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%I #16 Jun 16 2016 23:27:24
%S 1,4,96,864,48384,1209600,5702400,25427001600,203416012800,
%T 31122649958400,53757304473600,71550972254361600,7446481275340800,
%U 278118629152703539200,278118629152703539200,40327201227142013184000,588302700254777604096000
%N Denominator of (5/2)*Sum_{i=1..n} (-1)^(i-1)/(i^3*C(2*i,i)).
%C Related to Apery's proof of the irrationality of zeta(3).
%H C. Elsner, <a href="http://www.fq.math.ca/Papers1/43-1/paper43-1-5.pdf">On recurrence formulas for sums involving binomial coefficients</a>, Fib. Q., 43,1 (2005), 31-45.
%F (5/2)*Sum_{i >= 1} (-1)^(i-1)/(i^3*C(2*i, i)) = zeta(3).
%e 0, 5/4, 115/96, 1039/864, 58157/48384, 1454021/1209600, 6854599/5702400, ... -> zeta(3).
%t Denominator[Table[5/2 Sum[(-1)^(i-1)/(i^3 Binomial[2i,i]),{i,n}],{n,0,20}]] (* _Harvey P. Dale_, Aug 25 2012 *)
%o (PARI) a(n)=denominator(5/2*sum(k=1,n,(-1)^(k+1)/k^3/binomial(2*k,k)))
%Y Cf. A002117, A089638.
%K nonn,frac
%O 0,2
%A _Benoit Cloitre_, Jan 01 2004
%E Edited by _N. J. A. Sloane_, Aug 23 2008 at the suggestion of _R. J. Mathar_
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