A368285 Expansion of e.g.f. exp(2*x) / (1 + 2*log(1 - x)).
1, 4, 22, 168, 1700, 21560, 328576, 5844608, 118827264, 2717955776, 69076424384, 1931128212992, 58895387322240, 1945869352171264, 69235812945551872, 2639436090012161024, 107329778640349652992, 4637225944423696109568, 212138681191492565180416
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=2^i+2*sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;
Formula
a(n) = 2^n + 2 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ n! * exp(n/2 + 2 - 2*exp(-1/2)) / (2 * (exp(1/2) - 1)^(n+1)). - Vaclav Kotesovec, Dec 29 2023