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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.
4
1, 1, 1, 1, 1, 7, 11, 8, 3, 1, 1, 31, 139, 219, 175, 86, 28, 6, 1, 1, 127, 1547, 5321, 8004, 6687, 3579, 1329, 359, 71, 10, 1, 1, 511, 16171, 118605, 333887, 472784, 398771, 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
OFFSET
0,6
COMMENTS
A generalization of ordinary Stirling set numbers to multisets that contain some m instances each of n elements, here we have m=3.
REFERENCES
F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.
EXAMPLE
The triangular array starts:
[0]: 1,
[1]: 1, 1, 1;
[2]: 1, 7, 11, 8, 3, 1;
[3]: 1, 31, 139, 219, 175, 86, 28, 6, 1;
[4]: 1, 127, 1547, 5321, 8004, 6687, 3579, 1329, 359, 71, 10, 1;
CROSSREFS
Cf. A008277, A358710, A358722, A322487 (row sums).
Sequence in context: A269485 A228954 A283651 * A133891 A071631 A054510
KEYWORD
nonn,tabf
AUTHOR
Marko Riedel, Nov 28 2022
STATUS
approved