(1/2)) revogf A015592 12.055 {-a(n+2)+10*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015593 26.2126 -(11+4*x)/(2*x^2-1+11*x) lgdogf A015593 34.9502 -1/(-1+11*x+2*x^2) ogf A015593 28.5956 -x+(1-11*x-2*x^2)*f(x) ogf A015593 34.9502 -x/(-1+11*x+2*x^2) ogf A015593 16.5554 1/4/x*(-1-11*x+(1+22*x+129*x^2)^(1/2)) revogf A015593 15.7276 {-a(n+2)+11*a(n+1)+2*a(n),a(0)=0,a(1)=1} ogf A015594 26.2126 -(11+6*x)/(3*x^2-1+11*x) lgdogf A015594 34.9502 -1/(-1+11*x+3*x^2) ogf A015594 28.5956 -x+(1-11*x-3*x^2)*f(x) ogf A015594 34.9502 -x/(-1+11*x+3*x^2) ogf A015594 16.5554 1/6/x*(-1-11*x+(1+22*x+133*x^2)^(1/2)) revogf A015594 15.7276 {-a(n+2)+11*a(n+1)+3*a(n),a(0)=0,a(1)=1} ogf A015595 23.0376 (x^26+x^48-1)/(x+1)/(x^48+x^13-1) ogf A015595 18.5424 -(x^26+x^48-1)/(-x^14+1+x-x^13-x^49-x^48) ogf A015595 18.5424 -(x^26-x^48-1)/(-x^14+1-x+x^13-x^49+x^48) ogf A015596 26.2126 -(11+8*x)/(4*x^2-1+11*x) lgdogf A015596 34.9502 -1/(-1+11*x+4*x^2) ogf A015596 28.5956 -x+(1-11*x-4*x^2)*f(x) ogf A015596 34.9502 -x/(-1+11*x+4*x^2) ogf A015596 16.5554 1/8/x*(-1-11*x+(1+22*x+137*x^2)^(1/2)) revogf A015596 15.7276 {-a(n+2)+11*a(n+1)+4*a(n),a(0)=0,a(1)=1} ogf A015597 25.284 -(11+10*x)/(5*x^2-1+11*x) lgdogf A015597 35.1166 -1/(-1+11*x+5*x^2) ogf A015597 28.7318 -x+(1-11*x-5*x^2)*f(x) ogf A015597 35.1166 -x/(-1+11*x+5*x^2) ogf A015597 16.2077 1/10/x*(-1-11*x+(1+22*x+141*x^2)^(1/2)) revogf A015597 15.8025 {-a(n+2)+11*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A015598 25.4038 -(11+12*x)/(6*x^2-1+11*x) lgdogf A015598 35.283 -1/(-1+11*x+6*x^2) ogf A015598 28.8679 -x+(1-11*x-6*x^2)*f(x) ogf A015598 35.283 -x/(-1+11*x+6*x^2) ogf A015598 16.2845 1/12/x*(-1-11*x+(1+22*x+145*x^2)^(1/2)) revogf A015598 15.8774 {-a(n+2)+11*a(n+1)+6*a(n),a(0)=0,a(1)=1} ogf A015601 25.5236 -(11+14*x)/(7*x^2-1+11*x) lgdogf A015601 35.4495 -1/(-1+11*x+7*x^2) ogf A015601 29.0041 -x+(1-11*x-7*x^2)*f(x) ogf A015601 35.4495 -x/(-1+11*x+7*x^2) ogf A015601 16.3613 1/14/x*(-1-11*x+(1+22*x+149*x^2)^(1/2)) revogf A015601 15.9523 {-a(n+2)+11*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015602 25.5236 -(11+16*x)/(8*x^2-1+11*x) lgdogf A015602 35.4495 -1/(-1+11*x+8*x^2) ogf A015602 29.0041 -x+(1-11*x-8*x^2)*f(x) ogf A015602 35.4495 -x/(-1+11*x+8*x^2) ogf A015602 16.3613 1/16/x*(-1-11*x+(1+22*x+153*x^2)^(1/2)) revogf A015602 15.9523 {-a(n+2)+11*a(n+1)+8*a(n),a(0)=0,a(1)=1} ogf A015603 25.6434 -(11+18*x)/(9*x^2-1+11*x) lgdogf A015603 35.6159 -1/(-1+11*x+9*x^2) ogf A015603 29.1403 -x+(1-11*x-9*x^2)*f(x) ogf A015603 35.6159 -x/(-1+11*x+9*x^2) ogf A015603 16.4381 1/18/x*(-1-11*x+(1+22*x+157*x^2)^(1/2)) revogf A015603 16.0272 {-a(n+2)+11*a(n+1)+9*a(n),a(0)=0,a(1)=1} ogf A015606 24.6572 -(11+20*x)/(10*x^2-1+11*x) lgdogf A015606 33.7414 -1/(-1+11*x+10*x^2) ogf A015606 27.8733 -x+(1-11*x-10*x^2)*f(x) ogf A015606 33.7414 -x/(-1+11*x+10*x^2) ogf A015606 16.4381 1/20/x*(-1-11*x+(1+22*x+161*x^2)^(1/2)) revogf A015606 15.6362 {-a(n+2)+11*a(n+1)+10*a(n),a(0)=0,a(1)=1} ogf A015607 8.45454 -(-x^3-x^11+x^10+1-x^9+x^2+x^38+x^12-x)/(-x^21-1+x^30-x^34+x^17+x^4+x^9-x^13-x^26+x^43-x^39) ogf A015609 20.117 -(11+24*x)/(x+1)/(12*x-1) lgdogf A015609 29.5838 -1/(x+1)/(12*x-1) ogf A015609 21.8663 -x+(1-11*x-12*x^2)*f(x) ogf A015609 26.4697 -x/(-1+11*x+12*x^2) ogf A015609 12.8955 1/24/x*(-1-11*x+(1+22*x+169*x^2)^(1/2)) revogf A015609 12.2664 {-a(n+2)+11*a(n+1)+12*a(n),a(0)=0,a(1)=1} ogf A015610 36.2816 -1/(-1+12*x+5*x^2) ogf A015610 29.685 -x+(1-12*x-5*x^2)*f(x) ogf A015610 36.2816 -x/(-1+12*x+5*x^2) ogf A015610 16.7454 1/10/x*(-1-12*x+(1+24*x+164*x^2)^(1/2)) revogf A015610 16.3267 {-a(n+2)+12*a(n+1)+5*a(n),a(0)=0,a(1)=1} ogf A015611 36.2816 -1/(-1+12*x+7*x^2) ogf A015611 29.685 -x+(1-12*x-7*x^2)*f(x) ogf A015611 36.2816 -x/(-1+12*x+7*x^2) ogf A015611 16.7454 1/14/x*(-1-12*x+(1+24*x+172*x^2)^(1/2)) revogf A015611 16.3267 {-a(n+2)+12*a(n+1)+7*a(n),a(0)=0,a(1)=1} ogf A015612 34.5297 -1/(-1+12*x+11*x^2) ogf A015612 24.2987 -2*(6+11*x)/(11*x^2-1+12*x) lgdogf A015612 28.5246 -x+(1-12*x-11*x^2)*f(x) ogf A015612 34.5297 -x/(-1+12*x+11*x^2) ogf A015612 16.8222 1/22/x*(-1-12*x+(1+24*x+188*x^2)^(1/2)) revogf A015612 16.0016 {-a(n+2)+12*a(n+1)+11*a(n),a(0)=0,a(1)=1} ogf A015615 23.3455 -(-x^11-1+x^62)/(-x^62+1+x-x^63) ogf A015615 24.9019 -(x^11-1-x^62)/(x^62+1-x-x^63) ogf A015621 7.19853 (-x^26-1+x^36)/(x-1)/(x+1)/(1+x^2+x)/(1-x+x^2)/(x^4-x^2+1)/(x^6+x^3+1)/(x^6-x^3+1)/(x^12-x^6+1)/(x^2+1)^2 ogf A015621 22.2307 -(-x^26-1+x^36)/(-x^36+1+x^2-x^38) ogf A015621 23.6202 -(x^26-1-x^36)/(x^36+1-x^2-x^38) ogf A015621 11.6284 -2*x*(-13+169*x^24+156*x^26+31*x^36)/(1+x^2)/(31*x^36-13*x^26-13) lgdogf A015624 49.1629 -1+x^4+x^16+x^18 ogf_with_Euler_Transform A015637 21.7138 -(-x^22-1+x^52)/(-x^52+1+x^2-x^54) ogf A015637 23.0709 -(x^22-1-x^52)/(x^52+1-x^2-x^54) ogf A015642 24.2404 -(-x^23+1-x^48)/(x^48-1+x-x^49) ogf A015642 6.89405 -(x^23-1+x^48)/(x+1)/(x^2+1)/(x^16-x^8+1)/(x^8-x^4+1)/(1+x^2+x)/(1-x+x^2)/(x^4-x^2+1)/(x^8+1)/(x^4+1)/(x-1)^2 ogf A015642 25.0484 -(x^23-1-x^48)/(x^48+1-x-x^49) ogf A015643 8.55007 (-x^4-x^10+x^11-x^14-1-x^12+x^13-x^2+x^3+x^38+x)/(-x^15-1+x^24+x^29+x^34-x^5-x^10+x^19+x^39) ogf A015648 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015648 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015648 117.918 1-x^10 ogf_with_Euler_Transform A015648 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015648 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015658 117.918 1-x^16 ogf_with_Euler_Transform A015658 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015659 6.57188 -(-x^5+x^15-1-x^25-x^30+x^40+x^45)/(x+1)/(x^4-x^3+x^2-x+1)/(x^20-x^15+x^10-x^5+1)/(x^4+1)/(x^16-x^12+x^8-x^4+1) ogf A015660 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015660 117.918 1-x^12 ogf_with_Euler_Transform A015660 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015660 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015661 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A015661 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A015670 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015670 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015670 117.918 1-x^10 ogf_with_Euler_Transform A015670 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015670 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015674 9.6092 3*x^2*(-1+3*x^6-4*x^9+5*x^12-7*x^18+8*x^21)/(1-x^3+x^9-x^12+x^15-x^21+x^24) lgdogf A015681 13.3431 (1+x^8-x^12-x^4+x^24-x^28+x^16-x^20+x^40)/(1+x^40-x^32) ogf A015686 6.9448 (-x^3-1+x^14-x^13+x^18-x^19-x^16+x^2+x^5-x^7-x^4+x^38)/(-1-x^4-x^5+x^14+x^18+x^38-x^8-x^9+x^22+x^26+x^30+x^34-x) ogf A015688 23.9568 -(-x^23+1-x^50)/(x^50-1+x-x^51) ogf A015688 6.75147 -(x^23-1+x^50)/(x+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x^20+x^15+x^10+x^5+1)/(x^20-x^15+x^10-x^5+1)/(x-1)^2 ogf A015688 24.7554 -(x^23-1-x^50)/(x^50+1-x-x^51) ogf A015692 10.2938 (-x^18+1+x^36)/(x-1)/(1+x^2+x)/(x^6+x^3+1)/(x^33-x^15-x^12-x^9-x^6-x^3-1) ogf A015700 8.84383 1+x+x^3+x^4+x^5+x^6+x^8+x^9+x^2+x^7+x^10+x^11+x^12+x^13+x^14+x^15+x^17+x^18+x^16 ogf A015700 117.918 1-x^18 ogf_with_Euler_Transform A015703 24.8514 -(-1+x^55-x^66)/(1+x^11-x^55) ogf A015703 24.8514 -(1+x^55+x^66)/(-1+x^11-x^55) ogf A015703 24.8514 -(1-x^55+x^66)/(-1-x^11+x^55) ogf A015703 19.4781 -11*x^10*(-1+7*x^55)/(-1-x^11+7*x^55) lgdogf A015712 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015712 117.918 1-x^12 ogf_with_Euler_Transform A015712 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015712 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015717 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A015717 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A015720 24.4538 -(-x^29+1-x^30)/(x^30-1+x-x^31) ogf A015720 13.0701 -(841*x^28-812*x^29+59*x^30-29)/(x-1)/(59*x^30+29*x^29-29) lgdogf A015720 25.2689 -(x^29-1-x^30)/(x^30+1-x-x^31) ogf A015726 117.918 1-x^16 ogf_with_Euler_Transform A015726 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015735 8.74387 (-2*(3*x-1)^(2/3)+3*(-1)^(2/3)*x-(-1)^(2/3))/(3*x-1)^(5/3) lgdegf A015735 6.85331 9-3*x+(-12+36*x)*f(x)+(6-36*x+54*x^2)*f(x)^2+(-1-27*x^2+27*x^3+9*x)*f(x)^3 lgdegf A015735 3.729 {-a(n+1)+(146*n+112+63*n^2+9*n^3)*a(n+2)+(-48*n^2-126*n-108-6*n^3)*a(n+3)+(26*n+24+9*n^2+n^3)*a(n+4),a(0)=1,a(1)=3,a(2)=17/2,a(3)=145/6} egf A015736 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015736 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015736 117.918 1-x^10 ogf_with_Euler_Transform A015736 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015736 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015737 24.8967 -(1+x^4+x^5-x^2-x^7)/(-1+x^2) ogf_with_Euler_Transform A015737 25.7859 -(1+x^4+x^5-x^7-x^2)/(x^2-1) ogf_with_Euler_Transform A015738 49.7122 -1+x^6+x^12+x^18 ogf_with_Euler_Transform A015739 27.723 -(-1+x^3-x^5-x^7+x^9)/(1-x^2) ogf_with_Euler_Transform A015740 23.402 -(1-x^4+x^6+x^9-x^11)/(-1+x^2) ogf_with_Euler_Transform A015740 24.209 -(1-x^4+x^6+x^9-x^11)/(x^2-1) ogf_with_Euler_Transform A015741 22.3898 -(-1+x^5-x^7-x^11+x^13)/(1-x^2) ogf_with_Euler_Transform A015742 22.2611 -(-1+x^6-x^8-x^13+x^15)/(1-x^2) ogf_with_Euler_Transform A015743 21.8751 -(1-x^7+x^9+x^15-x^17)/(-1+x^2) ogf_with_Euler_Transform