OFFSET
0,4
COMMENTS
FORMULA
a(n) ~ c * d^n * phi^(n^3/3 + n^2/2) / 5^(n^2/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio, d = 0.120965069090607877853843907542896935455225485213927649233956250456604334... and c = 197.96410442333389877538426269... - Vaclav Kotesovec, Apr 08 2021
EXAMPLE
v(4) = (2-1)*(3-1)*(3-2)*(5-1)*(5-2)*(5-3).
MAPLE
with(LinearAlgebra): F:= combinat[fibonacci]:
a:= n-> Determinant(VandermondeMatrix([F(i)$i=2..n+1])):
seq(a(n), n=0..12); # Alois P. Heinz, Jul 23 2017
MATHEMATICA
PROG
(Python)
from sympy import fibonacci, factorial
from operator import mul
from functools import reduce
def f(j): return fibonacci(j + 1)
def v(n): return 1 if n==1 else reduce(mul, [reduce(mul, [f(k) - f(j) for j in range(1, k)]) for k in range(2, n + 1)])
print([v(n) for n in range(1, 16)]) # Indranil Ghosh, Jul 26 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 01 2012
STATUS
approved