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

1,2

Links

Table of n, a(n) for n=1..21.

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!.

Prog

(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)))

Crossrefs

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

Sequence in context: A002713 A221763 A362750 * A009318 A081682 A068788

Adjacent sequences: A356403 A356404 A356405 * A356407 A356408 A356409

Keyword

nonn

Author

Seiichi Manyama, Aug 05 2022

Status

approved