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 A202518 G.f. satisfies: A(x) = exp( Sum_{n>=1} (2^n - A(x))^n * x^n/n ). 4
 1, 1, 4, 111, 12600, 5722258, 10419647136, 76124127132667, 2234758718926030048, 263964471372716219981614, 125532541357451846737479404864, 240382906462440786858510574342553910, 1852958218856132372722626702327036659515008 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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). LINKS EXAMPLE G.f.: A(x) = 1 + x + 4*x^2 + 111*x^3 + 12600*x^4 + 5722258*x^5 +... where 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 +... PROG (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)} CROSSREFS Cf. A163138, A155200. Sequence in context: A201450 A181272 A214107 * A212655 A181485 A135917 Adjacent sequences:  A202515 A202516 A202517 * A202519 A202520 A202521 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 20 2011 STATUS approved

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