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%I #12 Jul 07 2021 11:11:40
%S 1,2,23,167,253,5581,13201,48413,823063,15638407,1117033,89921239,
%T 256917887,60848977,134111147453,4157445588203,1385815197541,
%U 9700706385439,358926136286437,358926136292897,474708760905697
%N Numerators of 6*((Sum_{k=1..n} 1/binomial(2*k,k)) - 1/3), n >= 1.
%C Denominators are given by A130548.
%C The partial sums (in lowest terms) r(n) = 6*((Sum_{k=1..n} 1/binomial(2*k,k)) - 1/3) tend, for n->infinity, to 4*Pi*sqrt(3)/9, which is approximately 2.418399153.
%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 89, Exercise (with a misprint).
%H W. Lang, <a href="/A130547/a130547.txt">Rationals and limit</a>.
%F a(n) = numerator(r(n)), n >= 1, with the rationals defined above.
%t Table[6*(Sum[1/Binomial[2k,k],{k,n}]-1/3),{n,30}]//Numerator (* _Harvey P. Dale_, Jul 07 2021 *)
%K nonn,frac,easy
%O 1,2
%A _Wolfdieter Lang_, Jul 13 2007
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