A354848 a(n) = (n-1)! * Sum_{d|n} d^(n/d + 1).

1, 5, 20, 150, 624, 9600, 36000, 811440, 6572160, 105235200, 442713600, 39437798400, 81430272000, 4956708556800, 137741700096000, 3014189418240000, 6067609067520000, 1977977787641856000, 2317659281473536000, 1297953221362237440000

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

a(n) = (n-1)! * A078308(n).

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

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

Mathematica

a[n_] := (n - 1)! * DivisorSum[n, #^(n/# + 1) &]; Array[a, 20] (* Amiram Eldar, Jun 08 2022 *)

Prog

(PARI) a(n) = (n-1)!*sumdiv(n, d, d^(n/d+1));
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k))))

Crossrefs

Cf. A038048, A078308, A354849, A354851.

Sequence in context: A009569 A061964 A133667 * A318433 A205338 A197857

Adjacent sequences: A354845 A354846 A354847 * A354849 A354850 A354851

Keyword

nonn

Author

Seiichi Manyama, Jun 08 2022

Status

approved