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 A281820 Numerator of Sum_{k=1..n} (30k-11)/(4*(2k-1)*k^3*binomial(2k,k)^2). 2
 19, 4153, 519283, 1424927267, 38473051777, 51207632802437, 112503169355608589, 7200202839028523, 884364913705304409923, 30329294715526225502633653, 30329294715526370166581653, 369016528803809437978645999301 (list; graph; refs; listen; history; text; internal format)
 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, ... CROSSREFS Cf. A002117, A281821. Sequence in context: A195756 A125197 A238563 * A213450 A099809 A271588 Adjacent sequences:  A281817 A281818 A281819 * A281821 A281822 A281823 KEYWORD nonn,frac AUTHOR Seiichi Manyama, Jan 31 2017 STATUS approved

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Last modified December 12 07:00 EST 2019. Contains 329948 sequences. (Running on oeis4.)