a(n,k) tabl head (triangle) for  A103919

Number of partitions of n with total number of odd parts equal k from {0,1,...,n},  
 

 a(n,m) tabl head (triangle) for  A103919
 
   n\m        0        1        2        3        4        5        6        7        8        9   10
 
   0          1        0        0        0        0        0        0        0        0        0    0
   
   1          0        1        0        0        0        0        0        0        0        0    0

   2          1        0        1        0        0        0        0        0        0        0    0

   3          0        2        0        1        0        0        0        0        0        0    0

   4          2        0        2        0        1        0        0        0        0        0    0

   5          0        4        0        2        0        1        0        0        0        0    0

   6          3        0        5        0        2        0        1        0        0        0    0

   7          0        7        0        5        0        2        0        1        0        0    0

   8          5        0        9        0        5        0        2        0        1        0    0

   9          0       12        0       10        0        5        0        2        0        1    0

  10          7        0       17        0       10        0        5        0        2        0    1 
   .
   .
   .

The row sums give the number of partitions of n: A000041(n).

The column sequences are (without leading zeros): 

Columns: k=0: A035363 (with zero entries) A000041 (without zero entries), 
         k=1: A000070, 
         k=2: A000097, 
         k=3: A000098, 
         k=4: A000710.