A354851 a(n) = (n-1)! * Sum_{d|n} d^(n/d).

1, 3, 8, 54, 144, 2880, 5760, 206640, 1491840, 24675840, 43545600, 10298534400, 6706022400, 1195587993600, 33476463820800, 775450900224000, 376610217984000, 553805325545472000, 128047474114560000, 339876410542276608000, 6208765924866785280000

Offset: 1

Author

Seiichi Manyama, Jun 08 2022

Keywords

• nonn

Crossrefs

Cf. A055225, A318249, A354848.

Programs

Mathematica

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

PARI

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

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k)))

Formula

a(n) = (n-1)! * A055225(n).

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

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