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%I #13 Oct 30 2019 19:53:27
%S 1,3,10,35,126,77,1716,6435,24310,46189,352716,676039,5200300,
%T 10029150,5170584,300540195,1166803110,756261275,17672631900,
%U 6892326441,89709645740,526024740930,4116715363800,2687300306925,63205303218876,123979633237026,973469712824056,136583760727865,15033633249770520,29566145391215356
%N Numerator of binomial(2n,n)/(2n).
%C There is at least one published paper that refers to binomial(2n,n)/(2n) as the Catalan numbers. Of course the Catalan numbers are really A000108.
%H Patrick Dehornoy, <a href="http://dx.doi.org/10.1016/j.aim.2009.09.016">On the rotation distance between binary trees</a>, Adv. Math. 223 (2010), no. 4, 1316-1355.
%e 1, 3/2, 10/3, 35/4, 126/5, 77, 1716/7, 6435/8, 24310/9, 46189/5, 352716/11, 676039/6, ...
%t Numerator[Table[Binomial[2n,n]/(2n),{n,30}]] (* _Harvey P. Dale_, Jan 06 2013 *)
%Y Cf. A000108, A201059.
%K nonn,frac
%O 1,2
%A _N. J. A. Sloane_, Nov 26 2011