A248847 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).

1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 62, 112, 182, 252, 252, 3, 9, 27, 81, 243, 726, 2142, 6174, 17178, 45486, 112266, 250866, 486486, 756756, 756756, 4, 16, 64, 256, 1024, 4092, 16296, 64428, 251664, 965832, 3618384, 13131888, 45741696, 151183032, 467170704, 1322304984, 3327708384, 7101398304, 11732745024, 11732745024, 5, 25, 125, 625

Offset

1,6

Links

Table of n, a(n) for n=1..54.

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=5

Example

Triangle T(n, m) is
1, 1, 1, 1, 1;
2, 4, 8, 16, 32, 62, 112, 182, 252, 252;
3, 9, 27, 81, 243, 726, 2142, 6174, 17178, 45486, 112266, 250866, 486486, 756756, 756756;
4, 16, 64, 256, 1024, 4092, 16296, 64428, 251664, 965832, 3618384, 13131888, 45741696, 151183032, 467170704, 1322304984, 3327708384, 7101398304, 11732745024, 11732745024

Maple

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

Crossrefs

Sequence in context: A289657 A005309 A078389 * A059173 A355520 A274005

Adjacent sequences: A248844 A248845 A248846 * A248848 A248849 A248850

Keyword

nonn,tabf

Author

Marko Riedel, Oct 15 2014

Status

approved