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%I #2 Mar 30 2012 18:37:10
%S 1,1,7,106,2545,84516,3599869,187549426,11569862497,825476139784,
%T 66913201813141,6077199111018366,611543851953714673,
%U 67563014389049920924,8132697862579447135021,1059750845948899631017906
%N E.g.f.: A(x) = exp(x*A(x)^2*exp(x*A(x)^3*exp(x*A(x)^4*exp(x*A(x)^5*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 A141361.
%F E.g.f.: A(x) = x/Series_Reversion(x*D(x)) where D(x) is the e.g.f. of A141363.
%F E.g.f.: A(x) = B(x*A(x)^2) where B(x) = exp(x*exp(x*B(x)*exp(x*B(x)^2*exp(x*B(x)^3*exp(...))))) is the e.g.f. of A141360 = [1,1,3,22,281,5276,132577,4209766,...].
%F E.g.f.: A(x) = C(x*A(x)) where C(x) = exp(x*C(x)*exp(x*C(x)^2*exp(x*C(x)^3*exp(...)))) is the e.g.f. of A141361 = [1,1,5,55,981,24621,803143,32390247,...].
%F E.g.f.: A(x) = D(x/A(x)) where D(x) = exp(x*D(x)^3*exp(x*D(x)^4*exp(x*D(x)^5*exp(...)))) is the e.g.f. of A141363 = [1,1,9,175,5357,225461,12112675,792855043,...].
%e E.g.f.: A(x) = 1 + x + 7*x^2/2! + 106*x^3/3! + 2545*x^4/4! +
%e 84516*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))^(n-j+2)*F)) ;A=F);n!*polcoeff(A,n)}
%Y Cf. A141360, A141361, A141363; variant: A141358.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 28 2008
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