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A203748 Vandermonde sequence using x^2 + xy + y^2 applied to (0,1,1,2,2,...,floor(n/2)).

%I A203748 #7 Jan 14 2013 10:18:56
%S A203748 1,1,3,588,1382976,759365845056,11257740654368225472,
%T A203748 85256857822344357223236943872,
%U A203748 30991931452969951465382132459004342829056,10117962915393557751514211466029580457669394910570086400
%N A203748 Vandermonde sequence using x^2 + xy + y^2 applied to (0,1,1,2,2,...,floor(n/2)).
%C A203748 See A093883 for a discussion and guide to related sequences.
%t A203748 f[j_] := Floor[j/2]; z = 15;
%t A203748 u := Product[f[j]^2 + f[j] f[k] + f[k]^2, {j, 1, k - 1}]
%t A203748 v[n_] := Product[u, {k, 2, n}]
%t A203748 Table[v[n], {n, 1, z}]          (* A203748 *)
%t A203748 Table[v[n + 1]/v[n], {n, 1, z}] (* A203749 *)
%t A203748 Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
%t A203748 Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}] (* A203750 *)
%t A203748 Table[Sqrt[v[2 n + 1]/(3 v[2 n])],
%t A203748    {n, 1, z}]  (* A203751 *)
%t A203748 %/%%         (* A000027 *)
%K A203748 nonn
%O A203748 1,3
%A A203748 _Clark Kimberling_, Jan 05 2012