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A191415 E.g.f. A(x) satisfies A(x) = x*(1 - A(x))^(-A(x)).

%I A191415 #16 Oct 13 2017 05:11:52
%S A191415 1,0,6,12,340,2340,58338,786240,20890224,428954400,12845444040,
%T A191415 351885980160,12049309321608,408370359196800,15960347878230000,
%U A191415 639599649237319680,28303809398414031360,1302999243310662912000,64651744760744124697536,3352722890027561625600000
%N A191415 E.g.f. A(x) satisfies A(x) = x*(1 - A(x))^(-A(x)).
%H A191415 Vaclav Kotesovec, <a href="/A191415/b191415.txt">Table of n, a(n) for n = 1..380</a>
%F A191415 a(n) = n!*Sum_{k=1..n-1} (n^(k-1)*(-1)^(n-2*k-1)*Stirling1(n-k-1, k))/(n-k-1)!, n > 1, a(1)=1.
%F A191415 a(n) ~ n^(n-1) / (sqrt(1-(2-s)*(1-s)*s) * exp(n) * s^(n-1) * (1-s)^(s*n-1)), where s = 0.530402312512063468084914246777198746... is the root of the equation (1-s)*(2 + s + s*log(1-s)) = 1. - _Vaclav Kotesovec_, Aug 10 2014
%t A191415 Flatten[{1,Table[n!*Sum[(n^(k-1)*(-1)^(n-2*k-1)*StirlingS1[n-k-1,k])/(n-k-1)!,{k,1,n-1}],{n,2,20}]}]  (* _Vaclav Kotesovec_, Aug 10 2014 after _Vladimir Kruchinin_ *)
%o A191415 (Maxima) a(n):=if n=1 then 1 else (n!*sum((n^(k-1)*(-1)^(n-2*k-1)*stirling1(n-k-1,k))/(n-k-1)!,k,1,n-1));
%o A191415 (PARI) a(n) = if (n==1, 1, n!*sum(k=1, n-1, (n^(k-1)*(-1)^(n-2*k-1)*stirling(n-k-1, k, 1))/(n-k-1)!)); \\ _Michel Marcus_, Oct 13 2017
%K A191415 nonn
%O A191415 1,3
%A A191415 _Vladimir Kruchinin_, Jun 01 2011