# Questions tagged [stirling-numbers]

For questions about the two kinds of Stirling numbers and related topics, such as Lah numbers.

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### Understanding distribution using Stirling number of the second kind

I have adapted this question from this question, I don't fully understand the answers given there/ Understanding distribution using Stirling number of the second kind inclusion exclusion approach ...
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### simplifying a sum containing the binomial coefficient and stirling numbers second kind [duplicate]

I'm working on this sum, I don't have to find out the actual value, I just have to simplify it as much as I can. But the problem is that I don't know how far I can simplify it before reaching the ...
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### Conjecture: If $f(x)=\prod\limits_{k=1}^n(x-k)$ then $\lim\limits_{n\to\infty}\frac1n [\text{largest root of$f(x)=f'(x)$}]=\frac{e}{e-1}$.

I was thinking about the polynomial $f(x)=\prod\limits_{k=1}^n(x-k)$. I noticed that if we draw the graphs of $y=f(x)$ and $y=f'(x)$ together, the $x$-coordinate of the rightmost intersection seems ...
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### Is there a combinatorial proof of this binomial-type formula involving Stirling numbers?

Suppose $\partial$ and $t$ are elements of a noncommutative ring which satisfy $[\partial,t]=1.$ Then one can show using an induction argument that (t\partial)^k=\sum_{i=0}^k{k \brace ...
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### Polylogarithm further generalized

Here I proposed a generalized formula for the polylogarithm. However, because of a slight mistake towards the end, visible prior to the edit, I was unaware that it yields just a result of an integral ...
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