It is shown that there are (n2n) - ∑m=0n-1 2n-m-1(m2m) permutations which are the union of an increasing sequence and a decreasing sequence.
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Atkinson, M. D. (1998). Permutations which are the union of an increasing and a decreasing subsequence. Electronic Journal of Combinatorics, 5(1). https://doi.org/10.37236/1344
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