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A277520 Denominator of 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1).

%I A277520 #33 Nov 05 2016 14:16:49
%S A277520 1,3,25,147,1089,20449,48841,312987,55190041,14322675,100100025,
%T A277520 32065374675,4546130625,29873533563,1859904071089,4089135109921,
%U A277520 9399479144449,22568149425822049,1293753708921104809,2835106739783283,3289668853728536041
%N A277520 Denominator of 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1).
%C A277520 Neil Calkin found the closed forms of 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1) in 2007.
%D A277520 Jonathan Borwein, David Bailey, Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century.
%H A277520 Seiichi Manyama, <a href="/A277520/b277520.txt">Table of n, a(n) for n = 0..1000</a>
%F A277520 (s(n) =) 3F2([3*n, -n, n+1],[2*n+1, n+1/2], 1) = A277170(n) / a(n).
%F A277520 s(2k) = (A005810(k) / A066802(k))^2 = (((4k)! * (3k)!) / ((6k)! * k!))^2.
%F A277520 s(2k+1) = -1/3 * (A052203(k) / A187364(k))^2 = -1/3 * (((4k+1)! * (3k)!) / ((6k+1)! * k!))^2.
%t A277520 a[n_] := HypergeometricPFQ[{3n, -n, n+1}, {2n+1, n+1/2}, 1] // Denominator;
%t A277520 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Oct 22 2016 *)
%Y A277520 Cf. A005810, A052203, A066802, A187364, A277170 (numerators).
%K A277520 nonn,frac
%O A277520 0,2
%A A277520 _Seiichi Manyama_, Oct 19 2016