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Vandermonde sequence using x^2 - xy + y^2 applied to (0,1,1,2,2,...,floor(n/2)).
4

%I #7 Jan 14 2013 10:24:12

%S 1,1,1,36,5184,112021056,21785966991936,1433615623503400157184,

%T 1509414758014670876688343105536,

%U 956401356293432867934306416285626820198400,15149970368698147242050701825966625432586471604224000000

%N Vandermonde sequence using x^2 - xy + 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[j] f[k] + f[k]^2, {j, 1, k - 1}]

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

%t Table[v[n], {n, 1, z}] (* A203752 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203753 *)

%t Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}] (* A203754 *)

%K nonn

%O 1,4

%A _Clark Kimberling_, Jan 05 2012