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%I #11 May 11 2019 09:31:12
%S 1,2,12,5,280,2520,220,120120,144144,1361360,25865840,77597520,
%T 22881320,371821450,11473347600,9242418900,6876359661600,
%U 20629078984800,281488407200,118731810156960,254425307479200,8113340360725600,36090376087365600,9419588158802421600
%N Denominator of Sum_{i=1..n} 1/(i*C(2*i,i)).
%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 Sum_{i >= 1} 1/(i*C(2*i, i)) = Pi*sqrt(3)/9.
%e 0, 1/2, 7/12, 3/5, 169/280, 1523/2520, 133/220, 72623/120120, 87149/144144, .... -> Pi*sqrt(3)/9.
%t Table[Sum[1/(i*Binomial[2i,i]),{i,n}],{n,0,30}]//Denominator (* _Harvey P. Dale_, May 11 2019 *)
%o (PARI) a(n) = denominator(sum(i=1, n, 1/(i*binomial(2*i, i)))); \\ _Michel Marcus_, Mar 10 2016
%Y Cf. A112099.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 30 2005
%E Definition corrected by _Wolfdieter Lang_, Oct 07 2008