A203752 Vandermonde sequence using x^2 - xy + y^2 applied to (0,1,1,2,2,...,floor(n/2)).

1, 1, 1, 36, 5184, 112021056, 21785966991936, 1433615623503400157184, 1509414758014670876688343105536, 956401356293432867934306416285626820198400, 15149970368698147242050701825966625432586471604224000000

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 = 20;
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}]          (* A203752 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203753 *)
Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]  (* A203754 *)