Fibonorial: Difference between revisions
m +iw |
bolding alternate name |
||
| Line 1: | Line 1: | ||
{{Notability|date=December 2009}} |
{{Notability|date=December 2009}} |
||
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: |
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: |
||
:<math>n!_F = F_n F_{n-1} \cdots F_1\text{ and }0!_F = 1, </math> |
:<math>n!_F = F_n F_{n-1} \cdots F_1\text{ and }0!_F = 1, </math> |
||
Revision as of 08:39, 11 November 2010
 | The topic of this article may not meet Wikipedia's general notability guideline. (December 2009) |
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:
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 (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.