a(n,m) tabl head (triangle) for  A116866

   n\m      0        1        2        3        4        5        6        7        8        9 ..
    
                            
   0        1        0        0        0        0        0        0        0        0        0

   1        1        1        0        0        0        0        0        0        0        0

   2        4        4        1        0        0        0        0        0        0        0

   3       25       25        7        1        0        0        0        0        0        0

   4      190      190       55       10        1        0        0        0        0        0

   5     1606     1606      472       94       13        1        0        0        0        0

   6    14506    14506     4300      898      142       16        1        0        0        0

   7   137089   137089    40861     8785     1495      199       19        1        0        0

   8  1338790  1338790   400567    87826    15655     2290      265       22        1        0

   9 13403950 13403950  4021720   894310   164581    25585     3310      340       25        1

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  The row sums give A116867: [1,2,9,58,446,3792,34369,325538,3184206,31917772,...].