The Roman factorial is an extension of the ordinary factorial into the negative integers.[1] 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 Edit

  1. [1]

See also Edit

Main article: Factorial
Multifactorials: Double factorial · Multifactorial
Falling and rising: Falling factorial · Rising factorial
Other mathematical variants: Alternating factorial · Hyperfactorial · q-factorial · Roman factorial · Subfactorial · Weak factorial · Bouncing Factorial
Tetrational growth: Exponential factorial · Expostfacto function · Superfactorial by Clifford Pickover
Array-based extensions: Hyperfactorial array notation · Nested factorial notation
Other googological variants: · Superfactorial by Sloane and Plouffe · Torian · Factorexation · Mixed factorial · Bouncing Factorial

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