Relation/connection between $n!$ or $e$ and $2^n$

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What is the relation/connection between $n!$ or $e$ and $2^n$ ? Is the there a relation/connection between $n!$ or $e$ and $2^n$?

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The first thing in my head after reading the question:$$\sum_{n=0}^{\infty} \dfrac{2^n}{n!} = e^2$$