A015743 22.6042 -(1-x^7+x^9+x^15-x^17)/(x^2-1) ogf_with_Euler_Transform A015744 33.2956 -(-1+x-2*x^3+x^5)/(1-x^2) ogf_with_Euler_Transform A015745 28.1619 -(1+x^4+x^5-x^2-x^7)/(-1+x^2) ogf_with_Euler_Transform A015745 29.1677 -(1+x^4+x^5-x^7-x^2)/(x^2-1) ogf_with_Euler_Transform A015746 28.1619 -(-1+x^3-x^5-x^7+x^9)/(1-x^2) ogf_with_Euler_Transform A015747 22.9335 -(-x^11-1+x^68)/(-x^68+1+x-x^69) ogf A015747 24.4624 -(x^11-1-x^68)/(x^68+1-x-x^69) ogf A015748 12.5731 -(-1+x^10+x^30-x^20+x^37)/(-x^21+1-x-x^10+x^11+x^20+x^31-x^30) ogf A015748 7.42411 -(-1+x^10+x^30-x^20+x^37)/(x+1)/(x^4+1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x^16-x^12+x^8-x^4+1)/(x-1)^2 ogf A015750 27.358 -(1-x^4+x^6+x^9-x^11)/(-1+x^2) ogf_with_Euler_Transform A015750 28.3013 -(1-x^4+x^6+x^9-x^11)/(x^2-1) ogf_with_Euler_Transform A015752 8.43121 (-1+6*x^5-8*x^7-4*x^3+12*x^11+9*x^8-11*x^10+3*x^2)/(x^3+1-x+x^12+x^6-x^4+x^9-x^8-x^11) lgdogf A015752 48.3389 -1+x^2+x^6-x^20 ogf_with_Euler_Transform A015752 21.9722 1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12 ogf A015753 26.6059 -(-1+x^5-x^7-x^11+x^13)/(1-x^2) ogf_with_Euler_Transform A015754 26.8667 -(-1+x^6-x^8-x^13+x^15)/(1-x^2) ogf_with_Euler_Transform A015755 26.8667 -(1-x^7+x^9+x^15-x^17)/(-1+x^2) ogf_with_Euler_Transform A015755 27.7623 -(1-x^7+x^9+x^15-x^17)/(x^2-1) ogf_with_Euler_Transform A015760 117.918 1-x^16 ogf_with_Euler_Transform A015760 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015777 17.6824 -(1+x^8-x^12-x^4-x^44+x^48)/(-1+x^44+x^16) ogf A015777 15.4721 -(x-1)*(x+1)*(x^2+1)*(x^44-x^8-1)/(-1+x^44+x^16) ogf A015778 12.9602 -(-29+841*x^28+61*x^32-812*x^29)/(x-1)/(61*x^32+29*x^29-29) lgdogf A015778 24.6662 -(-x^29+1-x^32)/(x^32-1+x-x^33) ogf A015778 12.5353 -(x^29-1+x^32)/(x+1)/(x^2+1)/(x^4+1)/(x^16+1)/(x^8+1)/(x-1)^2 ogf A015778 25.4885 -(x^29-1-x^32)/(x^32+1-x-x^33) ogf A015790 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015790 117.918 1-x^12 ogf_with_Euler_Transform A015790 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015790 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015802 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015802 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015802 117.918 1-x^10 ogf_with_Euler_Transform A015802 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015802 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015807 17.3031 -(1+x^2+x^29+x^31+x^33)/(-1-x-x^2-x^3+x^31+x^32) ogf A015807 17.3031 -(1-x^2-x^29-x^33+x^31)/(-1+x+x^2-x^3+x^31-x^32) ogf A015811 23.5702 (x^34+x^36-1)/(x+1)/(x^36+x^17-1) ogf A015811 18.9712 -(x^34+x^36-1)/(-x^18+1+x-x^17-x^37-x^36) ogf A015811 18.9712 -(x^34-x^36-1)/(-x^18+1-x+x^17-x^37+x^36) ogf A015813 15.5208 1-x^2+x^4-x^6+x^8-x^10+x^12-x^14+x^16-x^18+x^20 ogf A015813 6.18202 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10-7*x^12+8*x^14-9*x^16+10*x^18)/(1-x^2+x^4-x^6+x^8-x^10+x^12-x^14+x^16-x^18+x^20) lgdogf A015816 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015816 117.918 1-x^12 ogf_with_Euler_Transform A015816 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015816 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015824 9.87246 (1-x^11+x^33)/(x^4+1)/(x^40-x^36+x^32-x^28+x^24-x^20+x^16-x^12+x^8-x^4+1) ogf A015824 30.0287 -(1-x^11+x^33)/(-1-x^44) ogf A015826 23.1063 -(-x^23+1-x^56)/(x^56-1+x-x^57) ogf A015826 23.8765 -(x^23-1-x^56)/(x^56+1-x-x^57) ogf A015828 117.918 1-x^16 ogf_with_Euler_Transform A015828 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015835 7.29479 (-1+2*x-3*x^2+4*x^3-5*x^4+6*x^5-7*x^6+8*x^7-9*x^8+10*x^9)/(1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10) lgdogf A015835 52.1056 -1+x+x^10-x^21 ogf_with_Euler_Transform A015835 18.237 1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10 ogf A015835 6.88187 {a(n+2)+a(n+1),a(0)=1,a(1)=-1,a(2)=1,a(3)=-1,a(4)=1,a(5)=-1,a(6)=1,a(7)=-1,a(8)=1,a(9)=-1,a(10)=1,a(11)=0} ogf A015836 7.17905 3*x^2*(-1+3*x^6-4*x^9+6*x^15-8*x^21+9*x^24-11*x^30+12*x^33)/(1-x^3+x^9-x^12+x^18-x^24+x^27-x^33+x^36) lgdogf A015838 13.2994 (31+930*x^31-961*x^30-59*x^28)/(x-1)/(31*x^31+59*x^28-31) lgdogf A015838 24.4538 -(-1+x^28+x^31)/(1-x-x^28+x^29) ogf A015838 24.4538 -(1+x^28-x^31)/(-1+x-x^28+x^29) ogf A015846 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015846 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015846 117.918 1-x^10 ogf_with_Euler_Transform A015846 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015846 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015852 8.84383 1+x+x^3+x^4+x^5+x^6+x^8+x^9+x^2+x^7+x^10+x^11+x^12+x^13+x^14+x^15+x^17+x^18+x^16 ogf A015852 117.918 1-x^18 ogf_with_Euler_Transform A015854 9.6092 3*x^2*(-1+3*x^6-4*x^9+5*x^12-7*x^18+8*x^21)/(1-x^3+x^9-x^12+x^15-x^21+x^24) lgdogf A015855 23.6202 -(-x^13-1+x^58)/(-x^58+1+x-x^59) ogf A015855 25.1948 -(x^13-1-x^58)/(x^58+1-x-x^59) ogf A015862 117.918 1-x^16 ogf_with_Euler_Transform A015862 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015868 11.5985 -1/(x-1)/(x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) ogf A015868 10.4045 -13*x^12/(-1+x)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015868 70.7506 1/(1-x^13) ogf A015868 176.877 x^12 ogf_with_Euler_Transform A015878 8.43121 (-1+6*x^5-8*x^7-4*x^3+12*x^11+9*x^8-11*x^10+3*x^2)/(x^3+1-x+x^12+x^6-x^4+x^9-x^8-x^11) lgdogf A015878 48.3389 -1+x^2+x^6-x^20 ogf_with_Euler_Transform A015878 21.9722 1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12 ogf A015885 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A015885 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A015890 7.65631 (1-x+x^2)*(1+x^2+x)*(x-1)*(x+1)*(x^2+1)*(x^4-x^2+1)*(x^4+1)*(x^8-x^4+1)/(x^6+x^3+1)/(x^33+x^24-1) ogf A015890 7.8175 -3*x^2*(-11-22*x^3+19*x^24+38*x^27+121*x^30+132*x^33+143*x^36)/(x^6+x^3+1)/(11*x^33+19*x^24-11) lgdogf A015900 15.2931 (31-1022*x^30+930*x^31)/(x-1)/(31*x^31+61*x^30-31) lgdogf A015900 24.6662 -(-1+x^30+x^31)/(1-x-x^30+x^31) ogf A015900 24.6662 -(1+x^30-x^31)/(-1+x-x^30+x^31) ogf A015901 15.5208 1-x^2+x^4-x^6+x^8-x^10+x^12-x^14+x^16-x^18+x^20 ogf A015901 6.18202 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10-7*x^12+8*x^14-9*x^16+10*x^18)/(1-x^2+x^4-x^6+x^8-x^10+x^12-x^14+x^16-x^18+x^20) lgdogf A015907 23.4828 -(-x^13-1+x^60)/(-x^60+1+x-x^61) ogf A015907 25.0484 -(x^13-1-x^60)/(x^60+1-x-x^61) ogf A015912 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015912 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015912 117.918 1-x^10 ogf_with_Euler_Transform A015912 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015912 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015918 7.07506 1+x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015918 117.918 1-x^22 ogf_with_Euler_Transform A015920 21.9722 -(1+x^7-x^35+x^21+x^28)/(-1+x^35) ogf A015920 21.9722 -(1-x^7+x^21-x^28+x^35)/(-1-x^35) ogf A015928 8.84383 1+x+x^3+x^4+x^5+x^6+x^8+x^9+x^2+x^7+x^10+x^11+x^12+x^13+x^14+x^15+x^17+x^18+x^16 ogf A015928 117.918 1-x^18 ogf_with_Euler_Transform A015930 117.918 1-x^16 ogf_with_Euler_Transform A015930 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015933 6.81341 (-x^26-1+x^48)/(x-1)/(x+1)/(x^16-x^8+1)/(x^8-x^4+1)/(1+x^2+x)/(1-x+x^2)/(x^4-x^2+1)/(x^8+1)/(x^4+1)/(x^2+1)^2 ogf A015933 21.843 -(-x^26-1+x^48)/(-x^48+1+x^2-x^50) ogf A015933 23.2082 -(x^26-1-x^48)/(x^48+1-x^2-x^50) ogf A015936 9.17096 (x+1)*(x^39+x^28+x^26+x^24+x^16+x^14+x^12+x^4+x^2+1)/(x^12+x^24+x^39-x^18-x^30-x^6+1) ogf A015944 9.6092 3*x^2*(-1+3*x^6-4*x^9+5*x^12-7*x^18+8*x^21)/(1-x^3+x^9-x^12+x^15-x^21+x^24) lgdogf A015946 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015946 117.918 1-x^12 ogf_with_Euler_Transform A015946 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015946 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015952 13.0344 -(-29+841*x^28+67*x^38-812*x^29)/(x-1)/(67*x^38+29*x^29-29) lgdogf A015952 24.8074 -(-x^29+1-x^38)/(x^38-1+x-x^39) ogf A015952 25.6343 -(x^29-1-x^38)/(x^38+1-x-x^39) ogf A015962 7.17905 3*x^2*(-1+3*x^6-4*x^9+6*x^15-8*x^21+9*x^24-11*x^30+12*x^33)/(1-x^3+x^9-x^12+x^18-x^24+x^27-x^33+x^36) lgdogf A015964 49.1629 -1+x^4+x^16+x^22 ogf_with_Euler_Transform A015966 8.84383 1+x+x^3+x^4+x^5+x^6+x^8+x^9+x^2+x^7+x^10+x^11+x^12+x^13+x^14+x^15+x^17+x^18+x^16 ogf A015966 117.918 1-x^18 ogf_with_Euler_Transform A015967 7.29479 (-1+2*x-3*x^2+4*x^3-5*x^4+6*x^5-7*x^6+8*x^7-9*x^8+10*x^9)/(1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10) lgdogf A015967 18.237 1-x+x^2-x^3+x^4-x^5+x^6-x^7+x^8-x^9+x^10 ogf A015967 56.1137 x^10-x^21+x-1 ogf_with_Euler_Transform A015967 6.88187 {a(n+2)+a(n+1),a(0)=1,a(1)=-1,a(2)=1,a(3)=-1,a(4)=1,a(5)=-1,a(6)=1,a(7)=-1,a(8)=1,a(9)=-1,a(10)=1,a(11)=0} ogf A015968 7.63796 (-1+111*x)/(-1+113*x) ogf A015968 6.97379 -1+111*x+(1-113*x)*f(x) ogf A015968 3.4127 1/222+113/222*x-1/222*(1-218*x+12769*x^2)^(1/2) revogf A015968 7.63796 2/(113*x-1)/(111*x-1) lgdogf A015968 4.86052 {a(n+2)-113*a(n+1),a(0)=1,a(1)=2} ogf A015970 7.10893 (x+x^2+1+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^3+x^4+x^32+x^33+x^34+x^35+x^36)/(1-x^16+x^32) ogf A015970 16.7455 -(1+x^32+x^16-x^37)/(x^33-1+x-x^16+x^17-x^32) ogf A015972 