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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 …