%I #14 Jun 16 2016 23:27:29
%S 1,2,3,60,420,630,13860,32760,120120,2042040,38798760,923780,74364290,
%T 212469400,150965100,332727080400,10314539492400,3438179830800,
%U 24067258815600,890488576177200,890488576177200,1177742955589200,1569931359800403600,2354897039700605400
%N Denominator of Sum_{i=1..n} 1/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/C(2*i, i) = (2*Pi*sqrt(3) + 9)/27.
%e 0, 1/2, 2/3, 43/60, 307/420, 463/630, 10201/13860, 24121/32760, 88453/120120, ... -> (2*Pi*sqrt(3) + 9)/27.
%p BB:=n->add(1/binomial(2*i,i), i=1..n): a:=n->denom(BB(n)): seq(a(n), n=0..23); # _Zerinvary Lajos_, Mar 28 2007
%t Denominator@ Table[Sum[1/Binomial[2 i, i], {i, n}], {n, 0, 23}] (* _Michael De Vlieger_, Mar 09 2016 *)
%o (PARI) a(n) = denominator(sum(i=1, n, 1/binomial(2*i, i))); \\ _Michel Marcus_, Mar 09 2016
%Y Cf. A112098.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 30 2005
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