cp's OEIS Frontend

A224797 E.g.f. satisfies: A(x) = Sum_{n>=0} (exp(x*A(x)^n) - 1)^n / n!.

%I A224797 #5 Apr 18 2013 19:18:22
%S A224797 1,1,4,35,503,10207,268865,8731102,337630732,15165277773,776576049655,
%T A224797 44683002944571,2855602714004089,200794017101260026,
%U A224797 15413426272667102594,1283152929854467388195,115198576226248396583523,11099504126776462035978911
%N A224797 E.g.f. satisfies: A(x) = Sum_{n>=0} (exp(x*A(x)^n) - 1)^n / n!.
%F A224797 E.g.f. satisfies: A(x) = Sum_{n>=0} Sum_{k=0..n} Stirling2(n, k)*A(x)^(n*k) * x^n/n!.
%e A224797 E.g.f.: A(x) = 1 + x + 4*x^2/2! + 35*x^3/3! + 503*x^4/4! + 10207*x^5/5! +...
%e A224797 where
%e A224797 A(x) = 1 + (exp(x*A(x)) - 1) + (exp(x*A(x)^2) - 1)^2/2! + (exp(x*A(x)^3) - 1)^3/3! + (exp(x*A(x)^4) - 1)^4/4! + (exp(x*A(x)^5) - 1)^5/5! +...
%o A224797 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, (exp(x*A^m +x*O(x^n))-1)^m/m!)); n!*polcoeff(A, n)}
%o A224797 for(n=0,21,print1(a(n),", "))
%o A224797 (PARI) {Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
%o A224797 {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, sum(k=0, m, Stirling2(m, k)*(A+x*O(x^n))^(m*k))*x^m/m!)); n!*polcoeff(A, n)}
%o A224797 for(n=0,21,print1(a(n),", "))
%Y A224797 Cf. A189981.
%K A224797 nonn
%O A224797 0,3
%A A224797 _Paul D. Hanna_, Apr 18 2013