A358710 Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 2, 2, ..., n, n] into k nonempty submultisets, for 1 <= k <= 2n.

1, 1, 1, 1, 4, 3, 1, 1, 13, 26, 19, 6, 1, 1, 40, 183, 259, 163, 55, 10, 1, 1, 121, 1190, 3115, 3373, 1896, 620, 125, 15, 1, 1, 364, 7443, 34891, 62240, 54774, 27610, 8706, 1795, 245, 21, 1, 1, 1093, 45626, 374059, 1072316, 1435175, 1063570, 485850, 146363, 30261, 4361, 434, 28, 1

Offset

0,5

Comments

A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=2.

References

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

Links

Sidney Cadot, Table of n, a(n) for n = 0..420 (terms 1..420 from Marko Riedel)

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;
[2] 1,   4,    3,     1;
[3] 1,  13,   26,    19,     6,     1;
[4] 1,  40,  183,   259,   163,    55,    10,    1;
[5] 1, 121, 1190,  3115,  3373,  1896,   620,  125,   15,   1;
[6] 1, 364, 7443, 34891, 62240, 54774, 27610, 8706, 1795, 245, 21, 1;

Crossrefs

Cf. A008277, A020555 (row sums), A358721, A358722.

Sequence in context: A189967 A139623 A278072 * A216482 A080758 A123683

Adjacent sequences: A358707 A358708 A358709 * A358711 A358712 A358713

Keyword

nonn,tabf

Author

Marko Riedel, Nov 27 2022

Status

approved