A356407 a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * ((k/d)!)^d).

1, 4, 15, 70, 375, 2411, 17598, 146490, 1359291, 13978597, 157393368, 1929989029, 25568858978, 364288345409, 5551537358188, 90142504077194, 1553345359200299, 28317316174307405, 544431381017568696, 11010510372888267555, 233653645911730002976

Offset: 1

Author

Seiichi Manyama, Aug 05 2022

Keywords

• nonn

Crossrefs

Cf. A182926, A356009, A356406, A356409.

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} A182926(k)/k!.