A203773 Vandermonde sequence using x^2 + y^2 applied to (0,1,1,2,2,...,floor(n/2)).

1, 1, 2, 200, 160000, 24336000000, 66627100800000000, 77020928524800000000000000, 2849158187989401600000000000000000000, 78690953969671659336819671040000000000000000000000

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[k]^2, {j, 1, k - 1}]
v[n_] := Product[u, {k, 2, n}]
Table[v[n], {n, 1, z}]         (* A203773 *)
Table[v[n + 1]/v[n], {n, 1, z}]
Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]
Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}]  (* A203774 *)
Table[Sqrt[v[2 n + 1]/(2 v[2 n])],
{n, 1, z}]  (* A203775 *)
%/%%          (* A000027 *)