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%I #13 May 08 2022 16:56:03
%S 0,1,7,3,169,1523,133,72623,87149,823077,15638477,46915441,13834041,
%T 224803169,6936783521,5587964507,4157445593923,12472336782289,
%U 170187831339,71785227258967,153825486983593,4905323862699739,21820233734078929,5695081004594650211
%N Numerator 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 Join[{0},Accumulate[Table[1/(x Binomial[2x,x]),{x,30}]]]//Numerator (* _Harvey P. Dale_, May 08 2022 *)
%o (PARI) a(n) = numerator(sum(i=1, n, 1/(i*binomial(2*i, i)))); \\ _Michel Marcus_, Mar 10 2016
%Y Cf. A112100, A112102, A112103, A130549, A130550, A134805.
%K nonn,frac
%O 0,3
%A _N. J. A. Sloane_, Nov 30 2005
%E Definition corrected by _Wolfdieter Lang_, Oct 07 2008
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