a(n,m) tabl head (triangle) for  A090447:  Partial row products in Pascal's triangle A007318.

    n\m     0      1      2       3         4           5              6                 7              8                9               

 
     0      1      0      0       0         0           0              0                 0              0                0

     1      1      1      0       0         0           0              0                 0              0                0
     
     2      1      2      2       0         0           0              0                 0              0                0
     
     3      1      3      9       9         0           0              0                 0              0                0               
     
     4      1      4     24      96        96           0              0                 0              0                0
     
     5      1      5     50     500      2500        2500              0                 0              0                0        
     
     6      1      6     90    1800     27000      162000         162000                 0              0                0
     
     7      1      7    147    5145    180075     3781575       26471025          26471025              0                0
     
     8      1      8    224   12544    878080    49172480     1376829440       11014635520    11014635520                0
     
     9      1      9    324   27216   3429216   432081216    36294822144     1306613597184  11759522374656  11759522374656