A360039 Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, ..., n, n, n, n, n] into k nonempty subsets, for 5 <= k <= 5n.

1, 1, 1, 1, 1, 1, 1, 1, 4, 11, 22, 32, 34, 22, 13, 7, 3, 1, 1, 14, 123, 611, 1703, 2916, 3371, 2935, 2046, 1171, 561, 226, 81, 25, 6, 1, 1, 51, 1622, 22172, 134766, 430780, 838335, 1110757, 1086681, 831650, 519000, 272212, 122736, 48255, 16670, 5087, 1371, 325, 65, 10, 1, 1, 202, 25223, 975478, 13471057, 84718407, 290637504, 619325134

Offset

1,9

Comments

A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=5.

References

F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.

Links

Marko Riedel, Rows 1 to 9 of triangle, flattened.

Example

The triangular array starts:
[1]: 1;
[2]: 1,  1,   1,   1,    1,    1;
[3]: 1,  4,  11,  22,   32,   34,   22,   13,    7,    3,   1;
[4]: 1, 14, 123, 611, 1703, 2916, 3371, 2935, 2046, 1171, 561, 226, 81, 25, 6, 1;

Crossrefs

Cf. A098233, A360037, A360038, A165436 (row sums).

Sequence in context: A318180 A301115 A050843 * A301152 A301083 A024990

Adjacent sequences: A360036 A360037 A360038 * A360040 A360041 A360042

Keyword

nonn,tabf

Author

Marko Riedel, Jan 22 2023

Status

approved