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v(n+1)/v(n), where v=A203773.
1

%I #12 Jan 09 2013 04:02:13

%S 1,2,100,800,152100,2737800,1156000000,36992000000,27619018944400,

%T 1380950947220000,1606635342973440000,115677744694087680000,

%U 193495923191341225000000,18962600472751440050000000

%N v(n+1)/v(n), where v=A203773.

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

%t f[j_] := Floor[j/2]; z = 20;

%t u := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]

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

%t Table[v[n], {n, 1, z}] (* A203773 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A202945 *)

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

%t Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}] (* A203774 *)

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

%t {n, 1, z}] (* A203775 *)

%t %/%% (* A000027 *)

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 05 2012