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%I #16 Sep 08 2024 13:48:51
%S 0,1,5,55,1001,25471,832265,33209695,1565233241,85089724831,
%T 5241027586025,360724089079135,27436914192242681,2285358551395272991,
%U 206893372546088226185,20226992715373747441375,2123855112711652849031321,238375283773978224211297951
%N E.g.f. satisfies A(x) = (exp(x) - 1)/(1 - A(x))^2.
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = Sum_{k=1..n} (3*k-2)!/(2*k-1)! * Stirling2(n,k).
%F a(n) ~ sqrt(31) * n^(n-1) / (sqrt(2) * 3^(3/2) * log(31/27)^(n - 1/2) * exp(n)). - _Vaclav Kotesovec_, Mar 19 2024
%F E.g.f.: Series_Reversion( log(1 + x * (1 - x)^2) ). - _Seiichi Manyama_, Sep 08 2024
%t Table[Sum[(3*k-2)!/(2*k-1)! * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Mar 19 2024 *)
%o (PARI) a(n) = sum(k=1, n, (3*k-2)!/(2*k-1)!*stirling(n, k, 2));
%Y Cf. A052886, A371317.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Mar 18 2024