A202518 G.f. satisfies: A(x) = exp( Sum_{n>=1} (2^n - A(x))^n * x^n/n ).

1, 1, 4, 111, 12600, 5722258, 10419647136, 76124127132667, 2234758718926030048, 263964471372716219981614, 125532541357451846737479404864, 240382906462440786858510574342553910, 1852958218856132372722626702327036659515008

Offset: 0

Author

Paul D. Hanna, Dec 20 2011

Keywords

• nonn

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).

Examples

			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 +...
		

Crossrefs

Cf. A163138, A155200.

Programs

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)}