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 Post subject: Dobiński’s formula
PostPosted: Sat Aug 12, 2017 4:29 pm 

Joined: Sat Nov 14, 2015 6:32 am
Posts: 123
Location: Melbourne, Australia
Let $n \in \mathbb{N}$ and $\mathcal{B}_n$ denote the $n$ - th Bell number. Prove that

$$\sum_{k=0}^{\infty} \frac{k^n}{k!}=\mathcal{B}_n \cdot e$$

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$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$


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