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A354843
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a(n) = n! * Sum_{d|n} (n/d)^d / d!.
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11
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1, 5, 19, 145, 601, 8521, 35281, 672001, 4898881, 82615681, 439084801, 21138606721, 80951270401, 3358578263041, 49506372115201, 1227603183206401, 6046686277632001, 611515751899852801, 2311256907767808001, 254421414038266675201, 4015778465971464192001
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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} (exp(k * x^k) - 1).
If p is prime, a(p) = 1 + p * p!.
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MATHEMATICA
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a[n_] := n! * DivisorSum[n, (n/#)^#/#! &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)
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PROG
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(PARI) a(n) = n!*sumdiv(n, d, (n/d)^d/d!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, exp(k*x^k)-1)))
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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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