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%I #16 Sep 10 2024 04:25:26
%S 0,1,7,109,2677,90226,3873007,202134997,12427851625,879806921041,
%T 70486590597331,6304879010400202,622838214328334077,
%U 67347956304168803173,7911963620634266270071,1003477119181096373029261,136658009168055564212000209,19889317400287888238121299854
%N E.g.f. satisfies A(x) = exp(x * exp(3 * A(x))) - 1.
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = Sum_{k=1..n} (3 * n)^(k-1) * Stirling2(n,k).
%F a(n) ~ n^(n-1) / (3 * sqrt(1 + LambertW(1/3)) * LambertW(1/3)^n * exp(n*(4 - 1/LambertW(1/3)))). - _Vaclav Kotesovec_, Nov 14 2022
%F E.g.f.: Series_Reversion( exp(-3*x) * log(1 + x) ). - _Seiichi Manyama_, Sep 10 2024
%t Table[Sum[(3*n)^(k-1) * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Nov 14 2022 *)
%o (PARI) a(n) = sum(k=1, n, (3*n)^(k-1)*stirling(n, k, 2));
%Y Cf. A052888, A357394.
%Y Cf. A357336.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 26 2022