Let $!$ be the D6: Natural number factorial function.
Let ${\sim}$ be the D3: Asymptotic equality relation.
Let ${\sim}$ be the D3: Asymptotic equality relation.
Then
\begin{equation}
n! \overset{n \to \infty}{\sim} \left( \frac{n}{e} \right)^n \sqrt{2 \pi n}
\end{equation}