A089638 Numerator of (5/2)*Sum_{i=1..n} (-1)^(i-1)/(i^3*C(2*i,i)).

0, 5, 115, 1039, 58157, 1454021, 6854599, 30564710941, 244517610353, 37411196579209, 64619338818497, 86008340157931507, 8951094220597141, 334314418075511195849, 334314418069194908729, 48475590620225838341897, 707173321988579559023843

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).

Prog

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

Crossrefs

Cf. A002117, A089639.

Sequence in context: A207999 A223057 A208783 * A209175 A209719 A208959

Adjacent sequences: A089635 A089636 A089637 * A089639 A089640 A089641

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