A213641 E.g.f. satisfies: A(x) = 1 - log(1 - x^2*A(x)^2) / x.

1, 1, 4, 33, 408, 6760, 140880, 3543120, 104469120, 3535037856, 135053291520, 5750579640960, 270067321117440, 13868724577593600, 773138898730598400, 46500352460941579200, 3001412657729335449600, 206946807350480534937600, 15180752044039172426035200

Offset: 0

Author

Paul D. Hanna, Jun 17 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 4*x^2/2! + 33*x^3/3! + 408*x^4/4! + 6760*x^5/5! +...
Related expansions:
A(x)^2 = 1 + 2*x + 10*x^2/2! + 90*x^3/3! + 1176*x^4/4! + 20240*x^5/5! +...
-log(1 - x^2*A(x)^2)/x = x + 4*x^2/2! + 33*x^3/3! + 408*x^4/4! +...
A(x + log(1-x^2)) = 1 + x + 2*x^2/2! + 9*x^3/3! + 48*x^4/4! + 340*x^5/5! +...
		

Crossrefs

Cf. A213640, A218653, A200320.

Programs

PARI

{a(n)=n!*polcoeff((1/x)*serreverse(x+log(1-x^2 +x^2*O(x^n))), n)}
for(n=0,25,print1(a(n),", "))

Formula

E.g.f. satisfies: A(x + log(1-x^2)) = x/(x + log(1-x^2)).

E.g.f.: A(x) = (1/x)*Series_Reversion(x + log(1-x^2)).

a(n) = A213640(n+1)/(n+1).