OFFSET
1,1
COMMENTS
In 1990, Gosper gave the following combinatorial identity: zeta(3) = Sum_{k>=1} (30k-11)/(4*(2k-1)*k^3*binomial(2k,k)^2).
REFERENCES
Lloyd James Peter Kilford, Modular Forms: A Classical and Computational Introduction, World Scientific, 2008 page 188.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..384
Eric Weisstein's World of Mathematics, Apery's Constant
EXAMPLE
19/16, 4153/3456, 519283/432000, 1424927267/1185408000, ...
MATHEMATICA
Table[Denominator@ Sum[(30 k - 11)/(4 (2 k - 1)*k^3*Binomial[2 k, k]^2), {k, n}], {n, 12}] (* Michael De Vlieger, Feb 02 2017 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Seiichi Manyama, Jan 31 2017
STATUS
approved