a(n,m) tabl head (triangle) for  A035342  S2(3) 
 
    n\m        1           2          3          4         5        6        7        8       9    10
 
    1          1           0          0          0         0        0        0        0       0     0
   
    2          3           1          0          0         0        0        0        0       0     0
   
    3         15           9          1          0         0        0        0        0       0     0
   
    4        105          87         18          1         0        0        0        0       0     0
   
    5        945         975        285         30         1        0        0        0       0     0
   
    6      10395       12645       4680        705        45        1        0        0       0     0
   
    7     135135      187425      82845      15960      1470       63        1        0       0     0
   
    8    2027025     3133935    1595790     370125     43890     2730       84        1       0     0
   
    9   34459425    58437855   33453945    8998290   1291815   103950     4662      108       1     0
   
   10  654729075  1203216525  760970700  231416325  38710035  3786615   220500     7470     135     1