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%I #21 Oct 21 2014 23:12:37
%S 1,1,1,2,4,8,14,20,20,3,9,27,78,210,510,1050,1680,1680,4,16,64,252,
%T 960,3480,11760,36120,97440,218400,369600,369600,5,25,125,620,3020,
%U 14300,65100,281400,1138200,4229400,14091000,40656000,96096000,168168000,168168000,6,36,216,1290,7620,44220,250320,1371720,7215600,36086400
%N Triangle read by rows: T(m,n) = number of ways of distributing n distinguishable balls into m distinguishable bins of size 3 where empty bins are permitted (m >= 1, 1 <= n <= 3m).
%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=3
%e Triangle T(n, m) is
%e 1, 1, 1;
%e 2, 4, 8, 14, 20, 20;
%e 3, 9, 27, 78, 210, 510, 1050, 1680, 1680;
%e 4, 16, 64, 252, 960, 3480, 11760, 36120, 97440, 218400, 369600, 369600;
%p P := proc(n, m, s) n!*coeftayl(add(z^k/k!, k=0..s)^m, z=0, n); end;
%K nonn,tabf
%O 1,4
%A _Marko Riedel_, Oct 15 2014
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