A360037 - OEIS

%I #28 May 07 2023 04:10:10

%S 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,

%T 4277,8806,9840,6945,3377,1206,325,65,10,1,1,186,8496,85941,320320,

%U 585960,627838,442321,221475,82985,24038,5496,995,140,15,1

%N 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.

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

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

%H Marko Riedel, <a href="/A360037/b360037.txt">Rows 1 to 10 of triangle, flattened.</a>

%H Marko Riedel, <a href="/A360037/a360037.pdf">Documentation of the algorithm used in the Maple code.</a>

%H Marko Riedel, <a href="/A360037/a360037_1.maple.txt">Maple code for sequence by plain enumeration and the Polya Enumeration Theorem, by substitution and by recurrence.</a>

%e The triangular array starts:

%e [1]: 1;

%e [2]: 1,  1,  1,   1;

%e [3]: 1,  4, 10,  13,   7,   3,  1;

%e [4]: 1, 14, 92, 221, 249, 172, 81, 25, 6, 1;

%p read "a360037maple":  # see link

%p A360037Row := n -> seq(T2(n, k, 3), k = 3..n*3): seq(A360037Row(n), n = 1..6);

%Y Row sums are A165434.

%Y Cf. A098233, A360038, A360039.

%K nonn,tabf

%O 1,7

%A _Marko Riedel_, Jan 22 2023