A358722 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 submultisets, for 1 <= k <= 4n.

1, 1, 2, 1, 1, 1, 12, 29, 32, 21, 10, 3, 1, 1, 62, 513, 1399, 1857, 1513, 855, 364, 119, 31, 6, 1, 1, 312, 8165, 55704, 155989, 231642, 215250, 139789, 68154, 26135, 8105, 2071, 435, 75, 10, 1, 1, 1562, 125121, 2076531, 12235869, 34100001, 53914814, 54898626, 39436580, 21332108, 9098469, 3160761, 914625, 223740, 46628, 8291, 1245, 155, 15, 1

Offset

0,3

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

Table of n, a(n) for n=0..60.

Marko Riedel et al., Number of ways to partition a multiset into k non-empty multisets, Mathematics Stack Exchange.

Marko Riedel, Maple code for sequence by plain enumeration, the Polya Enumeration Theorem, and Power Group Enumeration

Example

The triangular array starts:
[0]: 1
[1]: 1,  2,   1,    1;
[2]: 1, 12,  29,   32,   21,   10,   3,   1;
[3]: 1, 62, 513, 1399, 1857, 1513, 855, 364, 119, 31, 6, 1;

Crossrefs

Cf. A008277, A358710, A358721, A358781 (row sums).

Sequence in context: A079834 A368811 A342458 * A256688 A372326 A029582

Adjacent sequences: A358719 A358720 A358721 * A358723 A358724 A358725

Keyword

nonn,tabf

Author

Marko Riedel, Nov 28 2022

Status

approved