A354260 - OEIS

%I #11 Jun 04 2022 04:20:58

%S 1,4,44,824,21624,730176,30144192,1470979968,82833047424,

%T 5286741547008,377135779749888,29736359948175360,2568013599548037120,

%U 241061197802997288960,24439230397588083240960,2661258811775918180474880,309780832909692738794987520

%N Expansion of e.g.f. 1/sqrt(1 - 8 * log(1+x)).

%F E.g.f.: Sum_{k>=0} binomial(2*k,k) * (2 * log(1+x))^k.

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

%F a(n) ~ n^n / (2 * (exp(1/8)-1)^(n + 1/2) * exp(n - 1/16)). - _Vaclav Kotesovec_, Jun 04 2022

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-8*log(1+x))))

%o (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 (PARI) a(n) = sum(k=0, n, 2^k*(2*k)!*stirling(n, k, 1)/k!);

%Y Cf. A320343, A354240, A354259.

%Y Cf. A354253, A354262.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 21 2022