A218653 E.g.f. satisfies: A(x) = 1 + log(1 + x^2*A(x)^2)/x.

1, 1, 4, 27, 264, 3400, 54480, 1045800, 23412480, 599157216, 17258814720, 552733695360, 19485393903360, 749871707270400, 31283408387911680, 1406370859616923200, 67780975948945459200, 3486485719168394342400, 190644828634476331315200, 11043310871932837194977280

Offset: 0

Author

Paul D. Hanna, Nov 03 2012

Keywords

• nonn

Examples

			E.g.f: A(x) = 1 + x + 4*x^2/2! + 27*x^3/3! + 264*x^4/4! + 3400*x^5/5! +...
Related expansions:
A(x)^2 = 1 + 2*x + 10*x^2/2! + 78*x^3/3! + 840*x^4/4! + 11600*x^5/5! +...
log(1 + x^2*A(x)^2)/x = x + 4*x^2/2! + 27*x^3/3! + 264*x^4/4! + 3400*x^5/5! +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A218652, A213641.

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) = A218652(n+1)/(n+1).

a(n) ~ Gamma(1/3) * n^(n - 5/6) / (6^(1/6) * sqrt(Pi) * exp(n) * (1 - log(2))^(n + 2/3)). - Vaclav Kotesovec, Oct 07 2020