# Category:Subfactorials

This category contains results about Subfactorials.

Let $n \in \Z_{\ge0}$ be a (strictly) positive integer.

The subfactorial of $n$ is defined and denoted as:

 $\displaystyle !n$ $:=$ $\displaystyle n! \sum_{k \mathop = 0}^n \frac {\left({-1}\right)^k} {k!}$ $\displaystyle$ $=$ $\displaystyle n! \left({1 - \dfrac 1 {1!} + \dfrac 1 {2!} - \dfrac 1 {3!} + \cdots + \dfrac {\left({-1}\right)^n} {n!} }\right)$

It arises as the number of derangements of $n$ distinct objects.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Subfactorials"

The following 5 pages are in this category, out of 5 total.