A203755 - OEIS

%I #7 Jan 14 2013 10:19:42

%S 1,1,2,9248,1368408064,7012482928301113344,

%T 5821608871192502942968054284288,

%U 827078717211493220641742410981240687143117914112,60161773220249337113595772781004931116549061984924929733289475833856

%N Vandermonde sequence using x^4 + y^4 applied to (0,1,1,2,2,...,floor(n/2)).

%C See A093883 for a discussion and guide to related sequences.

%t f[j_] := Floor[j/2]; z = 16;

%t u := Product[f[j]^4 + f[k]^4, {j, 1, k - 1}]

%t v[n_] := Product[u, {k, 2, n}]

%t Table[v[n], {n, 1, z}]        (* A203755 *)

%t Table[v[n + 1]/v[n], {n, 1, z}]  (* A203756 *)

%t Table[Sqrt[v[n + 1]/v[n]], {n, 1, z}]

%t Table[Sqrt[v[2 n]/v[2 n - 1]], {n, 1, z}]  (* A203757 *)

%t Table[Sqrt[v[2 n + 1]/(2 v[2 n])],

%t   {n, 1, z}]  (* A203758 *)

%t %/%%   (* A000290 *)

%K nonn

%O 1,3

%A _Clark Kimberling_, Jan 05 2012