Fibonacci factorial

The fibonorial n!_F, also called the Fibonacci factorial, is defined as n!_F = product_(k = 1)^n F_k, where F_k is a Fibonacci number. For n = 1, 2, ..., the first few fibonorials are 1, 1, 2, 6, 30, 240, 3120, 65520, ... (OEIS A003266). The fibonorials are asymptotic to n!_F ~Cϕ^(n(n + 1)/2)/5^(n/2), where C is the Fibonacci factorial constant and ϕ is the golden ratio. The first few values of n such that n!_F - 1 is prime are given by 4, 5, 6, 7, 8, 14, 15, ... (OEIS A059709), with no others less than 500.

factorial | Fibonacci factorial constant | Fibonacci number | fibonomial coefficient | integer sequence primes | primorial