A356406 a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * (k/d)^d).

1, 4, 16, 79, 443, 2968, 22216, 189698, 1792402, 18745036, 213452996, 2653142952, 35448861576, 509724975264, 7824794618208, 128006170541328, 2217950478978576, 40686737647774368, 785852762719168992, 15974195890305405696, 340376906088298319616

Offset: 1

Author

Seiichi Manyama, Aug 05 2022

Keywords

• nonn

Crossrefs

Cf. A308345, A356009, A356010, A356407, A356408.

Programs

PARI

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

PARI

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

Formula

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

a(n) = n! * Sum_{k=1..n} A308345(k)/k!.