A351276 a(n) = Sum_{k=0..n} (2*k)^k * Stirling2(n,k).

1, 2, 18, 266, 5506, 146602, 4772162, 183618794, 8152995138, 410307648938, 23079780216386, 1434953808618090, 97716253164212034, 7233006174407149866, 578233606405444793410, 49651123488091636885994, 4557474786380802233761090, 445324385454834015896585386

Offset

0,2

Links

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

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: 1/(1 + LambertW( 2 * (1 - exp(x)) )), where LambertW() is the Lambert W-function.

a(n) ~ n^n / (sqrt(1 + 2*exp(1)) * (log(exp(1) + 1/2) - 1)^(n + 1/2) * exp(n)). - Vaclav Kotesovec, Feb 06 2022

Prog

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

Crossrefs

Cf. A282190, A308490, A351274, A351277.

Sequence in context: A141009 A143154 A032037 * A138275 A292693 A351275

Adjacent sequences: A351273 A351274 A351275 * A351277 A351278 A351279

Keyword

nonn

Author

Seiichi Manyama, Feb 05 2022

Status

approved