%I #17 Dec 05 2022 06:26:21
%S 1,1,2,1,1,1,12,29,32,21,10,3,1,1,62,513,1399,1857,1513,855,364,119,
%T 31,6,1,1,312,8165,55704,155989,231642,215250,139789,68154,26135,8105,
%U 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 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 A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=4.
%D F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
%H 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 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 The triangular array starts:
%e [0]: 1
%e [1]: 1, 2, 1, 1;
%e [2]: 1, 12, 29, 32, 21, 10, 3, 1;
%e [3]: 1, 62, 513, 1399, 1857, 1513, 855, 364, 119, 31, 6, 1;
%Y Cf. A008277, A358710, A358721, A358781 (row sums).
%K nonn,tabf
%O 0,3
%A _Marko Riedel_, Nov 28 2022