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A015972 117.918 1-x^12 ogf_with_Euler_Transform A015972 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A015972 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A015978 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A015978 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A015978 117.918 1-x^10 ogf_with_Euler_Transform A015978 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A015978 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A015981 23.3039 -(1+x^24-x^34)/(-1+x^2-x^24+x^26) ogf A015981 23.3039 -(1-x^24+x^34)/(-1-x^2+x^24+x^26) ogf A015981 8.73896 -(1-x^24+x^34)/(x-1)/(x+1)/(x^8-x^4+1)/(1+x^2+x)/(1-x+x^2)/(x^4-x^2+1)/(x^4+1)/(x^2+1)^2 ogf A015981 12.0161 2*x*(-17+29*x^24+289*x^32+272*x^34)/(1+x^2)/(17*x^34-29*x^24+17) lgdogf A015985 14.1975 -(x-1)*(x+1)*(x^2+1)*(x^44-x^16-x^8-1)/(x^44-1+x^24) ogf A015989 8.10532 (x-1)*(x+1)*(x^2+1)*(1+x^2+x)*(1-x+x^2)*(x^4-x^2+1)*(x^6+x^3+1)*(x^6-x^3+1)/(-1-x^30+x^36) ogf A015989 22.1054 -(-1-x^6+x^18+x^24)/(1+x^30-x^36) ogf A015989 19.1968 -(1-x^12+x^30+x^18)/(-1+x^6+x^42-x^30) ogf A015990 6.40298 -(-1397-90*x-90*x^3+1307*x^8-90*x^2-90*x^4-90*x^5-90*x^6-459*x^7+63*x^15+27*x^14)/(x+1)/(x^2+1)/(x^4+1)/(x-1)^2 ogf A015990 7.48138 -(-1397-90*x-90*x^6-90*x^3-90*x^4+1307*x^8-459*x^7+27*x^14+63*x^15-90*x^2-90*x^5)/(x^9+1-x-x^8) ogf A015993 6.83395 -(-2069-90*x-90*x^6-90*x^3-90*x^4-90*x^8-90*x^9+1970*x^11-90*x^7-90*x^10-90*x^2-90*x^5)/(-x^11+1-x+x^12) ogf A015997 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A015997 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A016000 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A016000 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A016000 117.918 1-x^10 ogf_with_Euler_Transform A016000 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A016000 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A016015 23.5702 (x^34+x^42-1)/(x+1)/(x^42+x^17-1) ogf A016015 18.9712 -(x^34+x^42-1)/(-x^18+1+x-x^17-x^43-x^42) ogf A016015 18.9712 -(x^34-x^42-1)/(-x^18+1-x+x^17-x^43+x^42) ogf A016022 6.86633 (x^33-x^28-1)/(x-1)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(1+x^2+x)/(x^4+1)/(x^24-x^20+x^16-x^12+x^8-x^4+1) ogf A016023 9.47719 (19-361*x^18-53*x^34+722*x^37+684*x^38-380*x^19)/(x+1)/(38*x^38+53*x^34+19*x^19-19) lgdogf A016023 8.55007 (x^4-x^2+1)*(x^34+x^32+x^30-x^26-x^24+x^20+x^18-x^14-x^12+x^8+x^6-x^2-1)/(x+1)/(x^34+x^19-1) ogf A016023 18.7287 -(-1+x^34+x^38)/(-x^20+1+x-x^19-x^34-x^35) ogf A016023 19.6652 -(1+x^34-x^38)/(x^20-1+x-x^19-x^34+x^35) ogf A016028 25.0824 -(1-x+x^4)/(-3*x^2-1+3*x+x^3) ogf A016028 40.4105 -(1-x+x^4)/(x-1)^3 ogf A016028 10.6969 -8+8*x-8*x^4+(7-23*x-8*x^3-x^4+24*x^2)*f(x)+(1-x^3-3*x+3*x^2)*f(x)^2 ogf A016028 5.12245 {(1725*n+579*n^2)*a(n+1)+(-2296-7839*n-2105*n^2)*a(n+2)+(1668+9785*n+2455*n^2)*a(n+3)+(-3707*n+36-929*n^2)*a(n+4),a(0)=1,a(1)=2,a(2)=3,a(3)=4} ogf A016029 21.3144 -(-1+x-x^2)/(x^2+1-2*x-2*x^3) ogf A016029 12.8775 -(1-4*x^3+2*x^4+5*x^2)/(2*x-1)/(x^2+1)/(x^2-x+1) lgdogf A016029 23.7738 -(1-x+x^2)/(2*x-1)/(x^2+1) ogf A016029 8.95823 3-3*x+3*x^2+(-10+13*x+6*x^3-10*x^2)*f(x)+(7-14*x+7*x^2-14*x^3)*f(x)^2 ogf A016029 11.8869 {a(n+3)-2*a(n+2)+a(n+1)-2*a(n),a(0)=1,a(1)=1,a(2)=2} ogf A016036 9.5743 (-3*(4*x-1)^(3/4)+4*(-1)^(3/4)*x-(-1)^(3/4))/(4*x-1)^(7/4) lgdegf A016036 7.40412 {(-16*n-28)*a(n+1)+(8*n+19)*a(n+2)+(-n-3)*a(n+3),a(0)=4,a(1)=15,a(2)=117/2} lgdegf A016042 117.918 1-x^18 ogf_with_Euler_Transform A016042 8.84383 x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016050 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A016050 117.918 1-x^12 ogf_with_Euler_Transform A016050 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016050 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A016051 25.3965 -(-3-3*x-3*x^2)/(-x^2+1-x+x^3) ogf A016051 19.0474 -(2+6*x+3*x^2+x^3)/(x-1)/(x+1)/(x^2+x+1) lgdogf A016051 9.76789 -387-387*x-387*x^2+(114-144*x+129*x^3-144*x^2)*f(x)+(5-5*x-5*x^2+5*x^3)*f(x)^2 ogf A016051 30.4758 3*(1+x^2+x)/(x+1)/(x-1)^2 ogf A016051 25.3965 {a(n+3),a(0)=2,a(1)=1,a(2)=-1} ogf_with_Euler_Transform A016051 15.5489 {a(n+3)-a(n+2)-a(n+1)+a(n),a(0)=3,a(1)=6,a(2)=12} ogf A016053 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A016053 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A016056 117.918 1-x^22 ogf_with_Euler_Transform A016056 7.07506 x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016061 55.9007 (x+3)/(x-1)^4 ogf A016061 20.7631 -(-3*x-x^2)/(1-4*x+x^4+6*x^2-4*x^3) ogf A016061 33.0322 -(13+3*x)/(x+3)/(-1+x) lgdogf A016061 5.22812 -1042089*x-347363*x^2+(347363-1923212*x-1389452*x^3+347363*x^4+1906258*x^2)*f(x)+(177920*x^4+177920-711680*x-711680*x^3+1067520*x^2)*f(x)^2 ogf A016061 10.532 {(6+3*n)*a(n+3)+(-15-2*n)*a(n+2)+(-3-n)*a(n+1),a(0)=0,a(1)=3,a(2)=13} ogf A016063 23.0709 -(-x^13-1+x^66)/(-x^66+1+x-x^67) ogf A016063 24.6089 -(x^13-1-x^66)/(x^66+1-x-x^67) ogf A016064 22.313 -(-1+2*x-3*x^2)/(5*x^2+1-5*x-x^3) ogf A016064 23.0103 -(1-2*x+3*x^2)/(x-1)/(x^2-4*x+1) ogf A016064 12.6954 -(3-4*x+3*x^4-4*x^3-2*x^2)/(x-1)/(x^2-4*x+1)/(3*x^2-2*x+1) lgdogf A016064 9.95041 -7+14*x-21*x^2+(22-65*x-7*x^3+80*x^2)*f(x)+(-75*x^2-15+75*x+15*x^3)*f(x)^2 ogf A016064 13.893 {a(n+3)-5*a(n+2)+5*a(n+1)-a(n),a(0)=1,a(1)=3,a(2)=13} ogf A016065 6.3315 {(n^2+7*n+12)*a(n+1)+(-n^2-7*n-13)*a(n+2)+a(n+3),a(0)=1,a(1)=3,a(2)=15} ogf A016068 24.2404 -(-x^29+1-x^42)/(x^42-1+x-x^43) ogf A016068 25.0484 -(x^29-1-x^42)/(x^42+1-x-x^43) ogf A016074 9.0991 (-x^24-1+x^35)/(x-1)/(x^6+x^5+x^4+x^3+x^2+x+1)/(x^4+x^3+x^2+x+1)/(x^8+1)/(x^16-x^8+1) ogf A016075 12.5496 -1/(-1+38*x-539*x^2+3382*x^3-7920*x^4) ogf A016075 7.01302 -2*(-19+539*x+15840*x^3-5073*x^2)/(9*x-1)/(10*x-1)/(11*x-1)/(-1+8*x) lgdogf A016075 13.6253 1/(9*x-1)/(10*x-1)/(11*x-1)/(8*x-1) ogf A016077 6.18202 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10-7*x^12+8*x^14-9*x^16+10*x^18)/(1-x^2+x^4-x^6+x^8-x^10+x^12-x^14+x^16-x^18+x^20) lgdogf A016077 15.5208 x^20-x^18+x^16-x^14+x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A016080 117.918 1-x^18 ogf_with_Euler_Transform A016080 8.84383 x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016083 23.5702 (x^34+x^44-1)/(x+1)/(x^44+x^17-1) ogf A016083 18.9712 -(x^34+x^44-1)/(-x^18+1+x-x^17-x^45-x^44) ogf A016083 18.9712 -(x^34-x^44-1)/(-x^18+1-x+x^17-x^45+x^44) ogf A016084 17.3651 (5+6*x^3-4*x^2+2*x^4)/(x+1)/(1-x+x^2)/(x-1)^2 ogf A016084 15.9475 -(-5-2*x^4+4*x^2-6*x^3)/(1-2*x+x^2+x^3-2*x^4+x^5) ogf A016084 9.08639 -(10-8*x+2*x^7+3*x^2+27*x^3-12*x^5+14*x^6)/(x-1)/(x+1)/(x^2-x+1)/(2*x^4+6*x^3-4*x^2+5) lgdogf A016086 13.0344 -(-31+961*x^30+67*x^36-930*x^31)/(x-1)/(67*x^36+31*x^31-31) lgdogf A016086 24.8074 -(-x^31+1-x^36)/(x^36-1+x-x^37) ogf A016086 7.32408 -(x^31-1+x^36)/(x+1)/(x^2+1)/(1+x^2+x)/(1-x+x^2)/(x^4-x^2+1)/(x^6+x^3+1)/(x^6-x^3+1)/(x^12-x^6+1)/(x-1)^2 ogf A016086 25.6343 -(x^31-1-x^36)/(x^36+1-x-x^37) ogf A016091 7.0538 -(-39+1132*x+34560*x^3-10872*x^2)/(12*x-1)/(9*x-1)/(-1+8*x)/(10*x-1) lgdogf A016091 12.6226 -1/(-1+39*x-566*x^2+3624*x^3-8640*x^4) ogf A016091 13.7045 1/(12*x-1)/(9*x-1)/(8*x-1)/(10*x-1) ogf A016092 12.8415 -1/(-1+40*x-595*x^2+3900*x^3-9504*x^4) ogf A016092 7.17612 -2*(-20+595*x+19008*x^3-5850*x^2)/(11*x-1)/(-1+8*x)/(12*x-1)/(9*x-1) lgdogf A016092 13.9422 1/(11*x-1)/(8*x-1)/(12*x-1)/(9*x-1) ogf A016093 7.15248 -(-41+1252*x+42240*x^3-12648*x^2)/(-1+12*x)/(10*x-1)/(11*x-1)/(8*x-1) lgdogf A016093 12.6544 -1/(-1+41*x-626*x^2+4216*x^3-10560*x^4) ogf A016093 13.7089 1/(12*x-1)/(10*x-1)/(11*x-1)/(8*x-1) ogf A016094 12.6544 -1/(-1+42*x-659*x^2+4578*x^3-11880*x^4) ogf A016094 7.15248 -2*(-21+659*x+23760*x^3-6867*x^2)/(9*x-1)/(-1+12*x)/(10*x-1)/(11*x-1) lgdogf A016094 13.7089 1/(9*x-1)/(12*x-1)/(10*x-1)/(11*x-1) ogf A016102 49.9869 -1+x^6+x^12+x^22 ogf_with_Euler_Transform A016103 12.0454 -(15-148*x+360*x^2)/(6*x-1)/(-1+4*x)/(5*x-1) lgdogf A016103 20.3846 -1/(6*x-1)/(4*x-1)/(5*x-1) ogf A016103 4.41666 -5772600+(12191257-86589000*x-692712000*x^3+427172400*x^2)*f(x)+(-474980618*x^2+770238840*x^3-6418657+96279855*x)*f(x)^2 ogf A016103 21.2 1/(1-15*x+74*x^2-120*x^3) ogf A016103 8.68851 {a(n+3)-15*a(n+2)+74*a(n+1)-120*a(n),a(0)=1,a(1)=15,a(2)=151} ogf A016109 12.0389 -1/(-1+34*x-431*x^2+2414*x^3-5040*x^4) ogf A016109 6.93148 -2*(-17+431*x+10080*x^3-3621*x^2)/(9*x-1)/(8*x-1)/(7*x-1)/(10*x-1) lgdogf A016109 13.4552 1/(9*x-1)/(8*x-1)/(7*x-1)/(10*x-1) ogf A016110 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A016110 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A016110 117.918 1-x^10 ogf_with_Euler_Transform A016110 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A016110 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A016111 5.20547 -(65-3370*x+1801800*x^4-561096*x^3+65325*x^2)/(13*x-1)/(15*x-1)/(12*x-1)/(14*x-1)/(11*x-1) lgdogf A016111 9.96793 -1/(13*x-1)/(15*x-1)/(12*x-1)/(14*x-1)/(11*x-1) ogf A016111 9.18613 1/(1-65*x+1685*x^2-21775*x^3+140274*x^4-360360*x^5) ogf A016116 24.9493 -(1+4*x+2*x^2)/(1+x)/(2*x^2-1) lgdogf A016116 44.0282 -(1+x)/(-1+2*x^2) ogf A016116 44.0282 -(x+1)/(-1+2*x^2) ogf A016116 16.2713 -5-5*x+(11+6*x-10*x^2)*f(x)+(-6+12*x^2)*f(x)^2 ogf A016116 17.4065 1/2*2^(1/2)*(-ln(1+2^(1/2))+arcsinh(1+2*x)) revegf A016116 20.7911 