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%I A354260 #11 Jun 04 2022 04:20:58
%S A354260 1,4,44,824,21624,730176,30144192,1470979968,82833047424,
%T A354260 5286741547008,377135779749888,29736359948175360,2568013599548037120,
%U A354260 241061197802997288960,24439230397588083240960,2661258811775918180474880,309780832909692738794987520
%N A354260 Expansion of e.g.f. 1/sqrt(1 - 8 * log(1+x)).
%F A354260 E.g.f.: Sum_{k>=0} binomial(2*k,k) * (2 * log(1+x))^k.
%F A354260 a(n) = Sum_{k=0..n} 2^k * (2*k)! * Stirling1(n,k)/k!.
%F A354260 a(n) ~ n^n / (2 * (exp(1/8)-1)^(n + 1/2) * exp(n - 1/16)). - _Vaclav Kotesovec_, Jun 04 2022
%o A354260 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-8*log(1+x))))
%o A354260 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, binomial(2*k, k)*(2*log(1+x))^k)))
%o A354260 (PARI) a(n) = sum(k=0, n, 2^k*(2*k)!*stirling(n, k, 1)/k!);
%Y A354260 Cf. A320343, A354240, A354259.
%Y A354260 Cf. A354253, A354262.
%K A354260 nonn
%O A354260 0,2
%A A354260 _Seiichi Manyama_, May 21 2022

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