A089639 Denominator of (5/2)*Sum_{i=1..n} (-1)^(i-1)/(i^3*C(2*i,i)).

1, 4, 96, 864, 48384, 1209600, 5702400, 25427001600, 203416012800, 31122649958400, 53757304473600, 71550972254361600, 7446481275340800, 278118629152703539200, 278118629152703539200, 40327201227142013184000, 588302700254777604096000

Offset

0,2

Comments

Related to Apery's proof of the irrationality of zeta(3).

Links

Table of n, a(n) for n=0..16.

C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fib. Q., 43,1 (2005), 31-45.

Formula

(5/2)*Sum_{i >= 1} (-1)^(i-1)/(i^3*C(2*i, i)) = zeta(3).

Example

0, 5/4, 115/96, 1039/864, 58157/48384, 1454021/1209600, 6854599/5702400, ... -> zeta(3).

Mathematica

Denominator[Table[5/2 Sum[(-1)^(i-1)/(i^3 Binomial[2i, i]), {i, n}], {n, 0, 20}]] (* Harvey P. Dale, Aug 25 2012 *)

Prog

(PARI) a(n)=denominator(5/2*sum(k=1, n, (-1)^(k+1)/k^3/binomial(2*k, k)))

Crossrefs

Cf. A002117, A089638.

Sequence in context: A203316 A359653 A202682 * A269091 A204973 A204700

Adjacent sequences: A089636 A089637 A089638 * A089640 A089641 A089642

Keyword

nonn,frac

Author

Benoit Cloitre, Jan 01 2004

Extensions

Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar

Status

approved