1/2/(2*x+1)*(-1+(1+8*x^2+4*x)^(1/2)) revogf A016116 24.9493 {-a(n+2)+2*a(n),a(0)=1,a(1)=1} ogf A016117 23.1707 -(1+x^28-x^34)/(-1+x^2-x^28+x^30) ogf A016117 23.1707 -(1-x^28+x^34)/(-1-x^2+x^28+x^30) ogf A016117 11.9474 2*x*(-17+31*x^28+289*x^32+272*x^34)/(1+x^2)/(17*x^34-31*x^28+17) lgdogf A016123 28.5995 -1/(-1+12*x-11*x^2) ogf A016123 13.5847 -1/22*(-1-12*x+(1+24*x+100*x^2)^(1/2))/x revogf A016123 10.0628 -11+(-50-132*x+121*x^2)*f(x)+(61-732*x+671*x^2)*f(x)^2 ogf A016123 20.1255 -2*(-6+11*x)/(11*x-1)/(x-1) lgdogf A016123 33.9618 1/(11*x-1)/(x-1) ogf A016123 12.9378 {-a(n+2)+12*a(n+1)-11*a(n),a(0)=1,a(1)=12} ogf A016124 9.6092 3*x^2*(-1+3*x^6-4*x^9+5*x^12-7*x^18+8*x^21)/(1-x^3+x^9-x^12+x^15-x^21+x^24) lgdogf A016125 18.8517 -(-13+24*x)/(12*x-1)/(x-1) lgdogf A016125 25.7971 -1/(-1+13*x-12*x^2) ogf A016125 12.2536 -1/24*(-1-13*x+(1+26*x+121*x^2)^(1/2))/x revogf A016125 8.45078 -24+(-121-312*x+288*x^2)*f(x)+(145-1885*x+1740*x^2)*f(x)^2 ogf A016125 30.6341 1/(12*x-1)/(x-1) ogf A016125 11.6701 {-a(n+2)+13*a(n+1)-12*a(n),a(0)=1,a(1)=13} ogf A016126 23.9568 -(-x^29+1-x^44)/(x^44-1+x-x^45) ogf A016126 24.7554 -(x^29-1-x^44)/(x^44+1-x-x^45) ogf A016127 18.5291 -(-7+20*x)/(-1+5*x)/(2*x-1) lgdogf A016127 27.7937 -1/(-1+7*x-10*x^2) ogf A016127 13.5213 -1/20*(-1-7*x+(1+14*x+9*x^2)^(1/2))/x revogf A016127 9.43938 -20+(-9-140*x+200*x^2)*f(x)+(29-203*x+290*x^2)*f(x)^2 ogf A016127 29.4286 1/(5*x-1)/(2*x-1) ogf A016127 12.5072 {-a(n+2)+7*a(n+1)-10*a(n),a(0)=1,a(1)=7} ogf A016128 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A016128 117.918 1-x^12 ogf_with_Euler_Transform A016128 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016128 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A016129 29.9573 -1/(-1+8*x-12*x^2) ogf A016129 14.1903 -1/24*(-1-8*x+(1+16*x+16*x^2)^(1/2))/x revogf A016129 9.29709 -135+(14-1080*x+1620*x^2)*f(x)+(1452*x^2+121-968*x)*f(x)^2 ogf A016129 19.9715 -8*(-1+3*x)/(6*x-1)/(2*x-1) lgdogf A016129 31.7195 1/(6*x-1)/(2*x-1) ogf A016129 13.4808 {-a(n+2)+8*a(n+1)-12*a(n),a(0)=1,a(1)=8} ogf A016130 19.7051 -(-9+28*x)/(7*x-1)/(2*x-1) lgdogf A016130 28.4629 -1/(-1+9*x-14*x^2) ogf A016130 13.4824 -1/28*(-1-9*x+(1+18*x+25*x^2)^(1/2))/x revogf A016130 9.48764 -28+(-25-252*x+392*x^2)*f(x)+(53-477*x+742*x^2)*f(x)^2 ogf A016130 30.1372 1/(7*x-1)/(2*x-1) ogf A016130 12.8083 {-a(n+2)+9*a(n+1)-14*a(n),a(0)=1,a(1)=9} ogf A016131 32.007 -1/(-1+10*x-16*x^2) ogf A016131 13.2203 -1/32*(-1-10*x+(2*x+1)^(1/2)*(1+18*x)^(1/2))/x revogf A016131 20.9701 -2*(-5+16*x)/(-1+8*x)/(2*x-1) lgdogf A016131 10.1356 -284+(-57-2840*x+4544*x^2)*f(x)+(5456*x^2+341-3410*x)*f(x)^2 ogf A016131 35.7725 1/(8*x-1)/(2*x-1) ogf A016131 14.4794 {-a(n+2)+10*a(n+1)-16*a(n),a(0)=1,a(1)=10} ogf A016132 7.14653 (5*x^4+6*x^5+1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3)/(x^2+1+x+x^8+x^4+x^9+x^3+x^10+x^6+x^5+x^7) lgdogf A016132 17.6877 1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x ogf A016132 117.918 1-x^10 ogf_with_Euler_Transform A016132 8.22682 {-a(n),a(0)=1,a(1)=0,a(2)=0,a(3)=0,a(4)=0,a(5)=0,a(6)=0,a(7)=0,a(8)=0,a(9)=0,a(10)=-1} ogf_with_Euler_Transform A016132 7.00501 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=0} ogf A016133 20.9382 -(-11+36*x)/(9*x-1)/(2*x-1) lgdogf A016133 29.7543 -1/(-1+11*x-18*x^2) ogf A016133 14.4957 -1/36*(-1-11*x+(1+22*x+49*x^2)^(1/2))/x revogf A016133 10.2788 -36+(-49-396*x+648*x^2)*f(x)+(85-935*x+1530*x^2)*f(x)^2 ogf A016133 33.2549 1/(9*x-1)/(2*x-1) ogf A016133 13.4603 {-a(n+2)+11*a(n+1)-18*a(n),a(0)=1,a(1)=11} ogf A016134 28.5995 -1/(-1+12*x-20*x^2) ogf A016134 13.9331 -1/40*(-1-12*x+(1+24*x+64*x^2)^(1/2))/x revogf A016134 18.113 -4*(-3+10*x)/(10*x-1)/(-1+2*x) lgdogf A016134 8.62523 -515+(-266-6180*x+10300*x^2)*f(x)+(15620*x^2+781-9372*x)*f(x)^2 ogf A016134 30.1883 1/(10*x-1)/(2*x-1) ogf A016134 12.9378 {-a(n+2)+12*a(n+1)-20*a(n),a(0)=1,a(1)=12} ogf A016135 18.7376 -(-13+44*x)/(11*x-1)/(-1+2*x) lgdogf A016135 28.5995 -1/(-1+13*x-22*x^2) ogf A016135 13.9331 -1/44*(-1-13*x+(1+26*x+81*x^2)^(1/2))/x revogf A016135 9.53315 -44+(-81-572*x+968*x^2)*f(x)+(125-1625*x+2750*x^2)*f(x)^2 ogf A016135 30.1883 1/(11*x-1)/(2*x-1) ogf A016135 12.9378 {-a(n+2)+13*a(n+1)-22*a(n),a(0)=1,a(1)=13} ogf A016136 25.9462 -1/(-1+14*x-24*x^2) ogf A016136 12.3245 -1/48*(-1-14*x+(1+28*x+100*x^2)^(1/2))/x revogf A016136 9.12923 -12+(-25-168*x+288*x^2)*f(x)+(37-518*x+888*x^2)*f(x)^2 ogf A016136 16.9993 -2*(-7+24*x)/(12*x-1)/(2*x-1) lgdogf A016136 27.3877 1/(12*x-1)/(2*x-1) ogf A016136 11.7376 {-a(n+2)+14*a(n+1)-24*a(n),a(0)=1,a(1)=14} ogf A016137 30.2902 -1/(-1+9*x-18*x^2) ogf A016137 14.7358 -1/36*(-1-9*x+(1+18*x+9*x^2)^(1/2))/x revogf A016137 10.2872 -50+(19-450*x+900*x^2)*f(x)+(558*x^2+31-279*x)*f(x)^2 ogf A016137 20.1934 -9*(-1+4*x)/(6*x-1)/(3*x-1) lgdogf A016137 32.0719 1/(6*x-1)/(3*x-1) ogf A016137 13.6306 {-a(n+2)+9*a(n+1)-18*a(n),a(0)=1,a(1)=9} ogf A016138 27.4298 -1/(-1+10*x-21*x^2) ogf A016138 13.3632 -1/42*(-1-10*x+(1+20*x+16*x^2)^(1/2))/x revogf A016138 9.83332 -21+(-8-210*x+441*x^2)*f(x)+(29-290*x+609*x^2)*f(x)^2 ogf A016138 30.6568 1/(7*x-1)/(3*x-1) ogf A016138 12.4087 {-a(n+2)+10*a(n+1)-21*a(n),a(0)=1,a(1)=10} ogf A016140 28.6695 -1/(-1+11*x-24*x^2) ogf A016140 13.9672 -1/48*(-1-11*x+(1+22*x+25*x^2)^(1/2))/x revogf A016140 9.72717 -48+(-25-528*x+1152*x^2)*f(x)+(73-803*x+1752*x^2)*f(x)^2 ogf A016140 32.0424 1/(8*x-1)/(3*x-1) ogf A016140 12.9696 {-a(n+2)+11*a(n+1)-24*a(n),a(0)=1,a(1)=11} ogf A016142 29.9093 -1/(-1+12*x-27*x^2) ogf A016142 14.5712 -1/54*(-1-12*x+(1+24*x+36*x^2)^(1/2))/x revogf A016142 11.8391 -3+(-2-36*x+81*x^2)*f(x)+(5-60*x+135*x^2)*f(x)^2 ogf A016142 21.0473 -6*(-2+9*x)/(9*x-1)/(3*x-1) lgdogf A016142 33.4281 1/(9*x-1)/(3*x-1) ogf A016142 13.5304 {-a(n+2)+12*a(n+1)-27*a(n),a(0)=1,a(1)=12} ogf A016143 7.29479 (-5*x^4+6*x^5-1-7*x^6+8*x^7+2*x-9*x^8-3*x^2+10*x^9+4*x^3)/(x^2+1-x+x^8+x^4-x^9-x^3+x^10+x^6-x^5-x^7) lgdogf A016143 52.1056 -1+x+x^10-x^21 ogf_with_Euler_Transform A016143 18.237 x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1 ogf A016143 6.88187 {a(n+2)+a(n+1),a(0)=1,a(1)=-1,a(2)=1,a(3)=-1,a(4)=1,a(5)=-1,a(6)=1,a(7)=-1,a(8)=1,a(9)=-1,a(10)=1,a(11)=0} ogf A016145 19.4068 -(-13+60*x)/(10*x-1)/(3*x-1) lgdogf A016145 28.5995 -1/(-1+13*x-30*x^2) ogf A016145 13.9331 -1/60*(-1-13*x+(1+26*x+49*x^2)^(1/2))/x revogf A016145 9.36879 -60+(-49-780*x+1800*x^2)*f(x)+(109-1417*x+3270*x^2)*f(x)^2 ogf A016145 30.1883 1/(10*x-1)/(3*x-1) ogf A016145 12.9378 {-a(n+2)+13*a(n+1)-30*a(n),a(0)=1,a(1)=13} ogf A016146 28.5995 -1/(-1+14*x-33*x^2) ogf A016146 13.9331 -1/66*(-1-14*x+(1+28*x+64*x^2)^(1/2))/x revogf A016146 18.7376 -2*(-7+33*x)/(11*x-1)/(3*x-1) lgdogf A016146 9.70338 -33+(-32-462*x+1089*x^2)*f(x)+(65-910*x+2145*x^2)*f(x)^2 ogf A016146 30.1883 1/(11*x-1)/(3*x-1) ogf A016146 12.9378 {-a(n+2)+14*a(n+1)-33*a(n),a(0)=1,a(1)=14} ogf A016147 25.9462 -1/(-1+15*x-36*x^2) ogf A016147 10.7169 -1/72*(-1-15*x+(1+27*x)^(1/2)*(1+3*x)^(1/2))/x revogf A016147 16.9993 -3*(-5+24*x)/(12*x-1)/(3*x-1) lgdogf A016147 9.48036 -8+(-9-120*x+288*x^2)*f(x)+(17-255*x+612*x^2)*f(x)^2 ogf A016147 27.3877 1/(12*x-1)/(3*x-1) ogf A016147 11.7376 {-a(n+2)+15*a(n+1)-36*a(n),a(0)=1,a(1)=15} ogf A016149 26.19 -1/(-1+10*x-24*x^2) ogf A016149 13.095 -1/48*(-1-10*x+(1+20*x+4*x^2)^(1/2))/x revogf A016149 9.38887 -12+(-1-120*x+288*x^2)*f(x)+(13-130*x+312*x^2)*f(x)^2 ogf A016149 17.7718 -2*(-5+24*x)/(6*x-1)/(4*x-1) lgdogf A016149 29.2712 1/(6*x-1)/(4*x-1) ogf A016149 11.8479 {-a(n+2)+10*a(n+1)-24*a(n),a(0)=1,a(1)=10} ogf A016150 19.4115 -(-11+56*x)/(7*x-1)/(4*x-1) lgdogf A016150 27.5848 -1/(-1+11*x-28*x^2) ogf A016150 13.7924 -1/56*(-1-11*x+(1+22*x+9*x^2)^(1/2))/x revogf A016150 9.52928 -56+(-9-616*x+1568*x^2)*f(x)+(65-715*x+1820*x^2)*f(x)^2 ogf A016150 30.83 1/(7*x-1)/(4*x-1) ogf A016150 12.4788 {-a(n+2)+11*a(n+1)-28*a(n),a(0)=1,a(1)=11} ogf A016152 14.5178 -1/64*(-1-12*x+(1+24*x+16*x^2)^(1/2))/x revogf A016152 19.5239 -4*(-3+16*x)/(8*x-1)/(-1+4*x) lgdogf A016152 33.3055 1/(8*x-1)/(4*x-1) ogf A016152 24.6171 x+(-1+12*x-32*x^2)*f(x) ogf A016152 33.3055 x/(1-12*x+32*x^2) ogf A016152 14.1548 {a(n+2)-12*a(n+1)+32*a(n),a(0)=0,a(1)=1} ogf A016153 21.8577 -(-13+72*x)/(9*x-1)/(4*x-1) lgdogf A016153 13.4127 -1/72*(-1-13*x+(1+x)^(1/2)*(1+25*x)^(1/2))/x revogf A016153 34.7152 1/(9*x-1)/(4*x-1) ogf A016153 25.6591 x+(-1+13*x-36*x^2)*f(x) ogf A016153 34.7152 x/(1-13*x+36*x^2) ogf A016153 14.754 {a(n+2)-13*a(n+1)+36*a(n),a(0)=0,a(1)=1} ogf A016156 117.918 1-x^18 ogf_with_Euler_Transform A016156 8.84383 x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016157 28.5995 -1/(-1+14*x-40*x^2) ogf A016157 13.9331 -1/80*(-1-14*x+(1+28*x+36*x^2)^(1/2))/x revogf A016157 18.113 -2*(-7+40*x)/(10*x-1)/(-1+4*x) lgdogf A016157 10.0628 -20+(-9-280*x+800*x^2)*f(x)+(29-406*x+1160*x^2)*f(x)^2 ogf A016157 30.1883 1/(10*x-1)/(4*x-1) ogf A016157 12.9378 {-a(n+2)+14*a(n+1)-40*a(n),a(0)=1,a(1)=14} ogf A016158 18.7376 -(-15+88*x)/(11*x-1)/(-1+4*x) lgdogf A016158 28.5995 -1/(-1+15*x-44*x^2) ogf A016158 13.9331 -1/88*(-1-15*x+(1+30*x+49*x^2)^(1/2))/x revogf A016158 9.20999 -88+(-49-1320*x+3872*x^2)*f(x)+(137-2055*x+6028*x^2)*f(x)^2 ogf A016158 30.1883 1/(11*x-1)/(4*x-1) ogf A016158 12.9378 {-a(n+2)+15*a(n+1)-44*a(n),a(0)=1,a(1)=15} ogf