%I #2 Mar 30 2012 18:37:10
%S 1,1,9,175,5321,221001,11659345,746678311,56273809905,4879911980017,
%T 478663176441401,52401160551586815,6333742154439370489,
%U 837795219321504405625,120379591345300309348929
%N E.g.f.: A(x) = exp(x*A(x)^4*exp(x^2*A(x)^8*exp(x^3*A(x)^12*exp(x^4*A(x)^16*exp(...))))), an infinite power tower.
%F E.g.f.: A(x) = (1/x)*Series_Reversion(x/D(x)) where D(x) is the e.g.f. of A141358.
%F E.g.f.: A(x) = B(x*A(x)^3) where B(x) = exp(x*B(x)*exp(x^2*B(x)^2*exp(x^3*B(x)^3*exp(...)))) is the e.g.f. of A141356 = [1,1,3,22,245,3516,63727,1405384,...].
%F E.g.f.: A(x) = C(x*A(x)^2) where C(x) = exp(x*C(x)^2*exp(x^2*C(x)^4*exp(x^3*C(x)^6*exp(...)))) is the e.g.f. of A141357 = [1,1,5,55,945,21961,645013,22948815,...].
%F E.g.f.: A(x) = D(x*A(x)) where D(x) = exp(x*D(x)^3*exp(x^2*D(x)^6*exp(x^3*D(x)^9*exp(...)))) is the e.g.f. of A141358 = [1,1,7,106,2509,80956,3313579,164514904,...].
%e E.g.f.: A(x) = 1 + x + 9*x^2/2! + 175*x^3/3! + 5321*x^4/4! + 221001*x^5/5! +...
%o (PARI) {a(n)=local(A=1+x,F);for(i=0,n,for(j=0,n,F=exp((x*(A+x*O(x^n))^4)^(n-j+1)*F));A=F);n!*polcoeff(A,n)}
%Y Cf. A141356, A141357, A141358; variant: A141363.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 28 2008