OFFSET
0,2
FORMULA
E.g.f.: Sum_{k>=0} binomial(2*k,k) * log(1+x)^k.
a(n) = Sum_{k=0..n} (2*k)! * Stirling1(n,k)/k!.
a(n) ~ n^n / (sqrt(2) * (exp(1/4)-1)^(n + 1/2) * exp(n - 1/8)). - Vaclav Kotesovec, Jun 04 2022
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * (4 - 2*k/n) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, Sep 11 2023
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-4*log(1+x))))
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(2*k, k)*log(1+x)^k)))
(PARI) a(n) = sum(k=0, n, (2*k)!*stirling(n, k, 1)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 20 2022
STATUS
approved