A351277 a(n) = Sum_{k=0..n} (-2*k)^k * Stirling2(n,k).
1, -2, 14, -170, 2910, -64202, 1733278, -55338250, 2039421598, -85204516298, 3979272245662, -205432301027978, 11616783053131934, -714082744228546890, 47409028234931260318, -3380871137079666543114, 257736986308003127354014
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
a(n) = sum(k=0, n, (-2*k)^k*stirling(n, k, 2));
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(2*(exp(x)-1)))))
Formula
E.g.f.: 1/(1 + LambertW( 2 * (exp(x) - 1) )), where LambertW() is the Lambert W-function.
a(n) ~ (-1)^n * n^n / (sqrt(2*exp(1) - 1) * exp(n) * (1 - log(exp(1) - 1/2))^(n + 1/2)). - Vaclav Kotesovec, Feb 06 2022