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A357336 E.g.f. satisfies A(x) = (exp(x) - 1) * exp(3 * A(x)).

%I A357336 #20 Feb 16 2025 08:34:04
%S A357336 0,1,7,100,2257,70021,2768740,133164109,7546722487,492531820066,
%T A357336 36381833190223,3000677194970137,273342303933512362,
%U A357336 27256107730344331879,2952882035628632383975,345384835617231362018764,43378466647737203462409829,5822506028894124326533926193
%N A357336 E.g.f. satisfies A(x) = (exp(x) - 1) * exp(3 * A(x)).
%H A357336 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%H A357336 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A357336 E.g.f.: -LambertW(3 * (1 - exp(x)))/3.
%F A357336 a(n) = Sum_{k=1..n} (3 * k)^(k-1) * Stirling2(n,k).
%F A357336 a(n) ~ sqrt(1 + 3*exp(1)) * n^(n-1) / (3 * exp(n) * log(1 + exp(-1)/3)^(n - 1/2)). - _Vaclav Kotesovec_, Nov 14 2022
%F A357336 E.g.f.: Series_Reversion( log(1 + x * exp(-3*x)) ). - _Seiichi Manyama_, Sep 09 2024
%o A357336 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(3*(1-exp(x)))/3)))
%o A357336 (PARI) a(n) = sum(k=1, n, (3*k)^(k-1)*stirling(n, k, 2));
%Y A357336 Cf. A048802, A357335.
%Y A357336 Cf. A349525, A356001.
%K A357336 nonn
%O A357336 0,3
%A A357336 _Seiichi Manyama_, Sep 24 2022