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A352013
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a(n) = Sum_{d|n} (-1)^(n/d+1) * (n-1)!/(d-1)!.
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4
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1, 0, 3, -11, 25, -59, 721, -10919, 60481, -15119, 3628801, -93471839, 479001601, -8648639, 134399865601, -2833553923199, 20922789888001, -174888473759999, 6402373705728001, -228084898487846399, 3652732042831872001, -14079294028799
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OFFSET
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1,3
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LINKS
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FORMULA
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E.g.f.: Sum_{k>0} log(1+x^k)/k!.
E.g.f.: -Sum_{k>0} (-1)^k * (exp(x^k) - 1)/k. - Seiichi Manyama, Jun 18 2023
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MATHEMATICA
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a[n_] := DivisorSum[n, (-1)^(n/#+1) * (n-1)!/(#-1)! &]; Array[a, 22] (* Amiram Eldar, Aug 30 2023 *)
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PROG
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(PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1)*(n-1)!/(d-1)!);
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k)/k!)))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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