A354341 a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} 1/(d * ((k/d)!)^d) )/(n-k)!.

1, 4, 12, 38, 130, 557, 2877, 18314, 136458, 1180457, 11389081, 122833207, 1446973931, 18594740348, 257507754524, 3835059283282, 60937544854850, 1030871972064485, 18469079943443229, 349656695460113159, 6969526853682012755, 145958486484692023936

Offset: 1

Author

Seiichi Manyama, Aug 15 2022

Keywords

• nonn

Crossrefs

Cf. A182926, A354339, A356407.

Programs

PARI

a182926(n) = n!*sumdiv(n, d, 1/(d*(n/d)!^d));
a(n) = sum(k=1, n, a182926(k)*binomial(n, k));

PARI

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

Formula

a(n) = Sum_{k=1..n} A182926(k) * binomial(n,k).

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