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A281821
Denominator of Sum_{k=1..n} (30k-11)/(4*(2k-1)*k^3*binomial(2k,k)^2).
2
16, 3456, 432000, 1185408000, 32006016000, 42600007296000, 93592216029312000, 5989901825875968, 735709691763215769600, 25231163879019484818432000, 25231163879019484818432000, 306987570916030071785862144000
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
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
Sequence in context: A266824 A249599 A364483 * A003773 A217021 A375121
KEYWORD
nonn,frac
AUTHOR
Seiichi Manyama, Jan 31 2017
STATUS
approved