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

0,3

Links

Table of n, a(n) for n=0..19.

Example

 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! +...

Prog

 (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), ", "))

Crossrefs

Cf. A189981, A033917.

Sequence in context: A042255 A152213 A259607 * A089471 A196193 A331817

Adjacent sequences: A214927 A214928 A214929 * A214931 A214932 A214933

Keyword

nonn

Author

Paul D. Hanna, Mar 09 2013

Status

approved