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A323776
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a(n) = Sum_{k = 1...n} binomial(k + 2^(n - k) - 1, k - 1).
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3
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1, 3, 7, 16, 40, 119, 450, 2253, 15207, 139190, 1731703, 29335875, 677864041, 21400069232, 924419728471, 54716596051100, 4443400439075834, 495676372493566749, 76041424515817042402, 16060385520094706930608, 4674665948889147697184915
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OFFSET
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1,2
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COMMENTS
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Number of multiset partitions of integer partitions of 2^(n - 1) whose parts are constant and have equal sums.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(4) = 16 partitions of partitions:
(1) (2) (4) (8)
(11) (22) (44)
(1)(1) (1111) (2222)
(2)(2) (4)(4)
(2)(11) (4)(22)
(11)(11) (22)(22)
(1)(1)(1)(1) (4)(1111)
(11111111)
(22)(1111)
(1111)(1111)
(2)(2)(2)(2)
(2)(2)(2)(11)
(2)(2)(11)(11)
(2)(11)(11)(11)
(11)(11)(11)(11)
(1)(1)(1)(1)(1)(1)(1)(1)
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MATHEMATICA
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Table[Sum[Binomial[k+2^(n-k)-1, k-1], {k, n}], {n, 20}]
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PROG
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(PARI) a(n) = sum(k=1, n, binomial(k+2^(n-k)-1, k-1)); \\ Michel Marcus, Jan 28 2019
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CROSSREFS
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Cf. A000123, A001970, A002577, A006171, A007716, A034729, A047968, A279787, A279789, A305551, A306017, A319056, A323766, A323774, A323775.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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