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%I #15 May 23 2022 09:14:29
%S 1,2,14,144,1936,32000,625952,14117152,360175584,10246079616,
%T 321313928448,11006050602624,408662128569984,16344011453662464,
%U 700254206319007488,31990601456727585792,1551985176120589820928,79669906174753878177792
%N Expansion of e.g.f. 1/(1 - x)^(2/(1 + 2 * log(1-x))).
%F a(0) = 1; a(n) = Sum_{k=1..n} A088500(k) * binomial(n-1,k-1) * a(n-k).
%F a(n) = Sum_{k=0..n} 2^k * A000262(k) * |Stirling1(n,k)|.
%F a(n) ~ n^(n - 1/4) / (2^(3/4) * (exp(1/2) - 1)^(n + 1/4) * exp(3/4 - 1/(4*(exp(1/2) - 1)) - sqrt(2*n/(exp(1/2) - 1)) + n/2)). - _Vaclav Kotesovec_, May 23 2022
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^(2/(1+2*log(1-x)))))
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, sum(k=0, j, 2^k*k!*abs(stirling(j, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v;
%Y Cf. A088815, A354287.
%Y Cf. A000262, A088500, A354288, A354290.
%K nonn
%O 0,2
%A _Seiichi Manyama_, May 23 2022