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

1, 1, 3, 588, 1382976, 759365845056, 11257740654368225472, 85256857822344357223236943872, 30991931452969951465382132459004342829056, 10117962915393557751514211466029580457669394910570086400

Offset: 1

Author

Clark Kimberling, Jan 05 2012

Keywords

• nonn

Comments

See A093883 for a discussion and guide to related sequences.

Programs

Mathematica

f[j_] := Floor[j/2]; z = 15;
u := Product[f[j]^2 + f[j] f[k] + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u, {k, 2, n}]
Table[v[n], {n, 1, z}]          (* A203748 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203749 *)
Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}] (* A203750 *)
Table[Sqrt[v[2 n + 1]/(3 v[2 n])],
   {n, 1, z}]  (* A203751 *)
%/%%         (* A000027 *)