a(n,m) tabl head (triangle) for  A049385 S2(6)
 
    n\m            1             2             3             4           5        6        7        8      9   10
 
    1              1             0             0             0           0        0        0        0      0    0
    
    2              6             1             0             0           0        0        0        0      0    0
    
    3             66            18             1             0           0        0        0        0      0    0
    
    4           1056           372            36             1           0        0        0        0      0    0
    
    5          22176          9240          1200            60           1        0        0        0      0    0
    
    6         576576        271656         42840          2940          90        1        0        0      0    0
    
    7       17873856       9269568       1685376        142800        6090      126        1        0      0    0
    
    8      643458816     360847872      73313856       7254576      386400    11256      168        1      0    0
    
    9    26381811456   15799069440    3513343680     392515200    24642576   904176    19152      216      1    0
   
   10  1213563326976  768938075136  184439566080   22746588480  1624644000 70755552  1900080    30600    270    1
  
   etc.