At some point, I wondered if n! is proportional to n^n.<p>Turns out, it is:<p>n! ~= (2 * pi * n)^1&#x2F;2 * (n&#x2F;e)^n<p>(<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Stirling%27s_approximation" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Stirling%27s_approximation</a>)