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A365643 Number of permutations whose reverse-complement shares the same recording tableau in the Robinson-Schensted correspondence.

Original entry on oeis.org

1, 1, 2, 2, 12, 24, 136, 344, 2872, 7108, 80672, 211056, 3032376

Offset: 0

Dang-Son Nguyen, Sep 14 2023

This is an open problem from Martin's "Algebraic Combinatorics" lecture.

Tucker J. Ervin, Blake Jackson, Jay Lane, Kyungyong Lee, Son Dang Nguyen, Jack O'Donohue, and Michael Vaughan, Permutations whose reverse shares the same recording tableau in the RS correspondence, Sém. Lothar. Combin. 86 (2022), Art. B86a, 15 pp.
Jeremy L. Martin, Lecture Notes on Algebraic Combinatorics, 2010-2023.
Wikipedia, Robinson-Schensted correspondence.

def a(n): return sum(StandardTableaux(T.shape()).cardinality()
               for T in StandardTableaux(n) if T == T.evacuation())
print([a(n) for n in range(13)])