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A203773 Vandermonde sequence using x^2 + y^2 applied to (0,1,1,2,2,...,floor(n/2)).

%I A203773 #8 Jan 14 2013 10:20:15
%S A203773 1,1,2,200,160000,24336000000,66627100800000000,
%T A203773 77020928524800000000000000,2849158187989401600000000000000000000,
%U A203773 78690953969671659336819671040000000000000000000000
%N A203773 Vandermonde sequence using x^2 + y^2 applied to (0,1,1,2,2,...,floor(n/2)).
%C A203773 See A093883 for a discussion and guide to related sequences.
%t A203773 f[j_] := Floor[j/2]; z = 20;
%t A203773 u := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]
%t A203773 v[n_] := Product[u, {k, 2, n}]
%t A203773 Table[v[n], {n, 1, z}]         (* A203773 *)
%t A203773 Table[v[n + 1]/v[n], {n, 1, z}]
%t A203773 Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
%t A203773 Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}]  (* A203774 *)
%t A203773 Table[Sqrt[v[2 n + 1]/(2 v[2 n])],
%t A203773 {n, 1, z}]  (* A203775 *)
%t A203773 %/%%          (* A000027 *)
%K A203773 nonn
%O A203773 1,3
%A A203773 _Clark Kimberling_, Jan 05 2012