A357335 E.g.f. satisfies A(x) = (exp(x) - 1) * exp(2 * A(x)).
0, 1, 5, 49, 757, 16081, 435477, 14345297, 556857973, 24894290257, 1259621627349, 71165987957329, 4440821632449077, 303338709537825105, 22512353926895739797, 1803812930088064925265, 155195078834104237961717, 14270228623788585753803089
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
- Index entries for reversions of series
Programs
-
PARI
my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(2*(1-exp(x)))/2))) -
PARI
a(n) = sum(k=1, n, (2*k)^(k-1)*stirling(n, k, 2));
Formula
E.g.f.: -LambertW(2 * (1 - exp(x)))/2.
a(n) = Sum_{k=1..n} (2 * k)^(k-1) * Stirling2(n,k).
a(n) ~ sqrt(1 + 2*exp(1)) * n^(n-1) / (2 * exp(n) * log(1 + exp(-1)/2)^(n - 1/2)). - Vaclav Kotesovec, Nov 14 2022
E.g.f.: Series_Reversion( log(1 + x * exp(-2*x)) ). - Seiichi Manyama, Sep 09 2024