A319253 Number of doubly sorted permutations of [2n].

1, 3, 31, 1186

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..4.

C. Defant, M. Engen, and J. A. Miller, Stack-sorting, set partitions, and Lassalle's sequence, arXiv:1809.01340 [math.CO], 2018.

Example

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}.

Crossrefs

Cf. A180874, A317551.

Sequence in context: A022514 A094579 A029729 * A328811 A136584 A194937

Adjacent sequences: A319250 A319251 A319252 * A319254 A319255 A319256

Keyword

nonn,more

Author

Colin Defant, Sep 15 2018

Status

approved