A134357 - OEIS

%I #13 Feb 05 2025 15:51:55

%S 2,1,1,3,13,34,133,115,435,59334,2294,19721,195693,4060189,12746447,

%T 331303,25369351,4959422,11092118,28745223797,16310849170,14814154260,

%U 348379527681,263145320733,1493627665569,100023828627,531705615333,156537259557,1047443521637

%N Denominator of binomial(6*n-2,2*n)/(2*binomial(4*n-1,2*n)).

%C It is conjectured that binomial(6*n-2,2*n)/(2*binomial(4*n-1,2*n)) = A005156(n+1)/A005156(n).

%D D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; see conjecture (6.18).

%H Harvey P. Dale, <a href="/A134357/b134357.txt">Table of n, a(n) for n = 0..1000</a>

%e 1/2, 1, 3, 26/3, 323/13, 2415/34, 26970/133, 66526/115, 717541/435, 278992987/59334, 30741431/2294, ...

%t Table[Binomial[6n-2,2n]/(2Binomial[4n-1,2n]),{n,0,30}]//Denominator (* _Harvey P. Dale_, Feb 05 2025 *)

%Y Cf. A109074, A005156.

%K nonn,frac

%O 0,1

%A _N. J. A. Sloane_, May 04 2008

%E Changed numerator to denominator in title, Arvind Ayyer, Jan 29 2012