A356436 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d) )/k.

1, 5, 23, 146, 874, 8124, 62628, 707664, 7860816, 103284000, 1179669600, 24454569600, 324615427200, 5740203974400, 119579523436800, 2688723275212800, 46084905896601600, 1383333631684300800, 26411386476116275200, 868104140064602112000

Offset: 1

Author

Seiichi Manyama, Aug 07 2022

Keywords

• nonn

Links

• Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)

Crossrefs

Cf. A055225, A353992, A356297, A356437, A356439.

Programs

PARI

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

PARI

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

Formula

a(n) = n! * Sum_{k=1..n} A055225(k)/k.

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

a(n) ~ (n-1)! * 3^((n + 3 - mod(n,3))/3)/2. - Vaclav Kotesovec, Aug 07 2022