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A143140
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Total number of all repeated partitions of the n-set {1,2,3,...,n}.
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2
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1, 1, 2, 11, 83, 787, 8965, 119170, 1810450, 30942699, 587606593, 12274606775, 279715819531, 6905395692990, 183588212652382, 5229549060414223, 158895798308201987, 5129671140284343035, 175343720698891809337, 6326623756471457351814, 240286954202031694593966
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OFFSET
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0,3
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COMMENTS
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The corresponding unlabeled counterpart is sequence A143141.
See also A131407 = Repeated set partitions or nested set partitions. Possible coalitions among n persons.
See also A137731 = Repeated set splitting, labeled elements.
a(n) is the number of set partitions of the n-set plus sum of a(k) for all the k-sets (1 < k < n) that are contained (with multiplicity) in these set partitions. - Alois P. Heinz, Jul 27 2012
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LINKS
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FORMULA
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EXAMPLE
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a(1) = |{{{1}}}| = 1.
a(2) = |{{{1,2}}, {{1},{2}}}| = 2.
a(3) = |{{{1,2,3}}, {{1,2},{3}}, {{2},{1,3}}, {{1},{2,3}}, {{1},{2},{3}}}| + 3*a(2) = 5 + 3*2 = 11.
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MAPLE
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with(combinat):
a:= proc(n) option remember;
bell(n)+ add(a(k)*binomial(n, k)*bell(n-k), k=2..n-1)
end:
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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