OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..444
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} ((k-1)! - 1) * binomial(n,k) * a(n-k).
a(n) ~ n! * (1-r) / ((1 - (1-r)*exp(r)) * r^(n+1)), where r = 0.9183335761894542037857295468680123485973875022318007816308... is the root of the equation exp(r) = -log(1-r). - Vaclav Kotesovec, Mar 06 2022
MATHEMATICA
m = 22; Range[0, m]! * CoefficientList[Series[1/(Exp[x] + Log[1 - x]), {x, 0, m}], x] (* Amiram Eldar, Mar 06 2022 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)+log(1-x))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, ((k-1)!-1)*binomial(n, k)*a(n-k)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 06 2022
STATUS
approved