A248846 Triangle read by rows: T(m,n) = number of ways of distributing n distinguishable balls into m distinguishable bins of size 4 where empty bins are permitted (m >= 1, 1 <= n <= 4m).

1, 1, 1, 1, 2, 4, 8, 16, 30, 50, 70, 70, 3, 9, 27, 81, 240, 690, 1890, 4830, 11130, 22050, 34650, 34650, 4, 16, 64, 256, 1020, 4020, 15540, 58380, 210840, 722400, 2310000, 6745200, 17417400, 37837800, 63063000, 63063000, 5, 25, 125, 625, 3120, 15500, 76300, 370300, 1761900, 8166900, 36613500, 157426500, 642642000, 2459457000

Offset

1,5

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=4.

Example

Triangle T(n, m) is
1, 1, 1, 1;
2, 4, 8, 16, 30, 50, 70, 70;
3, 9, 27, 81, 240, 690, 1890, 4830, 11130, 22050, 34650, 34650;
4, 16, 64, 256, 1020, 4020, 15540,58380, 210840, 722400, 2310000, 6745200, 17417400, 37837800, 63063000, 63063000;

Maple

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

Crossrefs

Sequence in context: A332835 A018469 A098904 * A046127 A271480 A226454

Adjacent sequences: A248843 A248844 A248845 * A248847 A248848 A248849

Keyword

nonn,tabf

Author

Marko Riedel, Oct 15 2014

Status

approved