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In [[mathematics]], the '''Fibonorial''' ''n''!<sub>''F''</sub>, 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.
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:<math>{n!}_F := \prod_{i=1}^{n} F_i,\quad n \ge 1, \text{ and } 0!_F := 1, </math>
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where ''F''<sub>''i''</sub> is the ''i''<sup>th</sup> Fibonacci number. (0!<sub>''F''</sub> is 1 since it is the [[empty product]].)
__TOC__
The Fibonorial of ''n'' (''n''!<sub>''F''</sub>) is defined analogously to the [[factorial]] of ''n'' (''n''!).
 
The Fibonorial numbers are used in the definition of [[Fibonomial coefficient]]s (or Fibonacci-binomial coefficients) similarly as the factorial numbers are used in the definition of [[binomial coefficients]].
 
== Almost-Fibonorial numbers ==
 
Almost-Fibonorial numbers: ''n''!<sub>''F''</sub> &minus; 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''!<sub>''F''</sub> + 1.
 
It is interesting to look for [[prime numbers]] among the [[quasi-Fibonorial numbers]], i.e. the [[quasi-Fibonorial primes]].
 
== Sequences ==
 
Cf. {{OEIS2C|A003266}} Product of first ''n'' nonzero Fibonacci numbers ''F''(1), ..., ''F''(''n'').  
 
Cf. {{OEIS2C|A059709}} and {{OEIS2C|A053408}} for ''n'' such that ''n''!<sub>''F''</sub> &minus; 1 and ''n''!<sub>''F''</sub> + 1 are primes.
 
==References==
 
* {{cite web
| url        = http://mathworld.wolfram.com/Fibonorial.html
| title      = Fibonorial
| first      = Eric W.
| last        = Weisstein
| work        = MathWorld
| publisher  = Wolfram Research
| accessdate = 19 December 2009
}}
 
 
[[Category:Fibonacci numbers]]
 
[[fr:Analogues de la factorielle#Factorielle de Fibonacci]]

Latest revision as of 06:02, 24 April 2014

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