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A358721 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 submultisets, for 1 <= k <= 3n.

%I A358721 #19 Dec 05 2022 06:26:15
%S A358721 1,1,1,1,1,7,11,8,3,1,1,31,139,219,175,86,28,6,1,1,127,1547,5321,8004,
%T A358721 6687,3579,1329,359,71,10,1,1,511,16171,118605,333887,472784,398771,
%U A358721 223700,89640,26853,6171,1100,150,15,1,1,2047,164651,2511653,13045458,31207637,41429946,34621129,19882236,8342411,2668319,669446,134075,21591,2785,281,21,1
%N A358721 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 submultisets, for 1 <= k <= 3n.
%C A358721 A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=3.
%D A358721 F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
%H A358721 Marko Riedel et al., <a href="https://math.stackexchange.com/questions/4585780/">Number of ways to partition a multiset into k non-empty multisets</a>, Mathematics Stack Exchange.
%H A358721 Marko Riedel, <a href="/A358721/a358721_1.maple.txt">Maple code for sequence by plain enumeration, the Polya Enumeration Theorem, and Power Group Enumeration</a>
%e A358721 The triangular array starts:
%e A358721 [0]: 1,
%e A358721 [1]: 1,   1,    1;
%e A358721 [2]: 1,   7,   11,    8,    3,    1;
%e A358721 [3]: 1,  31,  139,  219,  175,   86,   28,    6,   1;
%e A358721 [4]: 1, 127, 1547, 5321, 8004, 6687, 3579, 1329, 359, 71, 10, 1;
%Y A358721 Cf. A008277, A358710, A358722, A322487 (row sums).
%K A358721 nonn,tabf
%O A358721 0,6
%A A358721 _Marko Riedel_, Nov 28 2022