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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.

%I A360037 #28 May 07 2023 04:10:10
%S A360037 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 A360037 4277,8806,9840,6945,3377,1206,325,65,10,1,1,186,8496,85941,320320,
%U A360037 585960,627838,442321,221475,82985,24038,5496,995,140,15,1
%N 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.
%C A360037 A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=3.
%D A360037 F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
%H A360037 Marko Riedel, <a href="/A360037/b360037.txt">Rows 1 to 10 of triangle, flattened.</a>
%H A360037 Marko Riedel, <a href="/A360037/a360037.pdf">Documentation of the algorithm used in the Maple code.</a>
%H A360037 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 A360037 The triangular array starts:
%e A360037 [1]: 1;
%e A360037 [2]: 1,  1,  1,   1;
%e A360037 [3]: 1,  4, 10,  13,   7,   3,  1;
%e A360037 [4]: 1, 14, 92, 221, 249, 172, 81, 25, 6, 1;
%p A360037 read "a360037maple":  # see link
%p A360037 A360037Row := n -> seq(T2(n, k, 3), k = 3..n*3): seq(A360037Row(n), n = 1..6);
%Y A360037 Row sums are A165434.
%Y A360037 Cf. A098233, A360038, A360039.
%K A360037 nonn,tabf
%O A360037 1,7
%A A360037 _Marko Riedel_, Jan 22 2023