A354261 Expansion of e.g.f. 1/sqrt(1 + 6 * log(1-x)).

1, 3, 30, 492, 11250, 330282, 11844288, 501822108, 24527880756, 1358556883308, 84094256900232, 5753027212816320, 431039748845205000, 35102411472973316040, 3087236653107610062240, 291627772873980244894800, 29447260745861893561906320

Offset: 0

Author

Seiichi Manyama, May 21 2022

Keywords

• nonn

Crossrefs

Cf. A346978, A354241, A354262.

Cf. A354252, A354259.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1+6*log(1-x))))

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(2*k, k)*(-3*log(1-x)/2)^k)))

PARI

a(n) = sum(k=0, n, (3/2)^k*(2*k)!*abs(stirling(n, k, 1))/k!);

Formula

E.g.f.: Sum_{k>=0} binomial(2*k,k) * (-3 * log(1-x)/2)^k.

a(n) = Sum_{k=0..n} (3/2)^k * (2*k)! * |Stirling1(n,k)|/k!.

a(n) ~ n^n / (sqrt(3) * (exp(1/6)-1)^(n + 1/2) * exp(5*n/6)). - Vaclav Kotesovec, Jun 04 2022