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v(n+1)/v(n), where v=A203755.
2

%I #7 Jan 09 2013 03:55:33

%S 1,2,4624,147968,5124555396,830177974152,142070471498727424,

%T 72740081407348441088,38931932500357955277610000,

%U 48664915625447444097012500000,63249728823972809508391754919837696

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

%C See A093883 for a discussion and guide to related sequences.

%t f[j_] := Floor[j/2]; z = 16;

%t u := Product[f[j]^4 + f[k]^4, {j, 1, k - 1}]

%t v[n_] := Product[u, {k, 2, n}]

%t Table[v[n], {n, 1, z}] (* A203755 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203756 *)

%t Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]

%t Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}] (* A203757 *)

%t Table[Sqrt[v[2 n + 1]/(2 v[2 n])],

%t {n, 1, z}] (* A203758 *)

%t %/%% (* A000290 *)

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 05 2012