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A354851
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a(n) = (n-1)! * Sum_{d|n} d^(n/d).
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1
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1, 3, 8, 54, 144, 2880, 5760, 206640, 1491840, 24675840, 43545600, 10298534400, 6706022400, 1195587993600, 33476463820800, 775450900224000, 376610217984000, 553805325545472000, 128047474114560000, 339876410542276608000, 6208765924866785280000
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OFFSET
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1,2
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LINKS
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FORMULA
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E.g.f.: -Sum_{k>0} log(1 - k * x^k)/k.
If p is prime, a(p) = (p-1)! + p!.
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MATHEMATICA
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a[n_] := (n - 1)! * DivisorSum[n, #^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)
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PROG
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(PARI) a(n) = (n-1)!*sumdiv(n, d, d^(n/d));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k)))
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CROSSREFS
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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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