A360038 Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 2, 2, 2, 2, ..., n, n, n, n] into k nonempty subsets, for 4 <= k <= 4n.

1, 1, 1, 1, 1, 1, 1, 4, 11, 19, 22, 13, 7, 3, 1, 1, 14, 117, 445, 873, 1002, 805, 483, 226, 81, 25, 6, 1, 1, 51, 1387, 12567, 47986, 96620, 120970, 104942, 67901, 34385, 14150, 4817, 1371, 325, 65, 10, 1, 1, 201, 18171, 396571, 3053216, 11003801, 22360580, 29114463, 26607981, 18227245, 9816458, 4301588, 1572206, 487670, 129880, 29828, 5901, 995, 140, 15, 1

Offset

1,8

Comments

A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=4.

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;
[3]: 1,  4,  11,  19,  22,   13,   7,   3,   1;
[4]: 1, 14, 117, 445, 873, 1002, 805, 483, 226, 81, 25, 6, 1;

Crossrefs

Cf. A098233, A360037, A360039, A165435 (row sums).

Sequence in context: A339214 A008061 A361434 * A304499 A063215 A278709

Adjacent sequences: A360035 A360036 A360037 * A360039 A360040 A360041

Keyword

nonn,tabf

Author

Marko Riedel, Jan 22 2023

Status

approved