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Results tagged with combinatorial-identities
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user 48831
4
votes
$\prod_k(x\pm k)$ in binomial basis?
Here is an argument for the leading coefficient (and more).
We use (formal) generating functions.
Let $f_{n,x}(t):= \sum_{m=0}^n {n-x \choose m } {n+x \choose n-m} e^{(x+2m-n)t}$, we are interested
i …
- 3,255
4
votes
Showing this formula counts these things
Here is a proof using (formal) generating functions.
The Lah number $L(n,m+1)$
$$L(n,m+1)=\frac{n!}{(m+1)!}[x^n] \bigg(\frac{x}{1-x}\bigg)^{m+1}$$
counts the number of unordered partitions of the se …
- 3,255