A118804 G.f.: 1 = Sum_{n>=0} a(n)*x^n / Product_{k=1..n+1} (1+k*x)^2.

1, 2, 9, 66, 685, 9294, 156697, 3169910, 74998081, 2035262154, 62391632417, 2134187066010, 80641239109677, 3337651407273846, 150239268816661137, 7310140430519234862, 382439924662714479457, 21413128578896024921298, 1277905479699750127195097

Offset

0,2

Comments

Compare to: 1 = Sum_{n>=0} n!*x^n / Product_{k=1..n+1} (1+k*x).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..32

Example

1 = 1/(1+x)^2 + 2*x/((1+x)*(1+2*x))^2 + 9*x^2/((1+x)*(1+2*x)*(1+3*x))^2 + 66*x^3/((1+x)*(1+2*x)*(1+3*x)*(1+4*x))^2 +...+ a(n)*x^n/((1+x)*(1+2x)*(1+3x)*...*(1+n*x))^2 +...

Prog

(PARI) {a(n)=if(n==0, 1, polcoeff(1-sum(k=0, n-1, a(k)*x^k/prod(j=1, k+1, 1+j*x+x*O(x^n))^2), n))}

Crossrefs

Cf. A118805 (variant).

Sequence in context: A089471 A196193 A331817 * A365995 A020555 A243281

Adjacent sequences: A118801 A118802 A118803 * A118805 A118806 A118807

Keyword

sign

Author

Paul D. Hanna, May 02 2006

Status

approved