a(n,m) tabl head (triangle) for  A112705

   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        1        2        1        0        0        0        0        0        0        0

   3        1        4        3        1        0        0        0        0        0        0

   4        1        9       11        4        1        0        0        0        0        0

   5        1       23       51       22        5        1        0        0        0        0

   6        1       65      275      157       37        6        1        0        0        0

   7        1      197     1619     1291      357       56        7        1        0        0

   8        1      626    10067    11497     3941      681       79        8        1        0

   9        1     2056    64979   107725    46949     9431     1159      106        9        1
   .
   .
   .

 Row sums give  A112706:

 [1,2,4,9,26,103,542,3529,26901,232416,...]


####################################################################################################