A351275 a(n) = Sum_{k=0..n} (-2*k)^k * Stirling1(n,k).

1, -2, 18, -268, 5580, -149368, 4887368, -189010176, 8434813760, -426626153664, 24118046539968, -1507010218083456, 103135804627122816, -7672260068001952512, 616407170000568900864, -53192668792451354284032, 4906864974307552234844160

Offset

0,2

Links

Table of n, a(n) for n=0..16.

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

Formula

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

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

Prog

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

Crossrefs

Cf. A351274, A351277.

Sequence in context: A351276 A138275 A292693 * A364400 A377503 A334242

Adjacent sequences: A351272 A351273 A351274 * A351276 A351277 A351278

Keyword

sign

Author

Seiichi Manyama, Feb 05 2022

Status

approved