

A281820


Numerator of Sum_{k=1..n} (30k11)/(4*(2k1)*k^3*binomial(2k,k)^2).


2



19, 4153, 519283, 1424927267, 38473051777, 51207632802437, 112503169355608589, 7200202839028523, 884364913705304409923, 30329294715526225502633653, 30329294715526370166581653, 369016528803809437978645999301
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OFFSET

1,1


COMMENTS

In 1990, Gosper gave the following combinatorial identity: zeta(3) = Sum_{k>=1} (30k11)/(4*(2k1)*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



