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Magical permututations!

Source: Cono Sur Olympiad 2024 P5

September 28, 2024
combinatorics

Problem Statement

A permutation of {1,2⋯ ,n}\{1, 2 \cdots, n \} is magic if each element kk of it has at least ⌊k2⌋\left\lfloor \frac{k}{2} \right\rfloor numbers less to it at the left. For each nn find the number of magical permutations.
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