a(n,k)  tabf head (staircase) for  A090216

  n\k   5      6        7       8       9      10     11    12   13  14  15  

  1     1      0        0       0       0       0      0     0    0   0   0
  2   120    600      600     200      25       1      0     0    0   0   0   
  3 14400 504000  2664000 4608000 3501000 1350360 284800 33800 2225  75   1  
  
 The row length of this tabf array is [1, 6, 11, 16, 21, 26, 31,...]= A016861(n-1), n>=1.

 The n=4 row (m=5..20) is:
  
 [1728000, 371520000, 7629120000, 42762240000, 97388280000, 110386900800, 70137648000, \

  26920728000, 6548346000, 1039382000, 109180720, 7585600, 342225, 9575, 150, 1]  

 The n=5 row (m=5..25) is
 
 [207360000, 268531200000, 19895155200000, 319850726400000, 1847846260800000, 4957507177920000,\
 
  7185232281600000, 6202620216000000, 3408553960200000, 1249670974200000, 316067865960000,\
 
  56460774000000, 7235689750000, 671044850000, 45121400000, 2187301200, 75276625, 1785375, 27625, 250, 1]