OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..400
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} ((-1)^(k-1) * k! + 1) * binomial(n,k) * a(n-k).
a(n) ~ n! * (1+r)^2 / ((3 + r*(3+r)) * r^(n+1)), where r = 0.50855472406037552... is the root of the equation 2 - exp(r) - r/(1+r) = 0. - Vaclav Kotesovec, Jul 25 2022
MATHEMATICA
m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x/(1 + x)), {x, 0, m}], x] (* Amiram Eldar, Mar 11 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x/(1+x))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, ((-1)^(k-1)*k!+1)*binomial(n, k)*a(n-k)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 11 2022
STATUS
approved