A363737 a(n) = n! * Sum_{d|n} (-1)^(d+1) / (d! * (n/d)!).

1, 0, 2, -6, 2, 0, 2, -1680, 10082, 0, 2, -665280, 2, 0, 3632428802, -36843206400, 2, 0, 2, -670442572800, 3379030566912002, 0, 2, -71812452903064473600, 1077167364120207360002, 0, 10002268381116211200002, -3497296636753920000, 2, 0, 2

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Formula

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

If p is an odd prime, a(p) = 2.

Mathematica

a[n_] := n! * DivisorSum[n, (-1)^(#+1)/(#! * (n/#)!) &]; Array[a, 30] (* Amiram Eldar, Jul 03 2023 *)

Prog

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

Crossrefs

Cf. A121860, A132962, A363736.

Sequence in context: A182918 A134301 A168294 * A004544 A010590 A049061

Adjacent sequences: A363734 A363735 A363736 * A363738 A363739 A363740

Keyword

sign

Author

Seiichi Manyama, Jun 18 2023

Status

approved