Anyone can help to solve this problem?
Let $\mathcal{F}$ be the combinatorial class of all functions $f : [1,n] \rightarrow [1,n]$. Derive the exponential generating function and use it to compute (or verify) the number of such functions.
2026-04-09 16:55:59.1775753759
How to derive this exponential generating function?
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Going the other way might be easier: the number $|\mathcal{F}(n)|$ is not hard to compute. Consider the function as a vector $(f(1),\ldots,f(n))$, where the coordinates can take the values $[1;n]$. How many such vectors are there?
Once you have this number, you can plug it in to the formula for an exponential generating function.