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A358904
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Number of finite sets of compositions with all equal sums and total sum n.
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3
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1, 1, 2, 4, 9, 16, 38, 64, 156, 260, 632, 1024, 2601, 4096, 10208, 16944, 40966, 65536, 168672, 262144, 656980, 1090240, 2620928, 4194304, 10862100, 16781584, 41940992, 69872384, 168403448, 268435456, 693528552, 1073741824, 2695006177, 4473400320, 10737385472
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n>0) = Sum_{d|n} binomial(2^(d-1),n/d).
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EXAMPLE
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The a(1) = 1 through a(4) = 9 sets:
{(1)} {(2)} {(3)} {(4)}
{(11)} {(12)} {(13)}
{(21)} {(22)}
{(111)} {(31)}
{(112)}
{(121)}
{(211)}
{(1111)}
{(2),(11)}
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MATHEMATICA
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Table[If[n==0, 1, Sum[Binomial[2^(d-1), n/d], {d, Divisors[n]}]], {n, 0, 30}]
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PROG
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(PARI) a(n) = if (n, sumdiv(n, d, binomial(2^(d-1), n/d)), 1); \\ Michel Marcus, Dec 14 2022
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CROSSREFS
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The case of sets of partitions is A359041.
A001970 counts multisets of partitions.
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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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