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A038043
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Number of ways to partition a labeled set into 2-colored subsets of equal size.
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0
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2, 4, 4, 10, 4, 54, 4, 284, 564, 2146, 4, 64068, 4, 273706, 3055056, 9322174, 4, 455865986, 4, 7379708912, 72557376324, 27499326586, 4, 28169911778038, 10389345718756, 15811717561854, 5955168301010504, 26845490776452304, 4
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = Sum_{ d divides n } ((2*n!)/(d!*((n/d)!)^d)).
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MAPLE
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with(numtheory): for n from 1 to 50 do d := divisors(n): s := 0: for k from 1 to nops(d) do s := s +(2*n!)/(d[k]!*((n/d[k])!)^d[k]) od: printf(`%d, `, s) od:
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PROG
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(PARI) a(n) = sumdiv(n, d, ((2*n!)/(d!*((n/d)!)^d))); \\ Michel Marcus, Jan 05 2021
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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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