# Specific values of factorials and binomial coefficients

Related topics: Factorials and binomial coefficients

## Tables

Table of $n !$ for $0 \le n \le 30$
Table of ${n \choose k}$ for $0 \le n \le 15$ and $0 \le k \le 15$
Table of $\left(n\right)_{k}$ for $0 \le n \le 10$ and $0 \le k \le 10$
Table of $\left(n\right)^{\underline{k}}$ for $0 \le n \le 10$ and $0 \le k \le 10$

## Special cases

$0 ! = 1$
${n \choose 0} = 1$
${n \choose n} = 1$
${n \choose n + m} = 0$
${z \choose 1} = z$
${z \choose 2} = \frac{z \left(z - 1\right)}{2}$
$\left(z\right)_{0} = 1$
$\left(z\right)_{1} = z$
$\left(1\right)_{k} = k !$
$\left(z\right)^{\underline{0}} = 1$
$\left(z\right)^{\underline{1}} = z$
$\left(k\right)^{\underline{k}} = k !$
${2 n \choose n} = \frac{\left(2 n\right)!}{{\left(n !\right)}^{2}}$

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC