Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #10 Jun 04 2022 04:22:49
%S 1,3,30,492,11250,330282,11844288,501822108,24527880756,1358556883308,
%T 84094256900232,5753027212816320,431039748845205000,
%U 35102411472973316040,3087236653107610062240,291627772873980244894800,29447260745861893561906320
%N Expansion of e.g.f. 1/sqrt(1 + 6 * log(1-x)).
%F E.g.f.: Sum_{k>=0} binomial(2*k,k) * (-3 * log(1-x)/2)^k.
%F a(n) = Sum_{k=0..n} (3/2)^k * (2*k)! * |Stirling1(n,k)|/k!.
%F a(n) ~ n^n / (sqrt(3) * (exp(1/6)-1)^(n + 1/2) * exp(5*n/6)). - _Vaclav Kotesovec_, Jun 04 2022
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1+6*log(1-x))))
%o (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)))
%o (PARI) a(n) = sum(k=0, n, (3/2)^k*(2*k)!*abs(stirling(n, k, 1))/k!);
%Y Cf. A346978, A354241, A354262.
%Y Cf. A354252, A354259.
%K nonn
%O 0,2
%A _Seiichi Manyama_, May 21 2022