%I #2 Mar 30 2012 18:37:10

%S 1,1,3,22,245,3516,63727,1405384,36336393,1077150160,36056947931,

%T 1345603208544,55390366280317,2493292939893952,121840258072947975,

%U 6423982984221479296,363498003830522845073,21972216426996693494016

%N E.g.f.: A(x) = exp(x*A(x)*exp(x^2*A(x)^2*exp(x^3*A(x)^3*exp(x^4*A(x)^4*exp(...))))), an infinite power tower.

%F E.g.f.: A(x) = x/Series_Reversion(x*B(x)) where B(x) is the e.g.f. of A141357.

%F E.g.f.: A(x) = B(x/A(x)) where B(x) = exp(x*B(x)^2*exp(x^2*B(x)^4*exp(x^3*B(x)^6*exp(...)))) is the e.g.f. of A141357 = [1,1,5,55,945,21961,645013,22948815,...].

%F E.g.f.: A(x) = C(x/A(x)^2) where C(x) = exp(x*C(x)^3*exp(x^2*C(x)^6*exp(x^3*C(x)^9*exp(...)))) is the e.g.f. of A141358 = [1,1,7,106,2509,80956,3313579,164514904,...].

%F E.g.f.: A(x) = D(x/A(x)^3) 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 + 3*x^2/2! + 22*x^3/3! + 245*x^4/4! + 3516*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+1)*F));A=F);n!*polcoeff(A,n)}

%Y Cf. A141357, A141358, A141359; variant: A141360.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 28 2008