[seqfan] A little challenge

[Peter Luschny]

What is the general law of this rectangular array?

[1, 2,  4, ...]
[1, 3, 10,  41,  196,   1057,    6322,    41393,    293608]
[1, 4, 20, 127,  967,   8549,   85829,   962308,  11895252]
[1, 5, 33, 280, 2883,  34817,  481477,  7489454, 129259662]
[1, 6, 49, 518, 6689, 101841, 1783170, 35250562, 775700824]
[1, 7, 68, 859, 13310,243946, 5155512,123294103,3288775809]
[1, 8, 90,1321, 23851,510502,12622252,353704058,11070101343]
[...]

Preferably submit your comments (with some code, s'il vous plaît) to
https://groups.google.com/group/seqcomp/browse_thread/thread/c8c8725327093f95
I'm curious to see different approaches to such a problem.

Peter