A358721 Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 2, 2, 2, ..., n, n, n] into k nonempty submultisets, for 1 <= k <= 3n.

1, 1, 1, 1, 1, 7, 11, 8, 3, 1, 1, 31, 139, 219, 175, 86, 28, 6, 1, 1, 127, 1547, 5321, 8004, 6687, 3579, 1329, 359, 71, 10, 1, 1, 511, 16171, 118605, 333887, 472784, 398771, 223700, 89640, 26853, 6171, 1100, 150, 15, 1, 1, 2047, 164651, 2511653, 13045458, 31207637, 41429946, 34621129, 19882236, 8342411, 2668319, 669446, 134075, 21591, 2785, 281, 21, 1

Offset

0,6

Comments

A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=3.

References

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

Links

Table of n, a(n) for n=0..63.

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,   1,    1;
[2]: 1,   7,   11,    8,    3,    1;
[3]: 1,  31,  139,  219,  175,   86,   28,    6,   1;
[4]: 1, 127, 1547, 5321, 8004, 6687, 3579, 1329, 359, 71, 10, 1;

Crossrefs

Cf. A008277, A358710, A358722, A322487 (row sums).

Sequence in context: A269485 A228954 A283651 * A133891 A071631 A054510

Adjacent sequences: A358718 A358719 A358720 * A358722 A358723 A358724

Keyword

nonn,tabf

Author

Marko Riedel, Nov 28 2022

Status

approved