A360037 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 subsets, for 3 <= k <= 3n.

1, 1, 1, 1, 1, 1, 4, 10, 13, 7, 3, 1, 1, 14, 92, 221, 249, 172, 81, 25, 6, 1, 1, 50, 872, 4277, 8806, 9840, 6945, 3377, 1206, 325, 65, 10, 1, 1, 186, 8496, 85941, 320320, 585960, 627838, 442321, 221475, 82985, 24038, 5496, 995, 140, 15, 1

Offset

1,7

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

Marko Riedel, Rows 1 to 10 of triangle, flattened.

Marko Riedel, Documentation of the algorithm used in the Maple code.

Marko Riedel, Maple code for sequence by plain enumeration and the Polya Enumeration Theorem, by substitution and by recurrence.

Example

The triangular array starts:
[1]: 1;
[2]: 1,  1,  1,   1;
[3]: 1,  4, 10,  13,   7,   3,  1;
[4]: 1, 14, 92, 221, 249, 172, 81, 25, 6, 1;

Maple

read "a360037maple":  # see link
A360037Row := n -> seq(T2(n, k, 3), k = 3..n*3): seq(A360037Row(n), n = 1..6);

Crossrefs

Row sums are A165434.

Cf. A098233, A360038, A360039.

Sequence in context: A074939 A038464 A366633 * A125966 A259725 A260936

Adjacent sequences: A360034 A360035 A360036 * A360038 A360039 A360040

Keyword

nonn,tabf

Author

Marko Riedel, Jan 22 2023

Status

approved