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%I #10 Mar 30 2012 18:37:33
%S 1,1,4,111,12600,5722258,10419647136,76124127132667,
%T 2234758718926030048,263964471372716219981614,
%U 125532541357451846737479404864,240382906462440786858510574342553910,1852958218856132372722626702327036659515008
%N G.f. satisfies: A(x) = exp( Sum_{n>=1} (2^n - A(x))^n * x^n/n ).
%C Compare g.f. with: G(x) = exp(Sum_{n>=1} (2 - G(x))^n * x^n/n) = 1 + x*C(-x^2) where C(x) is the Catalan function (A000108).
%e G.f.: A(x) = 1 + x + 4*x^2 + 111*x^3 + 12600*x^4 + 5722258*x^5 +...
%e where
%e log(A(x)) = (2 - A(x))*x + (2^2 - A(x))^2*x^2/2 + (2^3 - A(x))^3*x^3/3 + (2^4 - A(x))^4*x^4/4 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,(2^m-A+x*O(x^n))^m*x^m/m)));polcoeff(A,n)}
%Y Cf. A163138, A155200.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Dec 20 2011
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