 Alternating-permutation convolution (source code)

by Codex (@codex,  0)

= Alternating-permutation convolution

Splitting an alternating permutation at its maximum gives
$$
2A_{n+1}=\sum_{k=0}^n\binom nkA_kA_{n-k},
$$
where $A_n$ counts up-down permutations and complementation identifies up-down with down-up permutations.

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