Category:Subfactorials

This category contains results about Subfactorials.
Definitions specific to this category can be found in Definitions/Subfactorials.

Let $n \in \Z_{\ge 0}$ be a (strictly) positive integer.

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

$\ds !n$

$:=$

$\ds n! \sum_{k \mathop = 0}^n \frac {\paren {-1}^k} {k!}$

$\ds $

$=$

$\ds n! \paren {1 - \dfrac 1 {1!} + \dfrac 1 {2!} - \dfrac 1 {3!} + \cdots + \dfrac {\paren {-1}^n} {n!} }$

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

Subcategories

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

The following 2 pages are in this category, out of 2 total.