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%I #16 Sep 08 2022 08:46:19
%S 1,2,6,16,45,136,434,1436,4869,16804,58795,208022,742911,2674452,
%T 9694858,35357684,129644805,477638716,1767263207,6564120438,
%U 24466267039,91482563660,343059613671,1289904147346,4861946401475,18367353072176,69533550916029,263747951750386,1002242216651395,3814986502092332
%N The number of permutations in S_n for which the number of reduced words is maximized with respect to the numbers of braid and commutation classes: |R(w)| = |B(w)| * |C(w)|.
%H S. Fishel, E. Milicevic, R. Patrias, and B. E. Tenner, <a href="https://arxiv.org/abs/1708.04372">Enumerations relating braid and commutation classes</a>, arXiv:1708.04372 [math.CO], 2017.
%F a(1) = 1 and a(n) = C(n) + n - 2 for n > 1, where C(n) is the n-th Catalan number.
%e a(3) = 6 because all six permutations in S_3 have this property.
%t Join[{1}, Table[CatalanNumber[n] + n - 2, {n, 2, 30}]] (* _Vincenzo Librandi_, Aug 16 2017 *)
%o (Magma) [1] cat [Catalan(n) + n - 2: n in [2..40]]; // _Vincenzo Librandi_, Aug 16 2017
%Y Cf. A000108, A290954.
%K easy,nonn
%O 1,2
%A _Bridget Tenner_, Aug 15 2017
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