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A203756 v(n+1)/v(n), where v=A203755.

%I A203756 #7 Jan 09 2013 03:55:33
%S A203756 1,2,4624,147968,5124555396,830177974152,142070471498727424,
%T A203756 72740081407348441088,38931932500357955277610000,
%U A203756 48664915625447444097012500000,63249728823972809508391754919837696
%N A203756 v(n+1)/v(n), where v=A203755.
%C A203756 See A093883 for a discussion and guide to related sequences.
%t A203756 f[j_] := Floor[j/2]; z = 16;
%t A203756 u := Product[f[j]^4 + f[k]^4, {j, 1, k - 1}]
%t A203756 v[n_] := Product[u, {k, 2, n}]
%t A203756 Table[v[n], {n, 1, z}]        (* A203755 *)
%t A203756 Table[v[n + 1]/v[n], {n, 1, z}]  (* A203756 *)
%t A203756 Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
%t A203756 Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}]  (* A203757 *)
%t A203756 Table[Sqrt[v[2 n + 1]/(2 v[2 n])],
%t A203756   {n, 1, z}]  (* A203758 *)
%t A203756 %/%%   (* A000290 *)
%K A203756 nonn
%O A203756 1,2
%A A203756 _Clark Kimberling_, Jan 05 2012