# Definition(s)
> [!NOTE] Definition 1 (Exponential Generating Function)
> Let $(a_{n})_{n\geq{0}}$ be a [[Sequences|sequence]] in $\mathbb{R}.$ The [[Power Series|formal power series]] $\sum_{n=0}^{\infty} a_{n} \frac{x^{n}}{n!}$is the exponential generating function of $(a_{n})_{n\geq0}.$
> [!Example] Example
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# Properties(s)
# Application(s)
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