OFFSET
0,2
FORMULA
E.g.f.: Sum_{k>=0} binomial(2*k,k) * (2 * log(1+x))^k.
a(n) = Sum_{k=0..n} 2^k * (2*k)! * Stirling1(n,k)/k!.
a(n) ~ n^n / (2 * (exp(1/8)-1)^(n + 1/2) * exp(n - 1/16)). - Vaclav Kotesovec, Jun 04 2022
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-8*log(1+x))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(2*k, k)*(2*log(1+x))^k)))
(PARI) a(n) = sum(k=0, n, 2^k*(2*k)!*stirling(n, k, 1)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 21 2022
STATUS
approved