# Fibonorial

In mathematics, the Fibonorial n!F, also called the Fibonacci factorial, where n is a nonnegative integer, is defined as the product of the first n positive Fibonacci numbers, i.e.

${n!}_F := \prod_{i=1}^{n} F_i,\quad n \ge 1, \text{ and } 0!_F := 1,$

where Fi is the ith Fibonacci number. (0!F is 1 since it is the empty product.)

The Fibonorial of n (n!F) is defined analogously to the factorial of n (n!).

The Fibonorial numbers are used in the definition of Fibonomial coefficients (or Fibonacci-binomial coefficients) similarly as the factorial numbers are used in the definition of binomial coefficients.

## Almost-Fibonorial numbers

Almost-Fibonorial numbers: n!F − 1.

It is interesting to look for prime numbers among the almost-Fibonorial numbers, i.e. the almost-Fibonorial primes.

## Quasi-Fibonorial numbers

Quasi-Fibonorial numbers: n!F + 1.

It is interesting to look for prime numbers among the quasi-Fibonorial numbers, i.e. the quasi-Fibonorial primes.

## Sequences

Cf. Product of first n nonzero Fibonacci numbers F(1), ..., F(n).

Cf. and for n such that n!F − 1 and n!F + 1 are primes.

## References

• Weisstein, Eric W. "Fibonorial". MathWorld. Wolfram Research. Retrieved 19 December 2009.