a(n,m) tabl head (triangle) for  A115154
  

   n\m      1        2        3        4        5        6        7        8        9        10 ...
                                

   0        1        0        0        0        0        0        0        0        0         0

   1        1        4        0        0        0        0        0        0        0         0

   2        1       13       25        0        0        0        0        0        0         0

   3        1       40      115      190        0        0        0        0        0         0

   4        1      121      466     1036     1606        0        0        0        0         0

   5        1      364     1762     4870     9688    14506        0        0        0         0

   6        1     1093     6379    20989    50053    93571   137089        0        0         0

   7        1     3280    22417    85384   235543   516256   927523  1338790        0         0

   8        1     9841    77092   333244  1039873  2588641  5371210  9387580 13403950         0

   9        1    29524   260800  1260532  4380151 12146074 28259704 56422444 96634294 136846144

   .
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  Row sums give A115187:
 
 [1, 5, 39, 346, 3230, 31191, 309175, 3129194, 32211432, 336239668, ...]

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