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%I A357395 #16 Sep 10 2024 04:25:26
%S A357395 0,1,7,109,2677,90226,3873007,202134997,12427851625,879806921041,
%T A357395 70486590597331,6304879010400202,622838214328334077,
%U A357395 67347956304168803173,7911963620634266270071,1003477119181096373029261,136658009168055564212000209,19889317400287888238121299854
%N A357395 E.g.f. satisfies A(x) = exp(x * exp(3 * A(x))) - 1.
%H A357395 <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL2luZGV4L1JlcyNyZXZlcnQ">Index entries for reversions of series</a>
%F A357395 a(n) = Sum_{k=1..n} (3 * n)^(k-1) * Stirling2(n,k).
%F A357395 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 A357395 E.g.f.: Series_Reversion( exp(-3*x) * log(1 + x) ). - _Seiichi Manyama_, Sep 10 2024
%t A357395 Table[Sum[(3*n)^(k-1) * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Nov 14 2022 *)
%o A357395 (PARI) a(n) = sum(k=1, n, (3*n)^(k-1)*stirling(n, k, 2));
%Y A357395 Cf. A052888, A357394.
%Y A357395 Cf. A357336.
%K A357395 nonn
%O A357395 0,3
%A A357395 _Seiichi Manyama_, Sep 26 2022

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