%I #9 Mar 18 2018 09:40:05
%S 1,28,280,520,416,608,1672,2200,700,217,4216,5032,2960,3440,7912,9016,
%T 1274,2860,12760,14152,7808,8576,18760,20440,5548,3002,25912,27880,
%U 14960,16016,34216,36472,2425,10300,43672,46216,24416,25760
%N Denominators of (1/8)*n*(5 + 3*n)/((1 + 3*n)*(4 + 3*n)), n >= 0.
%C The numerators are given in A300296, where details and the Jolley reference are given.
%F a(n) = denominator(r(n)), with r(n) = n*(5 + 3*n)/(8*(1 + 3*n)*(4 + 3*n)).
%F a(n) = (1 + 3*n)*(4 + 3*n)/4 if n == 0 or 9 (mod 32), a(n) = (1 + 3*n)*(4 + 3*n)/2 if n == 16 or 25 (mod 32), a(n) = (1 + 3*n)*(4 + 3*n) if n == 1 or 8 or 17 or 24 (mod 32), and for other n one has a(n) = 2*(1 + 3*n)*(4 + 3*n) if n == 0 or 1 (mod 4) and a(n) = 4*(1 + 3*n)*(4 + 3*n) if n == 2 or 3 (mod 4).
%F G.f.: G(x) = (1/24)*(1 - hypergeometric([1, 2], [7/3], -x/(1-x)))/(1-x).
%e For the first rationals r(n) see A300296.
%o (PARI) a(n) = denominator((1/8)*n*(5 + 3*n)/((1 + 3*n)*(4 + 3*n))); \\ _Altug Alkan_, Mar 18 2018
%Y Cf. A300296.
%K nonn,frac,easy
%O 0,2
%A _Wolfdieter Lang_, Mar 17 2018