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%I #16 Sep 12 2015 11:00:20
%S 1,1,2,10,72,704,8640,127968,2220288,44179200,991802880,24799656960,
%T 683533762560,20589288993792,672920058230784,23717386619136000,
%U 896730039462297600,36203980633475973120,1554541449858851143680
%N E.g.f. satisfies: A'(x) = 1/(1 - x*A(x))^2 with A(0)=1.
%H Vaclav Kotesovec, <a href="/A144011/b144011.txt">Table of n, a(n) for n = 0..335</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Asymptotic of implicit functions if Fww = 0</a>
%F E.g.f. A(x) satisfies: A(x) = 1 + Integral 1/(1 - x*A(x))^2 dx.
%F E.g.f. A(x) satisfies: x/(x*A(x)-1) = tan(1-A(x)). - _Vaclav Kotesovec_, Jun 15 2013
%F a(n) ~ GAMMA(1/3) * n^(n-5/6) * (2+Pi)^(n+1/3) / (3^(1/6) * sqrt(Pi) * exp(n) * 2^(n+5/6)). - _Vaclav Kotesovec_, Feb 23 2014
%t nn=10;Flatten[{1,Table[Subscript[c,j]*j!,{j,1,nn}]/.Solve[Table[SeriesCoefficient[x/(x*(1+Sum[Subscript[c,j]*x^j,{j,1,nn}])-1),{x,0,k}]==SeriesCoefficient[Tan[-Sum[Subscript[c,j]*x^j,{j,1,nn}]],{x,0,k}],{k,0,nn}]]}] (* _Vaclav Kotesovec_, Jun 15 2013 *)
%o (PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal(1/(1-x*A+x*O(x^n))^2 )); n!*polcoeff(A, n)}
%Y Cf. A144010, A238302.
%K nonn,nice
%O 0,3
%A _Paul D. Hanna_, Sep 10 2008
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