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A357335 E.g.f. satisfies A(x) = (exp(x) - 1) * exp(2 * A(x)).

%I A357335 #20 Feb 16 2025 08:34:04
%S A357335 0,1,5,49,757,16081,435477,14345297,556857973,24894290257,
%T A357335 1259621627349,71165987957329,4440821632449077,303338709537825105,
%U A357335 22512353926895739797,1803812930088064925265,155195078834104237961717,14270228623788585753803089
%N A357335 E.g.f. satisfies A(x) = (exp(x) - 1) * exp(2 * A(x)).
%H A357335 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%H A357335 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A357335 E.g.f.: -LambertW(2 * (1 - exp(x)))/2.
%F A357335 a(n) = Sum_{k=1..n} (2 * k)^(k-1) * Stirling2(n,k).
%F A357335 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
%F A357335 E.g.f.: Series_Reversion( log(1 + x * exp(-2*x)) ). - _Seiichi Manyama_, Sep 09 2024
%o A357335 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(2*(1-exp(x)))/2)))
%o A357335 (PARI) a(n) = sum(k=1, n, (2*k)^(k-1)*stirling(n, k, 2));
%Y A357335 Cf. A048802, A357336.
%Y A357335 Cf. A349524, A356000.
%Y A357335 Cf. A357347.
%K A357335 nonn
%O A357335 0,3
%A A357335 _Seiichi Manyama_, Sep 24 2022