A203763 Vandermonde sequence using x^2 - xy + y^2 applied to (1,1,2,2,...,[n/2]).

1, 1, 9, 324, 777924, 16810159716, 69136555917409344, 4549499535875623543259136, 115306876482136485813839025883201536, 73061199694724861313901918528002630365482598400

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 + 1)/2]; z = 16;
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}]        (* A203763 *)
Table[v[n + 1]/v[n], {n, 1, z}]  (* A203764 *)
Table[Sqrt[v[n + 1]/v[n]], {n, 1, 20}]  (* A203765 *)