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%I #11 Feb 01 2023 18:48:57
%S 1,1,5,55,981,24621,803143,32390247,1560845289,87688371385,
%T 5637912173451,408922311037659,33077570245035517,2956347175261764597,
%U 289716070585295689455,30931475430329804121871,3578416722896540323224657,446526125468639494991613297
%N E.g.f.: A(x) = exp(x*A(x) * exp(x*A(x)^2 * exp(x*A(x)^3 * exp(x*A(x)^4 * exp(...))))), an infinite power tower.
%F E.g.f.: A(x) = (1/x)*Series_Reversion(x/B(x)) where B(x) is the e.g.f. of A141360.
%F E.g.f.: A(x) = x/Series_Reversion(x*C(x)) where C(x) is the e.g.f. of A141362.
%F E.g.f.: A(x) = B(x*A(x)) 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)^2*exp(x*C(x)^3*exp(x*C(x)^4*exp(...)))) is the e.g.f. of A141362 = [1,1,7,106,2545,84516,3599869,187549426,...].
%F E.g.f.: A(x) = D(x/A(x)^2) 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 + 5*x^2/2! + 55*x^3/3! + 981*x^4/4! + 24621*x^5/5! +...
%o (PARI) {a(n) = my(A=1+x + x*O(x^n),F); for(i=0,n+1, for(j=0,n, F = exp(x*(A + x*O(x^n))^(n-j+1) * F)); A=F); n!*polcoeff(A,n)}
%o for(n=0,20, print1(a(n),", "))
%Y Cf. A141360, A141362, A141363; variant: A141357.
%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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