A358594 Expansion of e.g.f. Sum_{k>0} x^k / ((k-1)! - x^k).
1, 4, 9, 52, 125, 1626, 5047, 81768, 408249, 7263910, 39916811, 990191676, 6227020813, 174356750582, 1348633786515, 41861724727696, 355687428096017, 12904788209623614, 121645100408832019, 4866124222538035620, 51490090294307945301, 2248001455555300717294
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := n! * DivisorSum[n, 1/(#-1)!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/((k-1)!-x^k)))) -
PARI
a(n) = n!*sumdiv(n, d, 1/(d-1)!^(n/d));
Formula
a(n) = n! * Sum_{d|n} 1/(d-1)!^(n/d).
If p is prime, a(p) = p + p!.