A141360 - OEIS

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

%S 1,1,3,22,281,5276,132577,4209766,162569969,7430664952,393986044961,

%T 23861309117834,1630730511310441,124533452791281028,

%U 10541716135649976929,982527040998772635286,100258434765654907227233

%N E.g.f.: A(x) = exp(x*exp(x*A(x)*exp(x*A(x)^2*exp(x*A(x)^3*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 A141361.

%F E.g.f.: A(x) = B(x/A(x)) where B(x) = exp(x*B(x)*exp(x*B(x)^2*exp(x*B(x)^3*exp(...)))) is the e.g.f. of A141361 = [1,1,5,55,981,24621,803143,32390247,...].

%F E.g.f.: A(x) = C(x/A(x)^2) 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)^3) 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 + 3*x^2/2! + 22*x^3/3! + 281*x^4/4! +

%e 5276*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)*F));A =F);n!*polcoeff(A,n)}

%Y Cf. A141361, A141362, A141363; variant: A141356.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 28 2008