A203744 Vandermonde sequence using x^2 - xy + y^2 applied to the first n Fibonacci numbers, A000045.

1, 1, 9, 3087, 491453487, 199355231015744076, 1670853975432258811676271416172, 1893588915901757181126922024000776555730414763148, 2071486075345864360727487613123282727407169939419132023198357982044106944

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_] := Fibonacci[j]; z = 11;
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}]          (* A203744 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203745 *)