%I #2 Mar 30 2012 18:37:10
%S 1,1,7,106,2509,80956,3313579,164514904,9608077945,645470256592,
%T 49038954301711,4157529546929056,389125813949115973,
%U 39853422352958799040,4433527105413108692851,532370587431255626482816
%N E.g.f.: A(x) = exp(x*A(x)^3*exp(x^2*A(x)^6*exp(x^3*A(x)^9*exp(x^4*A(x)^12*exp(...))))), an infinite power tower.
%F E.g.f.: A(x) = (1/x)*Series_Reversion(x/C(x)) where C(x) is the e.g.f. of A141357.
%F E.g.f.: A(x) = x/Series_Reversion(x*D(x)) where D(x) is the e.g.f. of A141359.
%F E.g.f.: A(x) = B(x*A(x)^2) 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)) 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)^4*exp(x^2*D(x)^8*exp(x^3*D(x)^12*exp(...)))) is the e.g.f. of A141359 = [1,1,9,175,5321,221001,11659345,746678311,...].
%e E.g.f.: A(x) = 1 + x + 7*x^2/2! + 106*x^3/3! + 2509*x^4/4! + 80956*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))^3)^(n-j+1)*F));A=F);n!*polcoeff(A,n)}
%Y Cf. A141356, A141357, A141359; variant: A141362.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 28 2008
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