A248844 Triangle read by rows: T(m,n) = number of ways of distributing n distinguishable balls into m distinguishable bins of size 2 where empty bins are permitted (m >= 1, 1 <= n <= 2m).

1, 1, 2, 4, 6, 6, 3, 9, 24, 54, 90, 90, 4, 16, 60, 204, 600, 1440, 2520, 2520, 5, 25, 120, 540, 2220, 8100, 25200, 63000, 113400, 113400, 6, 36, 210, 1170, 6120, 29520, 128520, 491400, 1587600, 4082400, 7484400, 7484400, 7, 49, 336, 2226, 14070, 83790, 463680, 2346120, 10636920, 42071400, 139708800, 366735600, 681080400, 681080400

Offset

1,3

Links

Table of n, a(n) for n=1..56.

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=2.

Example

Triangle T(n, m) is:
1, 1;
2, 4, 6, 6;
3, 9, 24, 54, 90, 90;
4, 16, 60, 204, 600, 1440, 2520, 2520;
5, 25, 120, 540, 2220, 8100, 25200, 63000, 113400, 113400;

Maple

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

Mathematica

Table[nn = 2 n; Drop[Range[0, nn]! CoefficientList[Series[(1 + x + x^2/2!)^n, {x, 0, nn}], x], 1], {n, 0, 7}] // Flatten (* Geoffrey Critzer, Aug 07 2015 *)

Crossrefs

Sequence in context: A213473 A134920 A011031 * A257821 A238365 A259935

Adjacent sequences: A248841 A248842 A248843 * A248845 A248846 A248847

Keyword

nonn,tabf

Author

Marko Riedel, Oct 15 2014

Status

approved