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A203749 v(n+1)/v(n), where v=A203748.

%I A203749 #7 Jan 09 2013 03:54:49
%S A203749 1,3,196,2352,549081,14825187,7573176576,363512475648,326470872935025,
%T A203749 24485315470126875,34169385402567926784,3690293623477336092672,
%U A203749 7392237545597804070571449,1086658919202877198374003003
%N A203749 v(n+1)/v(n), where v=A203748.
%C A203749 See A093883 for a discussion and guide to related sequences.
%t A203749 f[j_] := Floor[j/2]; z = 15;
%t A203749 u := Product[f[j]^2 + f[j] f[k] + f[k]^2, {j, 1, k - 1}]
%t A203749 v[n_] := Product[u, {k, 2, n}]
%t A203749 Table[v[n], {n, 1, z}]          (* A203748 *)
%t A203749 Table[v[n + 1]/v[n], {n, 1, z}] (* A203749 *)
%t A203749 Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
%t A203749 Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}]  (* A203750 *)
%t A203749 Table[Sqrt[v[2 n + 1]/(3 v[2 n])],
%t A203749 {n, 1, z}]  (* A203751 *)
%t A203749 %/%%  (* A000027 *)
%K A203749 nonn
%O A203749 1,2
%A A203749 _Clark Kimberling_, Jan 05 2012