Stirling's Formula

Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials, or Gamma function

One way of stating the approximation involves the logarithm of the factorial

$$\ln (n!)=n\ln n-n+O(\ln n)$$

where $O(\cdot )$ is the big O notation

An approximate formula for the factorial itself is that

$$n!\sim \sqrt{2\pi n}{\left(\frac{n}{e}\right)}^n$$

This formula leads to accurate results even for small values $n$