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A356661
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a(n) = n! * Sum_{d|n} 1/d^(n/d - 1).
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2
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1, 4, 12, 60, 240, 1860, 10080, 95760, 766080, 8210160, 79833600, 1100484000, 12454041600, 188172784800, 2683799838720, 44951306400000, 711374856192000, 13745322470880000, 243290200817664000, 5142812718440517120, 103294640229580800000, 2351280996859354560000
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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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a(p) = 2 * p! for prime p.
E.g.f.: Sum_{k>=1} x^k/(1 - x^k/k).
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MATHEMATICA
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a[n_] := n! * DivisorSum[n, 1/#^(n/# - 1) &]; Array[a, 22] (* Amiram Eldar, Aug 21 2022 *)
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PROG
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(PARI) a(n) = n!*sumdiv(n, d, 1/d^(n/d-1));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(1-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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