A098233 -id:A098233 - cp's OEIS frontend

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

Marko Riedel, Jan 22 2023

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

			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;

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

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.

Row sums are A165434.

Cf. A098233, A360038, A360039.

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

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.

Original entry on oeis.org

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

Marko Riedel, Jan 22 2023

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

			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;

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

Marko Riedel, Rows 1 to 9 of triangle, flattened.

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

A360039 Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, ..., n, n, n, n, n] into k nonempty subsets, for 5 <= k <= 5n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 4, 11, 22, 32, 34, 22, 13, 7, 3, 1, 1, 14, 123, 611, 1703, 2916, 3371, 2935, 2046, 1171, 561, 226, 81, 25, 6, 1, 1, 51, 1622, 22172, 134766, 430780, 838335, 1110757, 1086681, 831650, 519000, 272212, 122736, 48255, 16670, 5087, 1371, 325, 65, 10, 1, 1, 202, 25223, 975478, 13471057, 84718407, 290637504, 619325134

Offset: 1

Marko Riedel, Jan 22 2023

A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=5.

			The triangular array starts:
[1]: 1;
[2]: 1,  1,   1,   1,    1,    1;
[3]: 1,  4,  11,  22,   32,   34,   22,   13,    7,    3,   1;
[4]: 1, 14, 123, 611, 1703, 2916, 3371, 2935, 2046, 1171, 561, 226, 81, 25, 6, 1;

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

Marko Riedel, Rows 1 to 9 of triangle, flattened.

Cf. A098233, A360037, A360038, A165436 (row sums).

cp's OEIS Frontend

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.

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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.

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A360039 Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, ..., n, n, n, n, n] into k nonempty subsets, for 5 <= k <= 5n.

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