A016159 26.0954 -1/(-1+16*x-48*x^2) ogf A016159 12.7131 -1/96*(-1-16*x+(1+32*x+64*x^2)^(1/2))/x revogf A016159 8.40359 -135+(14-2160*x+6480*x^2)*f(x)+(5808*x^2+121-1936*x)*f(x)^2 ogf A016159 17.7076 -16*(6*x-1)/(12*x-1)/(4*x-1) lgdogf A016159 27.5451 1/(12*x-1)/(4*x-1) ogf A016159 11.805 {-a(n+2)+16*a(n+1)-48*a(n),a(0)=1,a(1)=16} ogf A016160 4.97342 -(-11+60*x)/(6*x-1)/(5*x-1) lgdogf A016160 3.73007 -1/60*(-1-11*x+(1+22*x+x^2)^(1/2))/x revogf A016160 7.89896 1/(6*x-1)/(5*x-1) ogf A016160 5.83837 x+(-1+11*x-30*x^2)*f(x) ogf A016160 7.89896 x/(1-11*x+30*x^2) ogf A016160 3.35706 {a(n+2)-11*a(n+1)+30*a(n),a(0)=0,a(1)=1} ogf A016161 28.0497 -1/(-1+12*x-35*x^2) ogf A016161 14.0248 -1/70*(-1-12*x+(1+24*x+4*x^2)^(1/2))/x revogf A016161 19.0337 -2*(-6+35*x)/(7*x-1)/(5*x-1) lgdogf A016161 9.68988 -35+(-2-420*x+1225*x^2)*f(x)+(37-444*x+1295*x^2)*f(x)^2 ogf A016161 31.3496 1/(7*x-1)/(5*x-1) ogf A016161 12.6891 {-a(n+2)+12*a(n+1)-35*a(n),a(0)=1,a(1)=12} ogf A016162 20.6111 -(-13+80*x)/(8*x-1)/(5*x-1) lgdogf A016162 29.2894 -1/(-1+13*x-40*x^2) ogf A016162 14.6447 -1/80*(-1-13*x+(1+26*x+9*x^2)^(1/2))/x revogf A016162 9.76314 -80+(-9-1040*x+3200*x^2)*f(x)+(89-1157*x+3560*x^2)*f(x)^2 ogf A016162 32.7352 1/(8*x-1)/(5*x-1) ogf A016162 13.25 {-a(n+2)+13*a(n+1)-40*a(n),a(0)=1,a(1)=13} ogf A016163 30.5292 -1/(-1+14*x-45*x^2) ogf A016163 14.8732 -1/90*(-1-14*x+(1+28*x+16*x^2)^(1/2))/x revogf A016163 20.7162 -2*(-7+45*x)/(9*x-1)/(5*x-1) lgdogf A016163 10.5464 -45+(-8-630*x+2025*x^2)*f(x)+(53-742*x+2385*x^2)*f(x)^2 ogf A016163 34.1209 1/(9*x-1)/(5*x-1) ogf A016163 13.8108 {-a(n+2)+14*a(n+1)-45*a(n),a(0)=1,a(1)=14} ogf A016164 28.5995 -1/(-1+15*x-50*x^2) ogf A016164 13.5847 -1/100*(-1-15*x+(1+30*x+25*x^2)^(1/2))/x revogf A016164 11.0896 -4+(-1-60*x+200*x^2)*f(x)+(5-75*x+250*x^2)*f(x)^2 ogf A016164 18.7376 -5*(-3+20*x)/(10*x-1)/(5*x-1) lgdogf A016164 30.1883 1/(10*x-1)/(5*x-1) ogf A016164 12.9378 {-a(n+2)+15*a(n+1)-50*a(n),a(0)=1,a(1)=15} ogf A016165 28.5995 -1/(-1+16*x-55*x^2) ogf A016165 13.5847 -1/110*(-1-16*x+(1+32*x+36*x^2)^(1/2))/x revogf A016165 18.7376 -2*(-8+55*x)/(11*x-1)/(5*x-1) lgdogf A016165 9.53315 -55+(-18-880*x+3025*x^2)*f(x)+(73-1168*x+4015*x^2)*f(x)^2 ogf A016165 30.1883 1/(11*x-1)/(5*x-1) ogf A016165 12.9378 {-a(n+2)+16*a(n+1)-55*a(n),a(0)=1,a(1)=16} ogf A016166 17.1947 -(-17+120*x)/(12*x-1)/(5*x-1) lgdogf A016166 26.2445 -1/(-1+17*x-60*x^2) ogf A016166 12.4661 -1/120*(-1-17*x+(1+34*x+49*x^2)^(1/2))/x revogf A016166 8.17451 -120+(-49-2040*x+7200*x^2)*f(x)+(169-2873*x+10140*x^2)*f(x)^2 ogf A016166 27.7025 1/(12*x-1)/(5*x-1) ogf A016166 11.8725 {-a(n+2)+17*a(n+1)-60*a(n),a(0)=1,a(1)=17} ogf A016167 5.82439 (-1+2*x-3*x^2+4*x^3-5*x^4+6*x^5-7*x^6+8*x^7-9*x^8+10*x^9-11*x^10+12*x^11)/(1-x-x^3-x^5-x^7-x^9-x^11+x^2+x^4+x^6+x^8+x^10+x^12) lgdogf A016167 14.6775 x^12-x^11+x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1 ogf A016167 5.96645 {a(n+2)+a(n+1),a(0)=1,a(1)=-1,a(2)=1,a(3)=-1,a(4)=1,a(5)=-1,a(6)=1,a(7)=-1,a(8)=1,a(9)=-1,a(10)=1,a(11)=-1,a(12)=1,a(13)=0} ogf A016168 117.918 1-x^16 ogf_with_Euler_Transform A016168 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016169 20.8592 -(-13+84*x)/(7*x-1)/(6*x-1) lgdogf A016169 15.6444 -1/84*(-1-13*x+(1+26*x+x^2)^(1/2))/x revogf A016169 33.1292 1/(7*x-1)/(6*x-1) ogf A016169 24.4868 x+(-1+13*x-42*x^2)*f(x) ogf A016169 33.1292 x/(1-13*x+42*x^2) ogf A016169 14.0799 {a(n+2)-13*a(n+1)+42*a(n),a(0)=0,a(1)=1} ogf A016170 29.9093 -1/(-1+14*x-48*x^2) ogf A016170 14.9547 -1/96*(-1-14*x+(1+28*x+4*x^2)^(1/2))/x revogf A016170 8.74272 -1620+(839-22680*x+77760*x^2)*f(x)+(37488*x^2+781-10934*x)*f(x)^2 ogf A016170 19.5958 -2*(-7+48*x)/(-1+8*x)/(6*x-1) lgdogf A016170 33.4281 1/(8*x-1)/(6*x-1) ogf A016170 13.5304 {-a(n+2)+14*a(n+1)-48*a(n),a(0)=1,a(1)=14} ogf A016172 27.5346 -1/(-1+15*x-54*x^2) ogf A016172 13.4143 -1/108*(-1-15*x+(1+30*x+9*x^2)^(1/2))/x revogf A016172 9.87089 -12+(-1-180*x+648*x^2)*f(x)+(13-195*x+702*x^2)*f(x)^2 ogf A016172 18.6842 -3*(-5+36*x)/(9*x-1)/(6*x-1) lgdogf A016172 30.7739 1/(9*x-1)/(6*x-1) ogf A016172 12.4561 {-a(n+2)+15*a(n+1)-54*a(n),a(0)=1,a(1)=15} ogf A016173 28.5995 -1/(-1+16*x-60*x^2) ogf A016173 13.5847 -1/120*(-1-16*x+(1+32*x+16*x^2)^(1/2))/x revogf A016173 10.0628 -15+(-2-240*x+900*x^2)*f(x)+(17-272*x+1020*x^2)*f(x)^2 ogf A016173 18.7376 -8*(-2+15*x)/(10*x-1)/(6*x-1) lgdogf A016173 30.1883 1/(10*x-1)/(6*x-1) ogf A016173 12.9378 {-a(n+2)+16*a(n+1)-60*a(n),a(0)=1,a(1)=16} ogf A016174 18.9369 -(-17+132*x)/(11*x-1)/(6*x-1) lgdogf A016174 28.9037 -1/(-1+17*x-66*x^2) ogf A016174 13.7293 -1/132*(-1-17*x+(1+34*x+25*x^2)^(1/2))/x revogf A016174 9.00279 -132+(-25-2244*x+8712*x^2)*f(x)+(157-2669*x+10362*x^2)*f(x)^2 ogf A016174 30.5095 1/(11*x-1)/(6*x-1) ogf A016174 13.0755 {-a(n+2)+17*a(n+1)-66*a(n),a(0)=1,a(1)=17} ogf A016175 26.3936 -1/(-1+18*x-72*x^2) ogf A016175 12.537 -1/144*(-1-18*x+(1+36*x+36*x^2)^(1/2))/x revogf A016175 9.11778 -50+(19-900*x+3600*x^2)*f(x)+(2232*x^2+31-558*x)*f(x)^2 ogf A016175 27.8599 1/(12*x-1)/(6*x-1) ogf A016175 11.94 {-a(n+2)+18*a(n+1)-72*a(n),a(0)=1,a(1)=18} ogf A016176 40.5064 -(-1+x^186+x^154)/(x-1)/(x^186-x^143-x^132-x^121-x^110-x^99-x^88-x^77-x^66-x^55-x^44-x^33-x^22-x^11-1) ogf A016177 21.2911 -(-15+112*x)/(8*x-1)/(7*x-1) lgdogf A016177 16.1122 -1/112*(-1-15*x+(1+30*x+x^2)^(1/2))/x revogf A016177 35.0677 1/(8*x-1)/(7*x-1) ogf A016177 25.9196 x+(-1+15*x-56*x^2)*f(x) ogf A016177 35.0677 x/(1-15*x+56*x^2) ogf A016177 14.9038 {a(n+2)-15*a(n+1)+56*a(n),a(0)=0,a(1)=1} ogf A016178 28.1431 -1/(-1+16*x-63*x^2) ogf A016178 13.7107 -1/126*(-1-16*x+(1+32*x+4*x^2)^(1/2))/x revogf A016178 9.38103 -63+(-2-1008*x+3969*x^2)*f(x)+(65-1040*x+4095*x^2)*f(x)^2 ogf A016178 31.454 1/(9*x-1)/(7*x-1) ogf A016178 12.7314 {-a(n+2)+16*a(n+1)-63*a(n),a(0)=1,a(1)=16} ogf A016180 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A016180 117.918 1-x^12 ogf_with_Euler_Transform A016180 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016180 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A016181 18.7376 -(-17+140*x)/(10*x-1)/(7*x-1) lgdogf A016181 28.5995 -1/(-1+17*x-70*x^2) ogf A016181 13.9331 -1/140*(-1-17*x+(1+34*x+9*x^2)^(1/2))/x revogf A016181 9.05649 -140+(-9-2380*x+9800*x^2)*f(x)+(149-2533*x+10430*x^2)*f(x)^2 ogf A016181 30.1883 1/(10*x-1)/(7*x-1) ogf A016181 12.9378 {-a(n+2)+17*a(n+1)-70*a(n),a(0)=1,a(1)=17} ogf A016183 25.648 -1/(-1+18*x-77*x^2) ogf A016183 12.1828 -1/154*(-1-18*x+(1+36*x+16*x^2)^(1/2))/x revogf A016183 16.8039 -2*(-9+77*x)/(11*x-1)/(7*x-1) lgdogf A016183 8.54934 -77+(-8-1386*x+5929*x^2)*f(x)+(85-1530*x+6545*x^2)*f(x)^2 ogf A016183 27.0729 1/(11*x-1)/(7*x-1) ogf A016183 11.6027 {-a(n+2)+18*a(n+1)-77*a(n),a(0)=1,a(1)=18} ogf A016184 16.8104 -(-19+168*x)/(-1+12*x)/(7*x-1) lgdogf A016184 26.5427 -1/(-1+19*x-84*x^2) ogf A016184 12.6078 -1/168*(-1-19*x+(1+38*x+25*x^2)^(1/2))/x revogf A016184 8.13405 -168+(-25-3192*x+14112*x^2)*f(x)+(193-3667*x+16212*x^2)*f(x)^2 ogf A016184 28.0173 1/(12*x-1)/(7*x-1) ogf A016184 12.0074 {-a(n+2)+19*a(n+1)-84*a(n),a(0)=1,a(1)=19} ogf A016185 19.9801 -(-17+144*x)/(9*x-1)/(8*x-1) lgdogf A016185 15.1201 -1/144*(-1-17*x+(1+34*x+x^2)^(1/2))/x revogf A016185 32.9084 1/(9*x-1)/(8*x-1) ogf A016185 24.3236 x+(-1+17*x-72*x^2)*f(x) ogf A016185 32.9084 x/(1-17*x+72*x^2) ogf A016185 13.9861 {a(n+2)-17*a(n+1)+72*a(n),a(0)=0,a(1)=1} ogf A016186 28.5995 -1/(-1+18*x-80*x^2) ogf A016186 13.9331 -1/160*(-1-18*x+(1+36*x+4*x^2)^(1/2))/x revogf A016186 18.113 -2*(-9+80*x)/(10*x-1)/(-1+8*x) lgdogf A016186 9.87981 -40+(-1-720*x+3200*x^2)*f(x)+(41-738*x+3280*x^2)*f(x)^2 ogf A016186 30.1883 1/(10*x-1)/(8*x-1) ogf A016186 12.9378 {-a(n+2)+18*a(n+1)-80*a(n),a(0)=1,a(1)=18} ogf A016187 16.5271 -(-19+176*x)/(11*x-1)/(-1+8*x) lgdogf A016187 26.0954 -1/(-1+19*x-88*x^2) ogf A016187 12.7131 -1/176*(-1-19*x+(1+38*x+9*x^2)^(1/2))/x revogf A016187 8.12806 -176+(-9-3344*x+15488*x^2)*f(x)+(185-3515*x+16280*x^2)*f(x)^2 ogf A016187 27.5451 1/(11*x-1)/(8*x-1) ogf A016187 11.805 {-a(n+2)+19*a(n+1)-88*a(n),a(0)=1,a(1)=19} ogf A016188 26.6918 -1/(-1+20*x-96*x^2) ogf A016188 12.6786 -1/192*(-1-20*x+(1+40*x+16*x^2)^(1/2))/x revogf A016188 9.22081 -12+(-1-240*x+1152*x^2)*f(x)+(13-260*x+1248*x^2)*f(x)^2 ogf A016188 16.9048 -4*(-5+48*x)/(-1+12*x)/(8*x-1) lgdogf A016188 28.1747 1/(12*x-1)/(8*x-1) ogf A016188 12.0749 {-a(n+2)+20*a(n+1)-96*a(n),a(0)=1,a(1)=20} ogf A016189 19.2912 -(-19+180*x)/(10*x-1)/(9*x-1) lgdogf A016189 15.1201 -1/180*(-1-19*x+(1+38*x+x^2)^(1/2))/x revogf A016189 31.0802 1/(10*x-1)/(9*x-1) ogf A016189 24.3236 x+(-1+19*x-90*x^2)*f(x) ogf A016189 32.9084 x/(1-19*x+90*x^2) ogf A016189 13.9861 {a(n+2)-19*a(n+1)+90*a(n),a(0)=0,a(1)=1} ogf A016190 26.3936 -1/(-1+20*x-99*x^2) ogf A016190 12.8584 -1/198*(-1-20*x+(1+40*x+4*x^2)^(1/2))/x revogf A016190 8.64618 -99+(-2-1980*x+9801*x^2)*f(x)+(101-2020*x+9999*x^2)*f(x)^2 ogf A016190 27.8599 1/(11*x-1)/(9*x-1) ogf A016190 11.94 {-a(n+2)+20*a(n+1)-99*a(n),a(0)=1,a(1)=20} ogf A016191 25.4989 -1/(-1+21*x-108*x^2) ogf A016191 13.0764 -1/216*(-1-21*x+(1+42*x+9*x^2)^(1/2))/x revogf A016191 9.27232 -24+(-1-504*x+2592*x^2)*f(x)+(25-525*x+2700*x^2)*f(x)^2 ogf A016191 17.5854 -3*(-7+72*x)/(12*x-1)/(9*x-1) lgdogf A016191 28.3321 1/(12*x-1)/(9*x-1) ogf A016191 