A379885 E.g.f. A(x) satisfies A(x) = 1/(exp(-x) - x*A(x)).

1, 2, 11, 118, 1885, 40266, 1080679, 34979134, 1326825497, 57744176914, 2836795756771, 155305155441030, 9376803979425205, 619006372481008474, 44357422104298022399, 3429215554499681260366, 284496868838293052890033, 25212167721275946619910178, 2377021703587467346833760315

Offset

0,2

Links

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

Formula

E.g.f.: 2/(exp(-x) + sqrt(exp(-2*x) - 4*x)).

a(n) = n! * Sum_{k=0..n} (2*n-2*k+1)^(k-1) * binomial(2*n-2*k+1,n-k)/k!.

a(n) ~ sqrt(1 + LambertW(1/2)) * 2^n * n^(n-1) / (LambertW(1/2)^(n + 1/2) * exp(n)). - Vaclav Kotesovec, Jan 05 2025

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(2/(exp(-x)+sqrt(exp(-2*x)-4*x))))
(PARI) a(n) = n!*sum(k=0, n, (2*n-2*k+1)^(k-1)*binomial(2*n-2*k+1, n-k)/k!);

Crossrefs

Cf. A377890, A377892.

Sequence in context: A304639 A374140 A130222 * A378092 A197993 A057076

Adjacent sequences: A379880 A379882 A379884 * A379886 A379887 A379894

Keyword

nonn,new

Author

Seiichi Manyama, Jan 05 2025

Status

approved