OFFSET
0,2
FORMULA
a(n) = (1/(n+1)!) * Sum_{k=0..n} 2^k * (n+k)! * Stirling1(n,k).
a(n) ~ LambertW(exp(1/2))^n * n^(n-1) / (sqrt(1 + LambertW(exp(1/2))) * 2^(n+1) * exp(n) * (1 - LambertW(exp(1/2)))^(2*n+1)). - Vaclav Kotesovec, Mar 06 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-2*log(1+x)))/x))
(PARI) a(n) = sum(k=0, n, 2^k*(n+k)!*stirling(n, k, 1))/(n+1)!;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 06 2024
STATUS
approved