11.8599 {-a(n+2)+21*a(n+1)-108*a(n),a(0)=1,a(1)=21} ogf A016192 12.8486 (37-1369*x^36+1332*x^37-59*x^22)/(x-1)/(37*x^37+59*x^22-37) lgdogf A016192 24.4538 -(-1+x^22+x^37)/(1-x-x^22+x^23) ogf A016192 6.59189 -(-1+x^22+x^37)/(x+1)/(1+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x)/(x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1)/(x-1)^2 ogf A016192 24.4538 -(1+x^22-x^37)/(-1+x-x^22+x^23) ogf A016193 13.1834 (1-x^12-x^16+x^4-x^32+x^40+x^44-x^28+x^48)/(1+x^48-x^24) ogf A016194 48.6136 -1+x^4+x^18+x^22 ogf_with_Euler_Transform A016195 16.876 -(-21+220*x)/(11*x-1)/(-1+10*x) lgdogf A016195 14.1394 -1/220*(-1-21*x+(1+42*x+x^2)^(1/2))/x revogf A016195 27.5346 1/(11*x-1)/(10*x-1) ogf A016195 21.7982 x+(-1+21*x-110*x^2)*f(x) ogf A016195 29.0643 x/(1-21*x+110*x^2) ogf A016195 12.7599 {a(n+2)-21*a(n+1)+110*a(n),a(0)=0,a(1)=1} ogf A016196 25.6406 -1/(-1+22*x-120*x^2) ogf A016196 13.149 -1/240*(-1-22*x+(1+44*x+4*x^2)^(1/2))/x revogf A016196 15.5397 -2*(-11+120*x)/(12*x-1)/(-1+10*x) lgdogf A016196 8.99668 -60+(-1-1320*x+7200*x^2)*f(x)+(61-1342*x+7320*x^2)*f(x)^2 ogf A016196 26.9901 1/(12*x-1)/(10*x-1) ogf A016196 11.9258 {-a(n+2)+22*a(n+1)-120*a(n),a(0)=1,a(1)=22} ogf A016197 17.3422 -(-23+264*x)/(-1+12*x)/(11*x-1) lgdogf A016197 14.53 -1/264*(-1-23*x+(1+46*x+x^2)^(1/2))/x revogf A016197 28.2952 1/(12*x-1)/(11*x-1) ogf A016197 22.4004 x+(-1+23*x-132*x^2)*f(x) ogf A016197 29.8672 x/(1-23*x+132*x^2) ogf A016197 13.1124 {a(n+2)-23*a(n+1)+132*a(n),a(0)=0,a(1)=1} ogf A016198 31.1184 -1/(x-1)/(2*x-1)/(5*x-1) ogf A016198 7.7796 -10100+(45071-80800*x-101000*x^3+171700*x^2)*f(x)+(-594507*x^2+349710*x^3-34971+279768*x)*f(x)^2 ogf A016198 18.2157 -2*(3*x-1)*(5*x-4)/(x-1)/(2*x-1)/(-1+5*x) lgdogf A016198 32.4714 1/(1-8*x+17*x^2-10*x^3) ogf A016198 13.1025 {a(n+3)-8*a(n+2)+17*a(n+1)-10*a(n),a(0)=1,a(1)=8,a(2)=47} ogf A016200 14.348 -(9-40*x+36*x^2)/(x-1)/(6*x-1)/(2*x-1) lgdogf A016200 22.7176 -1/(x-1)/(6*x-1)/(2*x-1) ogf A016200 5.99146 -2214+(11363-19926*x-26568*x^3+44280*x^2)*f(x)+(-182980*x^2+109788*x^3-9149+82341*x)*f(x)^2 ogf A016200 23.7053 1/(1-9*x+20*x^2-12*x^3) ogf A016200 9.56531 {a(n+3)-9*a(n+2)+20*a(n+1)-12*a(n),a(0)=1,a(1)=9,a(2)=61} ogf A016201 21.5926 -1/(x-1)/(2*x-1)/(7*x-1) ogf A016201 12.9555 -2*(5-23*x+21*x^2)/(x-1)/(2*x-1)/(7*x-1) lgdogf A016201 4.66866 -256172+(1487567-2561720*x-3586408*x^3+5891956*x^2)*f(x)+(-28322085*x^2+17239530*x^3-1231395+12313950*x)*f(x)^2 ogf A016201 21.5926 1/(1-10*x+23*x^2-14*x^3) ogf A016201 8.78341 {a(n+3)-10*a(n+2)+23*a(n+1)-14*a(n),a(0)=1,a(1)=10,a(2)=77} ogf A016203 22.6967 -1/(x-1)/(8*x-1)/(2*x-1) ogf A016203 5.50224 -13408+(86941-147488*x-214528*x^3+348608*x^2)*f(x)+(-1911858*x^2+1176528*x^3-73533+808863*x)*f(x)^2 ogf A016203 22.6967 1/(1-11*x+26*x^2-16*x^3) ogf A016203 9.23257 {a(n+3)-11*a(n+2)+26*a(n+1)-16*a(n),a(0)=1,a(1)=11,a(2)=95} ogf A016204 23.6782 -1/(x-1)/(2*x-1)/(9*x-1) ogf A016204 13.8604 -2*(6-29*x+27*x^2)/(x-1)/(-1+2*x)/(9*x-1) lgdogf A016204 4.98489 -677484+(4853093-8129808*x-12194712*x^3+19647036*x^2)*f(x)+(-121092661*x^2+75160962*x^3-4175609+50107308*x)*f(x)^2 ogf A016204 23.6782 1/(1-12*x+29*x^2-18*x^3) ogf A016204 9.47128 {a(n+3)-12*a(n+2)+29*a(n+1)-18*a(n),a(0)=1,a(1)=12,a(2)=115} ogf A016205 13.2534 -(13-64*x+60*x^2)/(x-1)/(-1+2*x)/(10*x-1) lgdogf A016205 21.7356 -1/(x-1)/(2*x-1)/(10*x-1) ogf A016205 5.54479 -7975+(62554-103675*x-159500*x^3+255200*x^2)*f(x)+(-1746528*x^2+1091580*x^3-54579+709527*x)*f(x)^2 ogf A016205 22.6412 1/(1-13*x+32*x^2-20*x^3) ogf A016205 9.05649 {a(n+3)-13*a(n+2)+32*a(n+1)-20*a(n),a(0)=1,a(1)=13,a(2)=137} ogf A016206 21.7356 -1/(x-1)/(2*x-1)/(11*x-1) ogf A016206 12.9378 -2*(7-35*x+33*x^2)/(x-1)/(-1+2*x)/(11*x-1) lgdogf A016206 4.8954 -211508+(1803101-2961112*x-4653176*x^3+7402780*x^2)*f(x)+(-1591593+22282302*x-55705755*x^2+35015046*x^3)*f(x)^2 ogf A016206 22.6412 1/(1-14*x+35*x^2-22*x^3) ogf A016206 9.05649 {a(n+3)-14*a(n+2)+35*a(n+1)-22*a(n),a(0)=1,a(1)=14,a(2)=161} ogf A016207 12.3245 -(15-76*x+72*x^2)/(x-1)/(2*x-1)/(12*x-1) lgdogf A016207 19.7191 -1/(x-1)/(2*x-1)/(12*x-1) ogf A016207 4.97958 -9288+(85513-139320*x-222912*x^3+352944*x^2)*f(x)+(-2896550*x^2+1829400*x^3-76225+1143375*x)*f(x)^2 ogf A016207 20.5408 1/(1-15*x+38*x^2-24*x^3) ogf A016207 8.21631 {a(n+3)-15*a(n+2)+38*a(n+1)-24*a(n),a(0)=1,a(1)=15,a(2)=187} ogf A016208 31.25 -1/(x-1)/(3*x-1)/(4*x-1) ogf A016208 7.07546 -128304+(624163-1026432*x-1539648*x^3+2437776*x^2)*f(x)+(-9421321*x^2+5950308*x^3-495859+3966872*x)*f(x)^2 ogf A016208 32.6087 1/(1-8*x+19*x^2-12*x^3) ogf A016208 13.1579 {a(n+3)-8*a(n+2)+19*a(n+1)-12*a(n),a(0)=1,a(1)=8,a(2)=45} ogf A016209 13.402 -(9-46*x+45*x^2)/(x-1)/(3*x-1)/(5*x-1) lgdogf A016209 21.2198 -1/(x-1)/(3*x-1)/(5*x-1) ogf A016209 4.58805 -296325+(1716338-2666925*x-4444875*x^3+6815475*x^2)*f(x)+(-32660299*x^2+21300195*x^3-1420013+12780117*x)*f(x)^2 ogf A016209 22.1424 1/(1-9*x+23*x^2-15*x^3) ogf A016209 8.93463 {a(n+3)-9*a(n+2)+23*a(n+1)-15*a(n),a(0)=1,a(1)=9,a(2)=58} ogf A016210 24.2404 -(-x^31+1-x^40)/(x^40-1+x-x^41) ogf A016210 25.0484 -(x^31-1-x^40)/(x^40+1-x-x^41) ogf A016211 20.6111 -1/(x-1)/(6*x-1)/(3*x-1) ogf A016211 6.10699 -116+(781-1160*x-2088*x^3+3132*x^2)*f(x)+(-17955*x^2+11970*x^3-665+6650*x)*f(x)^2 ogf A016211 12.3666 -2*(5-27*x+27*x^2)/(x-1)/(6*x-1)/(3*x-1) lgdogf A016211 20.6111 1/(1-10*x+27*x^2-18*x^3) ogf A016211 8.38417 {a(n+3)-10*a(n+2)+27*a(n+1)-18*a(n),a(0)=1,a(1)=10,a(2)=73} ogf A016212 21.7152 -1/(x-1)/(3*x-1)/(7*x-1) ogf A016212 4.45441 -1067661+(8200162-11744271*x-22420881*x^3+33097491*x^2)*f(x)+(-221107531*x^2+149782521*x^3-7132501+78457511*x)*f(x)^2 ogf A016212 21.7152 1/(1-11*x+31*x^2-21*x^3) ogf A016212 8.83332 {a(n+3)-11*a(n+2)+31*a(n+1)-21*a(n),a(0)=1,a(1)=11,a(2)=90} ogf A016213 8.22791 (1-x^2+x^4-x^6+x^8-x^10+x^12-x^14+x^16-x^18+x^38)/(x^8-x^4+1)/(x^32+x^28-x^20-x^16-x^12+x^4+1) ogf A016214 22.9421 -1/(x-1)/(3*x-1)/(8*x-1) ogf A016214 4.58842 -1785024+(15409043-21420288*x-42840576*x^3+62475840*x^2)*f(x)+(-476840665*x^2+326976456*x^3-13624019+163488228*x)*f(x)^2 ogf A016214 13.4295 -2*(9*x-2)*(4*x-3)/(x-1)/(3*x-1)/(-1+8*x) lgdogf A016214 22.9421 1/(1-12*x+35*x^2-24*x^3) ogf A016214 9.17684 {a(n+3)-12*a(n+2)+35*a(n+1)-24*a(n),a(0)=1,a(1)=12,a(2)=109} ogf A016215 27.4409 -1/(x-1)/(3*x-1)/(10*x-1) ogf A016215 16.7322 -2*(7-43*x+45*x^2)/(x-1)/(3*x-1)/(10*x-1) lgdogf A016215 5.53244 -4236300+(44664883-59308200*x-127089000*x^3+182160900*x^2)*f(x)+(-1738429069*x^2+1212857490*x^3-40428583+566000162*x)*f(x)^2 ogf A016215 28.5843 1/(1-14*x+43*x^2-30*x^3) ogf A016215 11.4337 {a(n+3)-14*a(n+2)+43*a(n+1)-30*a(n),a(0)=1,a(1)=14,a(2)=153} ogf A016216 17.1506 -(15-94*x+99*x^2)/(x-1)/(3*x-1)/(11*x-1) lgdogf A016216 27.4409 -1/(x-1)/(3*x-1)/(11*x-1) ogf A016216 5.53244 -6138693+(70601378-92080395*x-202576869*x^3+288518571*x^2)*f(x)+(-3029746195*x^2+2127268605*x^3-64462685+966940275*x)*f(x)^2 ogf A016216 28.5843 1/(1-15*x+47*x^2-33*x^3) ogf A016216 11.4337 {a(n+3)-15*a(n+2)+47*a(n+1)-33*a(n),a(0)=1,a(1)=15,a(2)=178} ogf A016217 28.5193 -1/(x-1)/(3*x-1)/(12*x-1) ogf A016217 6.99004 -11824+(147323-189184*x-425664*x^3+603024*x^2)*f(x)+(-6910449*x^2+4877964*x^3-135499+2167984*x)*f(x)^2 ogf A016217 17.3898 -2*(8-51*x+54*x^2)/(x-1)/(3*x-1)/(12*x-1) lgdogf A016217 29.7077 1/(1-16*x+51*x^2-36*x^3) ogf A016217 11.8831 {a(n+3)-16*a(n+2)+51*a(n+1)-36*a(n),a(0)=1,a(1)=16,a(2)=205} ogf A016218 29.6565 -1/(x-1)/(4*x-1)/(5*x-1) ogf A016218 17.7939 -2*(5-29*x+30*x^2)/(x-1)/(4*x-1)/(5*x-1) lgdogf A016218 6.18918 -849200+(6178349-8492000*x-16984000*x^3+24626800*x^2)*f(x)+(-154545321*x^2+106582980*x^3-5329149+53291490*x)*f(x)^2 ogf A016218 29.6565 1/(1-10*x+29*x^2-20*x^3) ogf A016218 12.0637 {a(n+3)-10*a(n+2)+29*a(n+1)-20*a(n),a(0)=1,a(1)=10,a(2)=71} ogf A016219 7.91871 (-1+x^18+x^39-x^26-x^35+x^4+x^13)/(x+1)/(x^4-x^3+x^2-x+1)/(x^33-x^32+x^31+x^20-x^19+x^18+x^3-x^2+x-1) ogf A016221 10.4448 2*x*(-1+2*x^2-3*x^4+4*x^6-5*x^8+6*x^10)/(1-x^2+x^4-x^6+x^8-x^10+x^12) lgdogf A016221 26.6922 x^12-x^10+x^8-x^6+x^4-x^2+1 ogf A016222 12.8347 -(11-68*x+72*x^2)/(x-1)/(6*x-1)/(4*x-1) lgdogf A016222 20.8564 -1/(x-1)/(6*x-1)/(4*x-1) ogf A016222 5.16036 -7560+(64403-83160*x-181440*x^3+257040*x^2)*f(x)+(-1932662*x^2+1364232*x^3-56843+625273*x)*f(x)^2 ogf A016222 20.8564 1/(1-11*x+34*x^2-24*x^3) ogf A016222 8.48398 {a(n+3)-11*a(n+2)+34*a(n+1)-24*a(n),a(0)=1,a(1)=11,a(2)=87} ogf A016223 22.0833 -1/(x-1)/(7*x-1)/(4*x-1) ogf A016223 4.49152 -1016848+(9936461-12202176*x-28471744*x^3+39657072*x^2)*f(x)+(-347864907*x^2+249749164*x^3-8919613+107035356*x)*f(x)^2 ogf A016223 12.9268 -6*(2-13*x+14*x^2)/(x-1)/(7*x-1)/(-1+4*x) lgdogf A016223 22.0833 1/(1-12*x+39*x^2-28*x^3) ogf A016223 8.83332 {a(n+3)-12*a(n+2)+39*a(n+1)-28*a(n),a(0)=1,a(1)=12,a(2)=105} ogf A016224 13.5732 -(13-88*x+96*x^2)/(-1+x)/(8*x-1)/(-1+4*x) lgdogf A016224 23.1875 -1/(x-1)/(8*x-1)/(4*x-1) ogf A016224 5.7371 -4976+(54887-64688*x-159232*x^3+218944*x^2)*f(x)+(-2196084*x^2+1597152*x^3-49911+648843*x)*f(x)^2 ogf A016224 23.1875 1/(1-13*x+44*x^2-32*x^3) ogf A016224 9.27499 {a(n+3)-13*a(n+2)+44*a(n+1)-32*a(n),a(0)=1,a(1)=13,a(2)=125} ogf A016225 21.7356 -1/(x-1)/(4*x-1)/(10*x-1) ogf A016225 4.8954 -125800+(1705469-1887000*x-5032000*x^3+6793200*x^2)*f(x)+(-85302126*x^2+63186760*x^3-1579669+23695035*x)*f(x)^2 