A354013 Expansion of e.g.f. 1/(1 + log(1-x) * (1 - log(1-x))).
1, 1, 5, 32, 278, 3014, 39226, 595608, 10335888, 201785688, 4377151464, 104444584848, 2718748442208, 76668029954736, 2328328726108368, 75759574181169792, 2629417097250852480, 96963968323279825920, 3786037089608099128320, 156041617540423798782720
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x)*(1-log(1-x))))) -
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;
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PARI
a(n) = sum(k=0, n, k!*fibonacci(k+1)*abs(stirling(n, k, 1)));
Formula
a(0) = 1; a(n) = Sum_{k=1..n} A000776(k-1) * binomial(n,k) * a(n-k).
a(n) = Sum_{k=0..n} k! * Fibonacci(k+1) * |Stirling1(n,k)|.
a(n) ~ n! / (sqrt(5) * exp((sqrt(5)-1)/2) * (1 - exp((1-sqrt(5))/2))^(n+1)). - Vaclav Kotesovec, May 15 2022