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
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, 1));
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(2*log(1+x)))))
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