A214930 E.g.f. satisfies: A(x) = Sum_{n>=0} 1/n! * Product_{k=1..n} log(1 + x*A(x)^k).

1, 1, 2, 9, 66, 650, 8250, 127519, 2318876, 48626556, 1154334060, 30589513350, 895415799960, 28693464851688, 999009599484624, 37554576369815400, 1516080931559327280, 65418533528228549744, 3004726893339734134128, 146370356574519380115240

Offset: 0

Author

Paul D. Hanna, Mar 09 2013

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 66*x^4/4! + 650*x^5/5! +...
where
A(x) = 1 + log(1+x*A(x)) + log(1+x*A(x))*log(1+x*A(x)^2)/2! + log(1+x*A(x))*log(1+x*A(x)^2)*log(1+x*A(x)^3)/3! + log(1+x*A(x))*log(1+x*A(x)^2)*log(1+x*A(x)^3)*log(1+x*A(x)^4)/4! +...
		

Crossrefs

Cf. A189981, A033917.

Programs

PARI

{a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,prod(k=1,m,log(1+x*A^k+x*O(x^n)))/m!));n!*polcoeff(A,n)}
for(n=0,20,print1(a(n),", "))