A368285 - OEIS

%I #9 Dec 29 2023 06:16:12

%S 1,4,22,168,1700,21560,328576,5844608,118827264,2717955776,

%T 69076424384,1931128212992,58895387322240,1945869352171264,

%U 69235812945551872,2639436090012161024,107329778640349652992,4637225944423696109568,212138681191492565180416

%N Expansion of e.g.f. exp(2*x) / (1 + 2*log(1 - x)).

%F a(n) = 2^n + 2 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).

%F a(n) ~ n! * exp(n/2 + 2 - 2*exp(-1/2)) / (2 * (exp(1/2) - 1)^(n+1)). - _Vaclav Kotesovec_, Dec 29 2023

%o (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;

%Y Cf. A088500, A343707, A368286, A368287.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 19 2023