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%I A281821 #17 Feb 03 2017 03:46:24
%S A281821 16,3456,432000,1185408000,32006016000,42600007296000,
%T A281821 93592216029312000,5989901825875968,735709691763215769600,
%U A281821 25231163879019484818432000,25231163879019484818432000,306987570916030071785862144000
%N A281821 Denominator of Sum_{k=1..n} (30k-11)/(4*(2k-1)*k^3*binomial(2k,k)^2).
%C A281821 In 1990, Gosper gave the following combinatorial identity: zeta(3) = Sum_{k>=1} (30k-11)/(4*(2k-1)*k^3*binomial(2k,k)^2).
%D A281821 Lloyd James Peter Kilford, Modular Forms: A Classical and Computational Introduction, World Scientific, 2008 page 188.
%H A281821 Seiichi Manyama, <a href="/A281821/b281821.txt">Table of n, a(n) for n = 1..384</a>
%H A281821 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AperysConstant.html">Apery's Constant</a>
%e A281821 19/16, 4153/3456, 519283/432000, 1424927267/1185408000, ...
%t A281821 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 *)
%Y A281821 Cf. A002117, A281820.
%K A281821 nonn,frac
%O A281821 1,1
%A A281821 _Seiichi Manyama_, Jan 31 2017

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