Fibonorial

In mathematics, the Fibonorial n!_F, also called the Fibonacci factorial, where n is a non-negative integer, is defined as the product of the first n nonzero Fibonacci numbers:

$n!_{F}=F_{n}F_{n-1}\cdots F_{1}{\text{ and }}0!_{F}=1,$

where F_i 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 (i.e. to 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.

It is interesting to look for prime numbers among the almost-Fibonorial numbers (n!_F − 1) and the quasi-Fibonorial numbers (n!_F + 1).

Cf. OEIS A003266 Product of first n nonzero Fibonacci numbers F(1), ..., F(n).

Cf. OEIS A059709 and A053408 for n such that n!_F − 1 and n!_F + 1 are primes.

Cf. Eric W. Weisstein's MathWorld Fibonorial.

References

• Weisstein, Eric W. "Fibonorial". MathWorld. Wolfram Research. Archived from the original on 19 December 2009. Retrieved 19 December 2009.