a(n,m) tabl head (triangle) for  A035469  S2(4)

 
    n\m         1            2           3           4          5         6        7        8      9   10
  
    1           1            0           0           0          0         0        0        0      0    0
    
    2           4            1           0           0          0         0        0        0      0    0
    
    3          28           12           1           0          0         0        0        0      0    0
    
    4         280          160          24           1          0         0        0        0      0    0
    
    5        3640         2520         520          40          1         0        0        0      0    0
    
    6       58240        46480       11880        1280         60         1        0        0      0    0
    
    7     1106560       987840      295960       40040       2660        84        1        0      0    0
    
    8    24344320     23826880     8090880     1296960     109200      4928      112        1      0    0
    
    9   608608000    643843200   242280640    44405760    4463760    257040     8400      144      1    0
   
   10 17041024000  19280060800  7912262400  1618859200  187246080  12946080   542640    13440    180    1
   
   etc.