Category:Subfactorials

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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.