a(k,n)  tabf head (staircase) for  A090221


  k\n         0           1             2               3                  4                   5       

  4           1           0             0               0                  0                   0 

  5          96           0             0               0                  0                   0          
           
  6          72       14400             0               0                  0                   0          
           
  7          16       38400       3456000               0                  0                   0          
           
  8           1       27000      22104000      1270080000                  0                   0          
           
  9        7200    34905600   16111872000    682795008000                  0                   0          
       
 10         856    21154176   48248363520  15279164006400    516193026048000                   0         
 
 11          48     6064128   54644474880  78083415244800  18787787440128000  530941398220800000    
   

 The row length sequence for this array is  A037915,  floor(3*(k-4)/4)+1, k>=4.

 [1, 1, 2, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 16, ...]