The Stirling's approximation part of it is about why exp(log(n!)/n) is nearly linear. I think what he's saying is basically: if you take the log version of Stir

The Stirling's approximation part of it is about why exp(log(n!)/n) is nearly linear. I think what he's saying is basically: if you take the log version of Stirling's approximation, ln(n!) = n*ln(n) - n + O(ln(n)), ignore the big O term, then divide both sides by n and take e to the power of each side, you get the formula for the `b` from the article on the left, and n/e on the right, which is linear. I've never actually worked with Stirling's approximation, but I guess if you have a certain set of context, this fact would be obvious?