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%I #25 Feb 21 2017 20:15:26
%S 1,2,6,20,70,252,924,1144,12870,48620,184756,705432,2704156,10400600,
%T 40116600,155117520,200360130,466721244,9075135300,11781754600,
%U 137846528820,538257874440,140273264248,8233430727600,32247603683100
%N Numerator of binomial(2n,n)/(2n+1).
%C The denominators are given in A056617.
%C It is easy to type binomial(2n,n)/(2n+1) by mistake, when one really wants the Catalan numbers binomial(2n,n)/(n+1), A000108.
%C Differs from A000984 at positions in A101681.
%H Robert Israel, <a href="/A056616/b056616.txt">Table of n, a(n) for n = 0..1663</a>
%F Numerators of the rationals r(n) = binomial(2n,n)/(2n+1) with G.f.: 1/(2*sqrt(x))*arcsin(2*sqrt(x)). [_Vladimir Kruchinin_, May 31 2013]
%e The rationals r(n) begin: 1, 2/3, 6/5, 20/7, 70/9, 252/11, 924/13, 1144/5, 12870/17, ...
%p seq(numer(binomial(2*n,n)/(2*n+1)), n=0..50); # _Robert Israel_, Feb 21 2017
%t Numerator[Table[Binomial[2n,n]/(2n+1),{n,0,30}]] (* _Harvey P. Dale_, Jul 25 2013 *)
%o (PARI) a(n) = numerator(binomial(2*n, n)/(2*n+1)) \\ _Felix Fröhlich_, Feb 21 2017
%Y Cf. A000984, A056617, A000108, A101681.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Aug 28 2000
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