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A358722 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 submultisets, for 1 <= k <= 4n.

%I A358722 #17 Dec 05 2022 06:26:21
%S A358722 1,1,2,1,1,1,12,29,32,21,10,3,1,1,62,513,1399,1857,1513,855,364,119,
%T A358722 31,6,1,1,312,8165,55704,155989,231642,215250,139789,68154,26135,8105,
%U A358722 2071,435,75,10,1,1,1562,125121,2076531,12235869,34100001,53914814,54898626,39436580,21332108,9098469,3160761,914625,223740,46628,8291,1245,155,15,1
%N A358722 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 submultisets, for 1 <= k <= 4n.
%C A358722 A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=4.
%D A358722 F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
%H A358722 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 A358722 Marko Riedel, <a href="/A358722/a358722_1.maple.txt">Maple code for sequence by plain enumeration, the Polya Enumeration Theorem, and Power Group Enumeration</a>
%e A358722 The triangular array starts:
%e A358722 [0]: 1
%e A358722 [1]: 1,  2,   1,    1;
%e A358722 [2]: 1, 12,  29,   32,   21,   10,   3,   1;
%e A358722 [3]: 1, 62, 513, 1399, 1857, 1513, 855, 364, 119, 31, 6, 1;
%Y A358722 Cf. A008277, A358710, A358721, A358781 (row sums).
%K A358722 nonn,tabf
%O A358722 0,3
%A A358722 _Marko Riedel_, Nov 28 2022