%I #21 May 15 2022 02:35:53
%S 1,1,5,32,278,3014,39226,595608,10335888,201785688,4377151464,
%T 104444584848,2718748442208,76668029954736,2328328726108368,
%U 75759574181169792,2629417097250852480,96963968323279825920,3786037089608099128320,156041617540423798782720
%N Expansion of e.g.f. 1/(1 + log(1-x) * (1 - log(1-x))).
%F a(0) = 1; a(n) = Sum_{k=1..n} A000776(k-1) * binomial(n,k) * a(n-k).
%F a(n) = Sum_{k=0..n} k! * Fibonacci(k+1) * |Stirling1(n,k)|.
%F a(n) ~ n! / (sqrt(5) * exp((sqrt(5)-1)/2) * (1 - exp((1-sqrt(5))/2))^(n+1)). - _Vaclav Kotesovec_, May 15 2022
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x)*(1-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, (j-1)!*(1+2*sum(k=1, j-1, 1/k))*binomial(i, j)*v[i-j+1])); v;
%o (PARI) a(n) = sum(k=0, n, k!*fibonacci(k+1)*abs(stirling(n, k, 1)));
%Y Cf. A000045, A000556, A000776, A005444, A320352, A354015, A354018.
%K nonn
%O 0,3
%A _Seiichi Manyama_, May 14 2022