A351762 Expansion of e.g.f. 1/(1 - 2*x*exp(x)).

1, 2, 12, 102, 1160, 16490, 281292, 5598110, 127326096, 3257961426, 92625793940, 2896747456262, 98827517418456, 3652643136982970, 145385563800940764, 6200097935648462190, 282035994269804870432, 13631368700936950044578, 697586352315912913754916

Offset

0,2

Links

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

Formula

a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k)^k/k!.

a(0) = 1 and a(n) = 2 * n * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.

a(n) ~ n! / ((1 + LambertW(1/2)) * LambertW(1/2)^n). - Vaclav Kotesovec, Feb 19 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*x*exp(x))))
(PARI) a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k)^k/k!);
(PARI) a(n) = if(n==0, 1, 2*n*sum(k=0, n-1, binomial(n-1, k)*a(k)));

Crossrefs

Column k=2 of A351761.

Cf. A000629, A351777.

Sequence in context: A113557 A245266 A123897 * A302357 A052693 A050621

Adjacent sequences: A351759 A351760 A351761 * A351763 A351764 A351765

Keyword

nonn

Author

Seiichi Manyama, Feb 18 2022

Status

approved