A248845 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).

1, 1, 1, 2, 4, 8, 14, 20, 20, 3, 9, 27, 78, 210, 510, 1050, 1680, 1680, 4, 16, 64, 252, 960, 3480, 11760, 36120, 97440, 218400, 369600, 369600, 5, 25, 125, 620, 3020, 14300, 65100, 281400, 1138200, 4229400, 14091000, 40656000, 96096000, 168168000, 168168000, 6, 36, 216, 1290, 7620, 44220, 250320, 1371720, 7215600, 36086400

Offset

1,4

Links

Table of n, a(n) for n=1..55.

Marko R. Riedel, Distinguishable balls into distinguishable boxes with a maximum capacity

Formula

E.g.f. for row m: (sum(k=0..s) z^k/k!)^m, s=3

Example

Triangle T(n, m) is
1, 1, 1;
2, 4, 8, 14, 20, 20;
3, 9, 27, 78, 210, 510, 1050, 1680, 1680;
4, 16, 64, 252, 960, 3480, 11760, 36120, 97440, 218400, 369600, 369600;

Maple

P := proc(n, m, s) n!*coeftayl(add(z^k/k!, k=0..s)^m, z=0, n); end;

Crossrefs

Sequence in context: A248379 A002132 A294065 * A370047 A169926 A140164

Adjacent sequences: A248842 A248843 A248844 * A248846 A248847 A248848

Keyword

nonn,tabf

Author

Marko Riedel, Oct 15 2014

Status

approved