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This is restating Stirling's approximation, which has been known for three centuries (1730, de Moivre 1721). https://en.wikipedia.org/wiki/Stirling%27s_approximation

Stirling’s approximation is mentioned in the article.

I know that, that was my point. I'm saying I don't see much point in restating it without adding something; it's been known for 300 years.