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A323291
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Denominator of the sum of inverse products of cycle sizes in all permutations of [n].
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5
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1, 1, 2, 6, 12, 20, 360, 2520, 1680, 15120, 151200, 554400, 9979200, 129729600, 605404800, 27243216000, 54486432000, 308756448000, 5557616064000, 8122669632000, 351982350720000, 22174888095360000, 25676186215680000, 3740164458750720000, 67322960257512960000
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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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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1, add(
b(n-j)*binomial(n-1, j-1)*(j-1)!/j, j=1..n))
end:
a:= n-> denom(b(n)):
seq(a(n), n=0..25);
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MATHEMATICA
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nmax = 30; Denominator[CoefficientList[Series[Exp[PolyLog[2, x]], {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Feb 12 2024 *)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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