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A364939 E.g.f. satisfies A(x) = exp( x*A(x) / (1 - x*A(x))^2 ).

%I A364939 #20 Dec 01 2024 10:51:25
%S A364939 1,1,7,82,1421,32856,953107,33316816,1364109273,64057409920,
%T A364939 3394727354591,200445915043584,13050860745456613,928976320999078912,
%U A364939 71773343988758253675,5982029183718123513856,535011546414154955711153,51110145581257562326401024
%N A364939 E.g.f. satisfies A(x) = exp( x*A(x) / (1 - x*A(x))^2 ).
%H A364939 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A364939 a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(n+k-1,n-k)/k!.
%F A364939 a(n) ~ sqrt(((321*(3852 + 215*sqrt(321)))^(1/3) - 321^(2/3)/(3852 + 215*sqrt(321))^(1/3)) / 107) * (4 + ((83 - 3*sqrt(321))/2)^(1/3) + ((83 + 3*sqrt(321))/2)^(1/3))^n * exp(((215 - 12*sqrt(321))^(1/3) + (215 + 12*sqrt(321))^(1/3) - 1) * (n+1)/12 - n) * n^(n-1) / 3^(n + 1/2). - _Vaclav Kotesovec_, Nov 11 2023
%F A364939 E.g.f.: (1/x) * Series_Reversion( x*exp(-x/(1 - x)^2) ). - _Seiichi Manyama_, Sep 23 2024
%t A364939 Table[n! * Sum[(n+1)^(k-1) * Binomial[n+k-1,n-k]/k!, {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Nov 11 2023 *)
%o A364939 (PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(n+k-1, n-k)/k!);
%Y A364939 Cf. A052873, A364940.
%Y A364939 Cf. A082579.
%K A364939 nonn
%O A364939 0,3
%A A364939 _Seiichi Manyama_, Aug 14 2023