login
A354341
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} 1/(d * ((k/d)!)^d) )/(n-k)!.
2
1, 4, 12, 38, 130, 557, 2877, 18314, 136458, 1180457, 11389081, 122833207, 1446973931, 18594740348, 257507754524, 3835059283282, 60937544854850, 1030871972064485, 18469079943443229, 349656695460113159, 6969526853682012755, 145958486484692023936
OFFSET
1,2
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!).
PROG
(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!))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 15 2022
STATUS
approved