ogf A016225 12.9378 -3*(5-36*x+40*x^2)/(x-1)/(-1+4*x)/(10*x-1) lgdogf A016225 22.6412 1/(1-15*x+54*x^2-40*x^3) ogf A016225 9.05649 {a(n+3)-15*a(n+2)+54*a(n+1)-40*a(n),a(0)=1,a(1)=15,a(2)=171} ogf A016226 21.7356 -1/(x-1)/(4*x-1)/(11*x-1) ogf A016226 4.11659 -17491760+(259284587-279868160*x-769637440*x^3+1032013840*x^2)*f(x)+(-14265776793*x^2+10638884388*x^3-241792827+3868685232*x)*f(x)^2 ogf A016226 12.637 -2*(6*x-1)*(11*x-8)/(x-1)/(-1+4*x)/(11*x-1) lgdogf A016226 22.6412 1/(1-16*x+59*x^2-44*x^3) ogf A016226 9.05649 {a(n+3)-16*a(n+2)+59*a(n+1)-44*a(n),a(0)=1,a(1)=16,a(2)=197} ogf A016227 11.8725 -(17-128*x+144*x^2)/(x-1)/(12*x-1)/(4*x-1) lgdogf A016227 19.9458 -1/(x-1)/(12*x-1)/(4*x-1) ogf A016227 5.14067 -2997+(48224-50949*x-143856*x^3+191808*x^2)*f(x)+(-2894528*x^2+2170896*x^3-45227+768859*x)*f(x)^2 ogf A016227 20.7769 1/(1-17*x+64*x^2-48*x^3) ogf A016227 8.31075 {a(n+3)-17*a(n+2)+64*a(n+1)-48*a(n),a(0)=1,a(1)=17,a(2)=225} ogf A016228 29.3649 -1/(x-1)/(6*x-1)/(5*x-1) ogf A016228 17.6189 -2*(6-41*x+45*x^2)/(x-1)/(6*x-1)/(5*x-1) lgdogf A016228 5.68353 -3890700+(40332161-46688400*x-116721000*x^3+159518700*x^2)*f(x)+(-1494099901*x^2+1093243830*x^3-36441461+437297532*x)*f(x)^2 ogf A016228 29.3649 1/(1-12*x+41*x^2-30*x^3) ogf A016228 11.746 {a(n+3)-12*a(n+2)+41*a(n+1)-30*a(n),a(0)=1,a(1)=12,a(2)=103} ogf A016230 13.1423 -(13-94*x+105*x^2)/(x-1)/(-1+7*x)/(5*x-1) lgdogf A016230 22.4514 -1/(x-1)/(7*x-1)/(5*x-1) ogf A016230 4.34542 -7003325+(83584322-91043225*x-245116375*x^3+329156275*x^2)*f(x)+(-3599306859*x^2+2680334895*x^3-76580997+995552961*x)*f(x)^2 ogf A016230 22.4514 1/(1-13*x+47*x^2-35*x^3) ogf A016230 8.98054 {a(n+3)-13*a(n+2)+47*a(n+1)-35*a(n),a(0)=1,a(1)=13,a(2)=122} ogf A016231 7.29479 (-5*x^4+6*x^5-1-7*x^6+8*x^7+2*x-9*x^8-3*x^2+10*x^9+4*x^3)/(x^2+1-x+x^8+x^4-x^9-x^3+x^10+x^6-x^5-x^7) lgdogf A016231 52.1056 -1+x+x^10-x^21 ogf_with_Euler_Transform A016231 18.237 x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1 ogf A016231 6.88187 {a(n+2)+a(n+1),a(0)=1,a(1)=-1,a(2)=1,a(3)=-1,a(4)=1,a(5)=-1,a(6)=1,a(7)=-1,a(8)=1,a(9)=-1,a(10)=1,a(11)=0} ogf A016232 16.9786 (1-x^15-x^6+x^9+x^36)/(x^36+1+x^3-x^21-x^18) ogf A016232 16.2404 -(-1+x^15+x^6-x^9-x^36)/(x^36+1+x^3-x^21-x^18) ogf A016233 23.4328 -1/(x-1)/(8*x-1)/(5*x-1) ogf A016233 4.3596 -11691200+(157955813-163676800*x-467648000*x^3+619633600*x^2)*f(x)+(-7752024489*x^2+5850584520*x^3-146264613+2047704582*x)*f(x)^2 ogf A016233 14.0597 -2*(7-53*x+60*x^2)/(x-1)/(8*x-1)/(5*x-1) lgdogf A016233 23.4328 1/(1-14*x+53*x^2-40*x^3) ogf A016233 9.37313 {a(n+3)-14*a(n+2)+53*a(n+1)-40*a(n),a(0)=1,a(1)=14,a(2)=143} ogf A016234 12.6189 -(15-118*x+135*x^2)/(x-1)/(9*x-1)/(5*x-1) lgdogf A016234 21.5573 -1/(x-1)/(9*x-1)/(5*x-1) ogf A016234 4.17239 -2630475+(39696182-39457125*x-118371375*x^3+155198025*x^2)*f(x)+(-2186876713*x^2+1667956815*x^3-37065707+555985605*x)*f(x)^2 ogf A016234 21.5573 1/(1-15*x+59*x^2-45*x^3) ogf A016234 8.62294 {a(n+3)-15*a(n+2)+59*a(n+1)-45*a(n),a(0)=1,a(1)=15,a(2)=166} ogf A016236 117.918 1-x^16 ogf_with_Euler_Transform A016236 10.1072 x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016237 21.7356 -1/(x-1)/(5*x-1)/(10*x-1) ogf A016237 13.2534 -2*(8-65*x+75*x^2)/(x-1)/(5*x-1)/(10*x-1) lgdogf A016237 5.38009 -8860+(147733-141760*x-443000*x^3+575900*x^2)*f(x)+(-9026745*x^2+6943650*x^3-138873+2221968*x)*f(x)^2 ogf A016237 22.6412 1/(1-16*x+65*x^2-50*x^3) ogf A016237 9.05649 {a(n+3)-16*a(n+2)+65*a(n+1)-50*a(n),a(0)=1,a(1)=16,a(2)=191} ogf A016238 12.7042 -(17-142*x+165*x^2)/(-1+x)/(5*x-1)/(11*x-1) lgdogf A016238 21.8512 -1/(x-1)/(5*x-1)/(11*x-1) ogf A016238 4.07672 -40090325+(732032786-681535525*x-2204967875*x^3+2846413075*x^2)*f(x)+(-49127914731*x^2+38056835355*x^3-691942461+11763021837*x)*f(x)^2 ogf A016238 22.7617 1/(1-17*x+71*x^2-55*x^3) ogf A016238 9.10467 {a(n+3)-17*a(n+2)+71*a(n+1)-55*a(n),a(0)=1,a(1)=17,a(2)=218} ogf A016239 19.9458 -1/(x-1)/(5*x-1)/(12*x-1) ogf A016239 12.1621 -2*(9-77*x+90*x^2)/(x-1)/(5*x-1)/(12*x-1) lgdogf A016239 20.7769 1/(1-18*x+77*x^2-60*x^3) ogf A016239 8.31075 {a(n+3)-18*a(n+2)+77*a(n+1)-60*a(n),a(0)=1,a(1)=18,a(2)=247} ogf A016240 117.918 1-x^22 ogf_with_Euler_Transform A016240 7.07506 x^22+x^21+x^20+x^19+x^18+x^17+x^16+x^15+x^14+x^13+x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016241 28.4155 -1/(x-1)/(6*x-1)/(7*x-1) ogf A016241 5.24594 -13933836+(196885807-195073704*x-585221112*x^3+766360980*x^2)*f(x)+(-10062358405*x^2+7683982782*x^3-182951971+2561327594*x)*f(x)^2 ogf A016241 17.0493 -2*(7-55*x+63*x^2)/(x-1)/(6*x-1)/(7*x-1) lgdogf A016241 28.4155 1/(1-14*x+55*x^2-42*x^3) ogf A016241 11.3662 {a(n+3)-14*a(n+2)+55*a(n+1)-42*a(n),a(0)=1,a(1)=14,a(2)=141} ogf A016243 13.6706 -(15-124*x+144*x^2)/(x-1)/(6*x-1)/(-1+8*x) lgdogf A016243 23.9236 -1/(x-1)/(6*x-1)/(8*x-1) ogf A016243 4.82492 -726624+(11646079-10899360*x-34877952*x^3+45050688*x^2)*f(x)+(-677006210*x^2+524133840*x^3-10919455+163791825*x)*f(x)^2 ogf A016243 23.9236 1/(1-15*x+62*x^2-48*x^3) ogf A016243 9.56943 {a(n+3)-15*a(n+2)+62*a(n+1)-48*a(n),a(0)=1,a(1)=15,a(2)=163} ogf A016244 21.9186 -1/(x-1)/(6*x-1)/(9*x-1) ogf A016244 4.61445 -150660+(2701439-2410560*x-8135640*x^3+10395540*x^2)*f(x)+(-176003751*x^2+137742066*x^3-2550779+40812464*x)*f(x)^2 ogf A016244 13.1512 -2*(8-69*x+81*x^2)/(x-1)/(6*x-1)/(9*x-1) lgdogf A016244 21.9186 1/(1-16*x+69*x^2-54*x^3) ogf A016244 8.76746 {a(n+3)-16*a(n+2)+69*a(n+1)-54*a(n),a(0)=1,a(1)=16,a(2)=187} ogf A016246 12.9378 -(17-152*x+180*x^2)/(x-1)/(6*x-1)/(10*x-1) lgdogf A016246 21.7356 -1/(x-1)/(6*x-1)/(10*x-1) ogf A016246 4.80876 -122850+(2437027-2088450*x-7371000*x^3+9336600*x^2)*f(x)+(-175877452*x^2+138850620*x^3-2314177+39341009*x)*f(x)^2 ogf A016246 22.6412 1/(1-17*x+76*x^2-60*x^3) ogf A016246 9.05649 {a(n+3)-17*a(n+2)+76*a(n+1)-60*a(n),a(0)=1,a(1)=17,a(2)=213} ogf A016247 22.0824 -1/(x-1)/(6*x-1)/(11*x-1) ogf A016247 4.2142 -11382228+(247526381-204880104*x-751227048*x^3+944724924*x^2)*f(x)+(-19599964699*x^2+15585514098*x^3-236144153+4250594754*x)*f(x)^2 ogf A016247 13.4649 -2*(9-83*x+99*x^2)/(x-1)/(6*x-1)/(11*x-1) lgdogf A016247 23.0025 1/(1-18*x+83*x^2-66*x^3) ogf A016247 9.20101 {a(n+3)-18*a(n+2)+83*a(n+1)-66*a(n),a(0)=1,a(1)=18,a(2)=241} ogf A016248 20.0591 -1/(x-1)/(6*x-1)/(12*x-1) ogf A016248 5.01478 -4792+(113369-91048*x-345024*x^3+431280*x^2)*f(x)+(-9771930*x^2+7817544*x^3-108577+2062963*x)*f(x)^2 ogf A016248 20.8949 1/(1-19*x+90*x^2-72*x^3) ogf A016248 8.35797 {a(n+3)-19*a(n+2)+90*a(n+1)-72*a(n),a(0)=1,a(1)=19,a(2)=271} ogf A016249 30.1915 -1/(x-1)/(8*x-1)/(7*x-1) ogf A016249 18.1149 -2*(8-71*x+84*x^2)/(x-1)/(8*x-1)/(7*x-1) lgdogf A016249 5.40743 -41806016+(776088167-668896256*x-2341136896*x^3+2968227136*x^2)*f(x)+(-52134032721*x^2+41119800456*x^3-734282151+11748514416*x)*f(x)^2 ogf A016249 30.1915 1/(1-16*x+71*x^2-56*x^3) ogf A016249 12.0766 {a(n+3)-16*a(n+2)+71*a(n+1)-56*a(n),a(0)=1,a(1)=16,a(2)=185} ogf A016250 13.1124 -(17-158*x+189*x^2)/(x-1)/(7*x-1)/(9*x-1) lgdogf A016250 22.4004 -1/(x-1)/(7*x-1)/(9*x-1) ogf A016250 3.89572 -65809989+(1368346018-1118769813*x-4146029307*x^3+5198989131*x^2)*f(x)+(-102900346291*x^2+82059769827*x^3-1302536029+22143112493*x)*f(x)^2 ogf A016250 22.4004 1/(1-17*x+79*x^2-63*x^3) ogf A016250 8.96015 {a(n+3)-17*a(n+2)+79*a(n+1)-63*a(n),a(0)=1,a(1)=17,a(2)=210} ogf A016251 23.8366 (x^38+x^40-1)/(x+1)/(x^40+x^19-1) ogf A016251 19.1855 -(x^38+x^40-1)/(-x^20+1+x-x^19-x^41-x^40) ogf A016251 19.1855 -(x^38-x^40-1)/(-x^20+1-x+x^19-x^41+x^40) ogf A016252 21.7356 -1/(x-1)/(7*x-1)/(10*x-1) ogf A016252 4.14801 -10990700+(253061143-197832600*x-769349000*x^3+956190900*x^2)*f(x)+(-21060128541*x^2+16944931010*x^3-242070443+4357267974*x)*f(x)^2 ogf A016252 13.2534 -6*(3-29*x+35*x^2)/(x-1)/(7*x-1)/(10*x-1) lgdogf A016252 22.6412 1/(1-18*x+87*x^2-70*x^3) ogf A016252 9.05649 {a(n+3)-18*a(n+2)+87*a(n+1)-70*a(n),a(0)=1,a(1)=18,a(2)=237} ogf A016254 11.6701 -(19-190*x+231*x^2)/(x-1)/(7*x-1)/(11*x-1) lgdogf A016254 19.6058 -1/(x-1)/(7*x-1)/(11*x-1) ogf A016254 3.77035 -7535759+(190358678-143179421*x-580253443*x^3+715897105*x^2)*f(x)+(-182822919+3473635461*x-17368177305*x^2+14077364763*x^3)*f(x)^2 ogf A016254 20.4227 1/(1-19*x+95*x^2-77*x^3) ogf A016254 8.16909 {a(n+3)-19*a(n+2)+95*a(n+1)-77*a(n),a(0)=1,a(1)=19,a(2)=266} ogf A016255 20.1725 -1/(x-1)/(7*x-1)/(12*x-1) ogf A016255 11.2069 -2*(10-103*x+126*x^2)/(x-1)/(7*x-1)/(-1+12*x) lgdogf A016255 20.1725 1/(1-20*x+103*x^2-84*x^3) ogf A016255 8.2674 {a(n+3)-20*a(n+2)+103*a(n+1)-84*a(n),a(0)=1,a(1)=20,a(2)=297} ogf A016256 28.5843 -1/(x-1)/(8*x-1)/(9*x-1) ogf A016256 16.3339 -2*(9-89*x+108*x^2)/(x-1)/(-1+8*x)/(9*x-1) lgdogf A016256 28.5843 1/(1-18*x+89*x^2-72*x^3) ogf A016256 11.4337 {a(n+3)-18*a(n+2)+89*a(n+1)-72*a(n),a(0)=1,a(1)=18,a(2)=235} ogf A016257 12.637 -(19-196*x+240*x^2)/(x-1)/(-1+8*x)/(10*x-1) lgdogf A016257 21.7356 -1/(x-1)/(8*x-1)/(10*x-1) ogf A016257 4.21232 -5154400+(135184369-97933600*x-412352000*x^3+505131200*x^2)*f(x)+(-12742936962*x^2+10402397520*x^3-130029969+2470569411*x)*f(x)^2 ogf A016257 22.6412 1/(1-19*x+98*x^2-80*x^3) ogf A016257 9.05649 {a(n+3)-19*a(n+2)+98*a(n+1)-80*a(n),a(0)=1,a(1)=19,a(2)=263} ogf A016258 5.66005 (1+7*x^6+8*x^7+2*x+9*x^8+3*x^2+10*x^9+4*x^3+11*x^10+5*x^4+12*x^11+6*x^5)/(x+x^2+x^5+x^6+x^3+x^4+x^7+x^8+x^11+x^9+x^10+x^12+1) lgdogf A016258 117.918 1-x^12 ogf_with_Euler_Transform A016258 14.1501 x^12+x^11+x^10+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1 ogf A016258 6.04706 {a(n+2)-a(n+1),a(0)=1,a(1)=1,a(2)=1,a(3)=1,a(4)=1,a(5)=1,a(6)=1,a(7)=1,a(8)=1,a(9)=1,a(10)=1,a(11)=1,a(12)=1,a(13)=0} ogf A016259 19.9458 -1/(x-1)/(11*x-1)/(8*x-1) ogf A016259 11.081 -2*(10-107*x+132*x^2)/(x-1)/(11*x-1)/(-1+8*x) lgdogf A016259 19.9458 1/(1-20*x+107*x^2-88*x^3) ogf A016259 8.17451 {a(n+3)-20*a(n+2)+107*a(n+1)-88*a(n),a(0)=1,a(1)=20,a(2)=293} ogf A016260 11.7941 -(21-232*x+288*x^2)/(x-1)/(8*x-1)/(-1+12*x) lgdogf A016260 20.2858 -1/(x-1)/(8*x-1)/(12*x-1) ogf A016260 4.29784 -327024+(10254353-6867504*x-31394304*x^3+37934784*x^2)*f(x)+(-1151570164*x^2+953023584*x^3-9927329+208473909*x)*f(x)^2 ogf A016260 20.2858 1/(1-21*x+116*x^2-96*x^3) ogf A016260 8.31385 {a(n+3)-21*a(n+2)+116*a(n+1)-96*a(n),a(0)=1,a(1)=21,a(2)=325} ogf A016261 27.4409 -1/(x-1)/(9*x-1)/(10*x-1) ogf A016261 15.5914 -2*(10-109*x+135*x^2)/(x-1)/(9*x-1)/(10*x-1) lgdogf A016261 27.4409 1/(1-20*x+109*x^2-90*x^3) ogf A016261 11.2463 {a(n+3)-20*a(n+2)+109*a(n+1)-90*a(n),a(0)=1,a(1)=20,a(2)=291} ogf A016262 12.0074 -(21-238*x+297*x^2)/(x-1)/(9*x-1)/(11*x-1) lgdogf A016262 20.1725 -1/(x-1)/(9*x-1)/(11*x-1) ogf A016262 20.1725 1/(1-21*x+119*x^2-99*x^3) ogf A016262 8.2674 {a(n+3)-21*a(n+2)+119*a(n+1)-99*a(n),a(0)=1,a(1)=21,a(2)=322} ogf A016263 20.3991 -1/(x-1)/(12*x-1)/(9*x-1) ogf A016263 11.5904 -2*(11-129*x+162*x^2)/(x-1)/(12*x-1)/(9*x-1) lgdogf A016263 4.24981 -309744+(10910893-6814368*x-33452352*x^3+39956976*x^2)*f(x)+(-1367548221*x^2+1144924092*x^3-10601149+233225278*x)*f(x)^2 ogf A016263 19.6145 1/(1-22*x+129*x^2-108*x^3) ogf A016263 8.22545 {a(n+3)-22*a(n+2)+129*a(n+1)-108*a(n),a(0)=1,a(1)=22,a(2)=355} ogf A016265 19.6145 -1/(x-1)/(10*x-1)/(11*x-1) ogf A016265 11.0865 -2*(11-131*x+165*x^2)/(x-1)/(-1+10*x)/(11*x-1) lgdogf A016265 19.6145 1/(1-22*x+131*x^2-110*x^3) ogf A016265 8.22545 {a(n+3)-22*a(n+2)+131*a(n+1)-110*a(n),a(0)=1,a(1)=22,a(2)=353} ogf A016266 12.9602 (37-61*x^24-1369*x^36+1332*x^37)/(x-1)/(37*x^37+61*x^24-37) lgdogf A016266 24.6662 -(-1+x^24+x^37)/(1-x-x^24+x^25) ogf A016266 8.59162 -(-1+x^24+x^37)/(x+1)/(x^8-x^4+1)/(x^4-x^2+1)/(1+x^2+x)/(1-x+x^2)/(x^2+1)/(x^4+1)/(x-1)^2 ogf A016266 24.6662 -(1+x^24-x^37)/(-1+x-x^24+x^25) ogf A016267 11.7192 -(23-284*x+360*x^2)/(x-1)/(12*x-1)/(-1+10*x) lgdogf A016267 19.8325 -1/(x-1)/(12*x-1)/(10*x-1) ogf A016267 3.7915 -24737400+(967279091-568960200*x-2968488000*x^3+3512710800*x^2)*f(x)+(-133840920122*x^2+113105002920*x^3-942541691+21678458893*x)*f(x)^2 ogf A016267 19.8325 1/(1-23*x+142*x^2-120*x^3) ogf A016267 8.31684 {a(n+3)-23*a(n+2)+142*a(n+1)-120*a(n),a(0)=1,a(1)=23,a(2)=387} ogf A016268 20.0504 -1/(x-1)/(12*x-1)/(11*x-1) ogf A016268 11.5847 -2*(12-155*x+198*x^2)/(x-1)/(12*x-1)/(11*x-1) lgdogf A016268 20.0504 1/(1-24*x+155*x^2-132*x^3) ogf A016268 8.40824 {a(n+3)-24*a(n+2)+155*a(n+1)-132*a(n),a(0)=1,a(1)=24,a(2)=421} ogf A016269 13.1675 -(9-52*x+72*x^2)/(3*x-1)/(2*x-1)/(4*x-1) lgdogf A016269 20.2578 -1/(3*x-1)/(2*x-1)/(4*x-1) ogf A016269 5.78793 -4104+(9703-36936*x-98496*x^3+106704*x^2)*f(x)+(-145574*x^2+134376*x^3-5599+50391*x)*f(x)^2 ogf A016269 22.9001 1/(1-9*x+26*x^2-24*x^3) ogf A016269 9.24039 {a(n+3)-9*a(n+2)+26*a(n+1)-24*a(n),a(0)=1,a(1)=9,a(2)=55} ogf A016270 50.2615 -1+x^6+x^16+x^18 ogf_with_Euler_Transform A016272 23.9568 -(-x^31+1-x^42)/(x^42-1+x-x^43) ogf A016272 24.7554 -(x^31-1-x^42)/(x^42+1-x-x^43) ogf A016273 20.0483 -1/(3*x-1)/(2*x-1)/(5*x-1) ogf A016273 12.4109 -2*(5-31*x+45*x^2)/(3*x-1)/(2*x-1)/(5*x-1) lgdogf A016273 4.4936 -2054700+(5359351-20547000*x-61641000*x^3+63695700*x^2)*f(x)+(-102444181*x^2+99139530*x^3-3304651+33046510*x)*f(x)^2 ogf A016273 21.719 1/(1-10*x+31*x^2-30*x^3) ogf A016273 8.83486 {a(n+3)-10*a(n+2)+31*a(n+1)-30*a(n),a(0)=1,a(1)=10,a(2)=69} ogf A016275 7.29479 (-5*x^4+6*x^5-1-7*x^6+8*x^7+2*x-9*x^8-3*x^2+10*x^9+4*x^3)/(x^2+1-x+x^8+x^4-x^9-x^3+x^10+x^6-x^5-x^7) lgdogf A016275 52.1056 -1+x+x^10-x^21 ogf_with_Euler_Transform A016275 18.237 x^10-x^9+x^8-x^7+x^6-x^5+x^4-x^3+x^2-x+1 ogf A016275 6.88187 {a(n+2)+a(n+1),a(0)=1,a(1)=-1,a(2)=1,a(3)=-1,a(4)=1,a(5)=-1,a(6)=1,a(7)=-1,a(8)=1,a(9)=-1,a(10)=1,a(11)=0} ogf A016276 20.2713 -1/(3*x-1)/(2*x-1)/(7*x-1) ogf A016276 12.5489 -2*(9*x-2)*(7*x-3)/(3*x-1)/(2*x-1)/(7*x-1) lgdogf A016276 4.32012 -7117740+(22390913-85412880*x-298945080*x^3+291827340*x^2)*f(x)+(-626200093*x^2+641473266*x^3-15273173+183278076*x)*f(x)^2 ogf A016276 21.9606 1/(1-12*x+41*x^2-42*x^3) ogf A016276 8.78425 {a(n+3)-12*a(n+2)+41*a(n+1)-42*a(n),a(0)=1,a(1)=12,a(2)=103} ogf A016277 12.5808 -(13-92*x+144*x^2)/(3*x-1)/(-1+2*x)/(-1+8*x) lgdogf A016277 21.2906 -1/(3*x-1)/(2*x-1)/(8*x-1) ogf A016277 4.94245 -367200+(1257719-4773600*x-17625600*x^3+16891200*x^2)*f(x)+(-40963874*x^2+42744912*x^3-890519+11576747*x)*f(x)^2 ogf A016277 23.0648 1/(1-13*x+46*x^2-48*x^3) ogf A016277 9.22591 {a(n+3)-13*a(n+2)+46*a(n+1)-48*a(n),a(0)=1,a(1)=13,a(2)=123} ogf A016278 22.1965 -1/(3*x-1)/(2*x-1)/(9*x-1) ogf A016278 13.4212 -2*(7-51*x+81*x^2)/(-1+3*x)/(2*x-1)/(9*x-1) lgdogf A016278 5.39355 -75492+(279929-1056888*x-4076568*x^3+3850092*x^2)*f(x)+(-10426287*x^2+11039598*x^3-204437+2862118*x)*f(x)^2 ogf A016278 24.0463 1/(1-14*x+51*x^2-54*x^3) ogf A016278 9.6185 {a(n+3)-14*a(n+2)+51*a(n+1)-54*a(n),a(0)=1,a(1)=14,a(2)=145} ogf A016279 12.0753 -(15-112*x+180*x^2)/(3*x-1)/(-1+2*x)/(10*x-1) lgdogf A016279 20.1255 -1/(3*x-1)/(2*x-1)/(10*x-1) ogf A016279 4.93991 -213975+(854467-3209625*x-12838500*x^3+11982600*x^2)*f(x)+(-35867552*x^2+38429520*x^3-640492+9607380*x)*f(x)^2 ogf A016279 22.6412 1/(1-15*x+56*x^2-60*x^3) ogf A016279 9.05649 {a(n+3)-15*a(n+2)+56*a(n+1)-60*a(n),a(0)=1,a(1)=15,a(2)=169} ogf A016280 20.1255 -1/(11*x-1)/(3*x-1)/(2*x-1) ogf A016280 12.3498 -2*(8-61*x+99*x^2)/(11*x-1)/(3*x-1)/(-1+2*x) lgdogf A016280 4.38217 -5632308+(24107251-90116928*x-371732328*x^3+343570788*x^2)*f(x)+(-1126971523*x^2+1219346238*x^3-18474943+295599088*x)*f(x)^2 ogf A016280 22.6412 1/(1-16*x+61*x^2-66*x^3) ogf A016280 9.05649 {a(n+3)-16*a(n+2)+61*a(n+1)-66*a(n),a(0)=1,a(1)=16,a(2)=195} ogf A016281 11.2684 -(17-132*x+216*x^2)/(12*x-1)/(3*x-1)/(2*x-1) lgdogf A016281 18.3634 -1/(12*x-1)/(3*x-1)/(2*x-1) ogf A016281 5.27459 -2360+(10781-40120*x-169920*x^3+155760*x^2)*f(x)+(-555786*x^2+606312*x^3-8421+143157*x)*f(x)^2 ogf A016281 20.6588 1/(1-17*x+66*x^2-72*x^3) ogf A016281 8.26353 {a(n+3)-17*a(n+2)+66*a(n+1)-72*a(n),a(0)=1,a(1)=17,a(2)=223} ogf A016282 27.4958 -1/(4*x-1)/(2*x-1)/(5*x-1) ogf A016282 6.61937 -172600+(493039-1898600*x-6904000*x^3+6558800*x^2)*f(x)+(-12176682*x^2+12817560*x^3-320439+3524829*x)*f(x)^2 ogf A016282 29.7872 1/(1-11*x+38*x^2-40*x^3) ogf A016282 12.1168 {a(n+3)-11*a(n+2)+38*a(n+1)-40*a(n),a(0)=1,a(1)=11,a(2)=83} ogf A016283 20.6091 -1/(6*x-1)/(2*x-1)/(4*x-1) ogf A016283 12.758 -4*(3-22*x+36*x^2)/(6*x-1)/(2*x-1)/(4*x-1) lgdogf A016283 16.7449 x^2+(-1+12*x-44*x^2+48*x^3)*f(x) ogf A016283 20.6091 x^2/(1-12*x+44*x^2-48*x^3) ogf A016283 9.40062 {a(n+3)-12*a(n+2)+44*a(n+1)-48*a(n),a(0)=0,a(1)=0,a(2)=1} ogf A016285 12.1124 -(13-100*x+168*x^2)/(-1+4*x)/(2*x-1)/(7*x-1) lgdogf A016285 20.4978 -1/(4*x-1)/(2*x-1)/(7*x-1) ogf A016285 4.71632 -592312+(2059549-7700056*x-33169472*x^3+29615600*x^2)*f(x)+(-73361850*x^2+82165272*x^3-1467237+19074081*x)*f(x)^2 ogf A016285 22.206 1/(1-13*x+50*x^2-56*x^3) ogf A016285 8.88239 {a(n+3)-13*a(n+2)+50*a(n+1)-56*a(n),a(0)=1,a(1)=13,a(2)=119} ogf A016286 8.16112 (x-1)*(x+1)*(x^2+1)*(1+x^2+x)*(1-x+x^2)*(x^6-x^3+1)*(x^4-x^2+1)*(x^12-x^6+1)/(-1+x^33+x^36) ogf A016287 7.03112 (-x^17-1+x^50)/(x-1)/(x^4+x^3+x^2+x+1)/(x^4-x^3+x^2-x+1)/(x^20+x^15+x^10+x^5+1)/(x^20-x^15+x^10-x^5+1)/(x+1)^2 ogf A016287 24.1695 -(-x^17-1+x^50)/(-x^50+1+x-x^51) ogf A016287 25.7808 -(x^17-1-x^50)/(x^50+1-x-x^51) ogf A016290 29.7215 -1/(8*x-1)/(2*x-1)/(4*x-1) ogf A016290 9.54025 -136+(517-1904*x-8704*x^3+7616*x^2)*f(x)+(-381+5334*x-21336*x^2+24384*x^3)*f(x)^2 ogf A016290 17.9712 -2*(7-56*x+96*x^2)/(8*x-1)/(2*x-1)/(-1+4*x) lgdogf A016290 32.1983 1/(1-14*x+56*x^2-64*x^3) ogf A016290 12.8793 {a(n+3)-14*a(n+2)+56*a(n+1)-64*a(n),a(0)=1,a(1)=14,a(2)=140} ogf A016291 16.8511 -(15-124*x+216*x^2)/(4*x-1)/(9*x-1)/(2*x-1) lgdogf A016291 27.8691 -1/(4*x-1)/(9*x-1)/(2*x-1) ogf A016291 6.14064 -1518264+(6271099-22773960*x-109315008*x^3+94132368*x^2)*f(x)+(-294675770*x^2+342204120*x^3-4752835+71292525*x)*f(x)^2 ogf A016291 30.1915 1/(1-15*x+62*x^2-72*x^3) ogf A016291 12.0766 {a(n+3)-15*a(n+2)+62*a(n+1)-72*a(n),a(0)=1,a(1)=15,a(2)=163} ogf A016292 25.4082 -1/(4*x-1)/(2*x-1)/(10*x-1) ogf A016292 6.92952 -10100+(45071-161600*x-808000*x^3+686800*x^2)*f(x)+(-2378028*x^2+2797680*x^3-34971+559536*x)*f(x)^2 ogf A016292 15.2449 -8*(6*x-1)*(5*x-2)/(-1+4*x)/(-1+2*x)/(10*x-1) lgdogf A016292 28.5843 1/(1-16*x+68*x^2-80*x^3) ogf A016292 11.4337 {a(n+3)-16*a(n+2)+68*a(n+1)-80*a(n),a(0)=1,a(1)=16,a(2)=188} ogf A016293 15.0438 -(17-148*x+264*x^2)/(11*x-1)/(-1+2*x)/(-1+4*x) lgdogf A016293 25.6301 -1/(11*x-1)/(2*x-1)/(4*x-1) ogf A016293 5.62613 -3251512+(15596329-55275704*x-286133056*x^3+240611888*x^2)*f(x)+(-913516458*x^