A202518 - OEIS

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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 (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	`Table of n, a(n) for n=0..12.`
	EXAMPLE	`G.f.: A(x) = 1 + x + 4x^2 + 111x^3 + 12600x^4 + 5722258x^5 +...` `where` `log(A(x)) = (2 - A(x))x + (2^2 - A(x))^2x^2/2 + (2^3 - A(x))^3x^3/3 + (2^4 - A(x))^4x^4/4 +...`
	PROG	`(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (2^m-A+xO(x^n))^mx^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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Last modified May 24 22:42 EDT 2013. Contains 225631 sequences.