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%I #20 Oct 21 2014 23:13:16
%S 1,1,1,1,1,2,4,8,16,32,62,112,182,252,252,3,9,27,81,243,726,2142,6174,
%T 17178,45486,112266,250866,486486,756756,756756,4,16,64,256,1024,4092,
%U 16296,64428,251664,965832,3618384,13131888,45741696,151183032,467170704,1322304984,3327708384,7101398304,11732745024,11732745024,5,25,125,625
%N Triangle read by rows: T(m,n) = number of ways of distributing n distinguishable balls into m distinguishable bins of size 5 where empty bins are permitted (m >= 1, 1 <= n <= 5m).
%H Marko R. Riedel, <a href="http://math.stackexchange.com/questions/975503">Distinguishable balls into distinguishable boxes with a maximum capacity</a>
%F E.g.f. for row m: (sum(k=0..s) z^k/k!)^m, s=5
%e Triangle T(n, m) is
%e 1, 1, 1, 1, 1;
%e 2, 4, 8, 16, 32, 62, 112, 182, 252, 252;
%e 3, 9, 27, 81, 243, 726, 2142, 6174, 17178, 45486, 112266, 250866, 486486, 756756, 756756;
%e 4, 16, 64, 256, 1024, 4092, 16296, 64428, 251664, 965832, 3618384, 13131888, 45741696, 151183032, 467170704, 1322304984, 3327708384, 7101398304, 11732745024, 11732745024
%p P := proc(n, m, s) n!*coeftayl(add(z^k/k!, k=0..s)^m, z=0, n); end;
%K nonn,tabf
%O 1,6
%A _Marko Riedel_, Oct 15 2014
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