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%I #8 Jan 14 2013 10:20:15
%S 1,1,2,200,160000,24336000000,66627100800000000,
%T 77020928524800000000000000,2849158187989401600000000000000000000,
%U 78690953969671659336819671040000000000000000000000
%N Vandermonde sequence using x^2 + y^2 applied to (0,1,1,2,2,...,floor(n/2)).
%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}]
%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 1,3
%A _Clark Kimberling_, Jan 05 2012
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