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%I #32 Sep 08 2022 08:45:01
%S 1,3,5,7,9,11,13,5,17,19,21,23,25,27,29,31,11,7,37,13,41,43,3,47,49,
%T 17,53,55,57,59,61,9,65,67,23,71,73,75,11,79,81,83,17,29,89,13,31,19,
%U 97,11,101,103,35,107,109,37,113,115,39,119,121,41,125
%N Denominator of binomial(2*n,n) / (2*n+1).
%C The numerators are given in A056616.
%H Michel Marcus, <a href="/A056617/b056617.txt">Table of n, a(n) for n = 0..2000</a>
%F a(n) = denominator(r(n)) with r(n) = binomial(2*n,n)/(2*n+1)).
%F G.f. of r(n): 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, ...
%t Table[Binomial[2 n, n]/(2 n + 1), {n, 0, 70}]//Denominator (* _Harvey P. Dale_, May 01 2019 *)
%o (Magma) [Denominator((Binomial (2*n, n)) / (2*n + 1)): n in [0..70]]; // _Vincenzo Librandi_, May 27 2019
%o (PARI) a(n) = denominator(binomial(2*n,n) / (2*n+1)); \\ _Michel Marcus_, May 27 2019
%Y Cf. A056616, A000108.
%K nonn,easy,frac
%O 0,2
%A _N. J. A. Sloane_, Aug 28 2000
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