_Paul D. Hanna (pauldhanna(AT)juno.com), _, Jun 28 2008

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.

1, 1, 3, 22, 281, 5276, 132577, 4209766, 162569969, 7430664952, 393986044961, 23861309117834, 1630730511310441, 124533452791281028, 10541716135649976929, 982527040998772635286, 100258434765654907227233

0,3

E.g.f.: A(x) = x/Series_Reversion(x*B(x)) where B(x) is the e.g.f. of A141361.

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,...].

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,...].

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.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 281*x^4/4! +

5276*x^5/5! +...

(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)}

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

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Jun 28 2008

approved