Roman factorial

The Roman factorial is an extension of the ordinary factorial into the negative integers. It is defined as
\begin{eqnarray*}
\lfloor n\rceil! &=& n! &\text{for }n \geq 0,\\
\lfloor n\rceil! &=& \displaystyle\frac{(-1)^{-n - 1}}{(-n - 1)!}&\text{for }n < 0.\\
\end{eqnarray*}
It satisfies the identity \(\lfloor n\rceil! = \lfloor n\rceil \lfloor n - 1\rceil!\), where \(\lfloor 0\rceil = 1\) and \(\lfloor n\rceil = n\) for all other \(n\).
== Sources ==
== See also ==
Category:Functions
Category:Factorials