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

%I A096538 #10 Jul 31 2014 11:58:12
%S A096538 1,1,5,73,2649,226881,45061213,20520985353,21182201493617,
%T A096538 48996888022427329,251357040234734546421,2834058902388354210737289,
%U A096538 69683890614563169975467620681,3711434364793976039520825570430593
%N A096538 E.g.f.: A(x) = exp(x*exp(2*x*exp(2^2*x*exp(...exp(2^n*x*exp(...))...)))), for n>=0.
%H A096538 Vaclav Kotesovec, <a href="/A096538/b096538.txt">Table of n, a(n) for n = 0..76</a>
%F A096538 E.g.f. satisfies: log(A(x)) = x*A(2*x).
%F A096538 a(n+1) = Sum_{i=0..n} (i+1)*2^i*binomial(n,i)*a(i)*a(n-i). - _Vladeta Jovovic_, Dec 29 2006
%F A096538 a(n) ~ c * n! * 2^(n*(n-1)/2), where c = 1.972549257529822552687919986141209749606505056... . - _Vaclav Kotesovec_, Jul 31 2014
%e A096538 A(x) = 1 + 1*x + 5*x^2/2! + 73*x^3/3! + 2649*x^4/4! + 226881*x^5/5! +...
%o A096538 (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)
%Y A096538 Cf. A096537.
%K A096538 nonn
%O A096538 0,3
%A A096538 _Paul D. Hanna_, Jun 24 2004