A363736 a(n) = (n-1)! * Sum_{d|n} (-1)^(d+1) / (d-1)!.

1, 0, 3, -1, 25, 59, 721, -841, 60481, 15119, 3628801, 12972959, 479001601, 8648639, 134399865601, -218205187201, 20922789888001, 174888473759999, 6402373705728001, -15205972772390401, 3652732042831872001, 14079294028799, 1124000727777607680001

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Formula

E.g.f.: Sum_{k>0} (1 - exp(-x^k))/k.

E.g.f.: Sum_{k>0} (-1)^k * log(1-x^k)/k!.

If p is an odd prime, a(p) = 1 + (p-1)!.

Mathematica

a[n_] := (n-1)! * DivisorSum[n, (-1)^(#+1)/(#-1)! &]; Array[a, 25] (* Amiram Eldar, Jul 03 2023 *)

Prog

(PARI) a(n) = (n-1)!*sumdiv(n, d, (-1)^(d+1)/(d-1)!);

Crossrefs

Cf. A087906, A132960, A352013, A363737.

Sequence in context: A217472 A156654 A087071 * A098815 A300457 A289329

Adjacent sequences: A363733 A363734 A363735 * A363737 A363738 A363739

Keyword

sign

Author

Seiichi Manyama, Jun 18 2023

Status

approved