A368444 Expansion of e.g.f. exp(x) / (1 + log(1 - 2*x)).

1, 3, 17, 155, 1937, 30499, 577793, 12784155, 323427041, 9207390211, 291277318065, 10136705490779, 384848820035057, 15829002092015267, 701141988610115617, 33275461169171553371, 1684504951149122303169, 90604594879948059236099

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

a(n) ~ sqrt(Pi) * exp(1/2 - exp(-1)/2) * 2^(n + 1/2) * n^(n + 1/2) / (exp(1) - 1)^(n+1). - Vaclav Kotesovec, Dec 25 2023

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=1, i, 2^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;

Crossrefs

Cf. A291979, A368445.

Cf. A343707, A368283.

Sequence in context: A208832 A377810 A135751 * A168441 A001469 A110501

Adjacent sequences: A368441 A368442 A368443 * A368445 A368446 A368447

Keyword

nonn

Author

Seiichi Manyama, Dec 24 2023

Status

approved