A096538 E.g.f.: A(x) = exp(x*exp(2*x*exp(2^2*x*exp(...exp(2^n*x*exp(...))...)))), for n>=0.

1, 1, 5, 73, 2649, 226881, 45061213, 20520985353, 21182201493617, 48996888022427329, 251357040234734546421, 2834058902388354210737289, 69683890614563169975467620681, 3711434364793976039520825570430593

Offset: 0

Author

Paul D. Hanna, Jun 24 2004

Keywords

• nonn

Examples

			A(x) = 1 + 1*x + 5*x^2/2! + 73*x^3/3! + 2649*x^4/4! + 226881*x^5/5! +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..76

Crossrefs

Cf. A096537.

Programs

PARI

a(n)=local(A=exp(x));for(i=1,n,A=exp(x*(2^(n-i))*A+x*O(x^n)));n!*polcoeff(A,n)

Formula

E.g.f. satisfies: log(A(x)) = x*A(2*x).

a(n+1) = Sum_{i=0..n} (i+1)*2^i*binomial(n,i)*a(i)*a(n-i). - Vladeta Jovovic, Dec 29 2006

a(n) ~ c * n! * 2^(n*(n-1)/2), where c = 1.972549257529822552687919986141209749606505056... . - Vaclav Kotesovec, Jul 31 2014