a(n,m)  tabf head (staircase) for  A090438 (from Blasiak et al ref. for r=4, s=2)

 
  n\k        2            3          4          5          6         7        8      9     10   11  12
  
  1          1            0          0          0          0         0        0      0      0    0   0
                       
  2         12            8          1          0          0         0        0      0      0    0   0
                      
  3        360          480        180         24          1         0        0      0      0    0   0 
                      
  4      20160        40320      25200       6720        840        48        1      0      0    0   0
                      
  5    1814400      4838400    4233600    1693440     352800     40320     2520     80      1    0   0
               
  6  239500800    798336000  898128000  479001600  139708800  23950080  2494800 158400   5940  120   1
                                                                     

 The sequence of row length for this tabf array is [1,3,5,7,9,11,...]=A005408(n-1), n>=1.