This is either incorrect or it does not really mean anything, depending on how you look at it.

It’s Stirling’s approximation, as the article mentions. The formula uses the ≈ character. The Wikipedia article gives bounds on the error—

https://en.wikipedia.org/wiki/Stirling's_approximation

but then isn't every integer a power of a (non integer) base? In this interpretation the statement is pretty useless.

And he really doesn't give a very nice formula for it.

Numerically, the point of the article is the fact that

n! \approx (0.826523 + n*0.373522)^n

For n in the range from 10 to 50, this is within 5% of the right answer.

But I really don't see that this is all that much simpler than Stirling's approximation and it is considerably less accurate and not asymptotically very good. Stirling's formula is within about 1% for all n>10 and within 0.1% for n>90.

Actually computing gamma(n) or lgamma(n) to high precision requires a bit more effort than this, but as an approximation, Stirling's formula is really pretty good.