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Vandermonde sequence using x^2 - xy + y^2 applied to the Fibonacci numbers (1,2,3,5,...F(n+1)).
3

%I #7 Jan 14 2013 08:31:44

%S 1,3,147,1114407,7930748737548,423375184354643258554908,

%T 1139699897999666959110654862545153285132,

%U 1110214943505579438451390880891356969725014603098351043391552

%N Vandermonde sequence using x^2 - xy + y^2 applied to the Fibonacci numbers (1,2,3,5,...F(n+1)).

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

%t f[j_] := Fibonacci[j + 1]; z = 11;

%t u[n_] := Product[f[j]^2 - f[j] f[k] + f[k]^2,

%t {j, 1, k - 1}]

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

%t Table[v[n], {n, 1, z}] (* A203699 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203700 *)

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 04 2012