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A360039 Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, ..., n, n, n, n, n] into k nonempty subsets, for 5 <= k <= 5n.

%I A360039 #15 Jan 25 2023 16:26:42
%S A360039 1,1,1,1,1,1,1,1,4,11,22,32,34,22,13,7,3,1,1,14,123,611,1703,2916,
%T A360039 3371,2935,2046,1171,561,226,81,25,6,1,1,51,1622,22172,134766,430780,
%U A360039 838335,1110757,1086681,831650,519000,272212,122736,48255,16670,5087,1371,325,65,10,1,1,202,25223,975478,13471057,84718407,290637504,619325134
%N A360039 Triangle read by rows. Number T(n, k) of partitions of the multiset [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, ..., n, n, n, n, n] into k nonempty subsets, for 5 <= k <= 5n.
%C A360039 A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=5.
%D A360039 F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
%H A360039 Marko Riedel, <a href="/A360039/b360039.txt">Rows 1 to 9 of triangle, flattened.</a>
%e A360039 The triangular array starts:
%e A360039 [1]: 1;
%e A360039 [2]: 1,  1,   1,   1,    1,    1;
%e A360039 [3]: 1,  4,  11,  22,   32,   34,   22,   13,    7,    3,   1;
%e A360039 [4]: 1, 14, 123, 611, 1703, 2916, 3371, 2935, 2046, 1171, 561, 226, 81, 25, 6, 1;
%Y A360039 Cf. A098233, A360037, A360038, A165436 (row sums).
%K A360039 nonn,tabf
%O A360039 1,9
%A A360039 _Marko Riedel_, Jan 22 2023