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%I #7 Jan 23 2023 09:05:13
%S 1,1,9,175,5357,225461,12112675,792855043,61249418585,5456747990665,
%T 550924441708031,62176714054787135,7758184127489208517,
%U 1060631125759075562797,157674821045525700085499
%N E.g.f.: A(x) = exp(x*A(x)^3*exp(x*A(x)^4*exp(x*A(x)^5*exp(x*A(x)^6*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 A141362.
%F E.g.f.: A(x) = B(x*A(x)^3) 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)^2) 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)^2*exp(x*D(x)^3*exp(x*D(x)^4*exp(...)))) is the e.g.f. of A141362 = [1,1,7,106,2545,84516,3599869,187549426,...].
%e E.g.f.: A(x) = 1 + x + 9*x^2/2! + 175*x^3/3! + 5357*x^4/4! + 225461*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+3)*F)) ;A=F);n!*polcoeff(A,n)}
%Y Cf. A141360, A141361, A141362; variant: A141359.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 28 2008
%E Typo in data corrected by _D. S. McNeil_, Aug 17 2010
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