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

0,2

Links

Table of n, a(n) for n=0..18.

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

Prog

(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;

Crossrefs

Cf. A088500, A343707, A368286, A368287.

Sequence in context: A113351 A001827 A363115 * A350268 A353186 A346665

Adjacent sequences: A368282 A368283 A368284 * A368286 A368287 A368288

Keyword

nonn

Author

Seiichi Manyama, Dec 19 2023

Status

approved