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%I #6 Sep 16 2018 16:41:52
%S 1,3,31,1186
%N Number of doubly sorted permutations of [2n].
%C A permutation pi is called doubly sorted if |s^{-1}(pi)| = 2, where s is West's stack-sorting map. There are no doubly sorted permutations of odd length.
%H C. Defant, M. Engen, and J. A. Miller, <a href="https://arxiv.org/abs/1809.01340"> Stack-sorting, set partitions, and Lassalle's sequence</a>, arXiv:1809.01340 [math.CO], 2018.
%e The a(2) = 3 doubly sorted permutations of [4] are 2314, 1324, and 3124. Specifically, letting s denote West's stack-sorting map, we have s^{-1}(2314) = {2341, 3241}, s^{-1}(1324) = {1342, 3142}, and s^{-1}(3124) = {3412, 3421}.
%Y Cf. A180874, A317551.
%K nonn,more
%O 1,2
%A _Colin Defant_, Sep 15 2018
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