# There can only be one

Discrete Mathematics Level pending

A unimodal permutation is a permutation with only one local maximum. That is, a unimodal permutation of $$n$$ elements, $$\sigma_1,\sigma_2,\cdots,\sigma_n$$, must have $$\sigma_1 < \sigma_2 < \cdots < \sigma_k$$ and $$\sigma_k > \sigma_{k+1} > \cdots > \sigma_n$$ for some positive integer $$k \le n$$.

How many unimodal permutations are there of the set $$\{1,2,3,4,5,6,7,8,9\}$$?

(Adapted from Analytic Combinatorics by Philippe Flajolet)

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