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%I #17 Apr 24 2019 11:48:53
%S 1,1,1,1,4,1,1,11,11,1,1,25,62,25,1,1,50,252,252,50,1,1,91,833,1644,
%T 833,91,1,1,154,2375,8183,8183,2375,154,1,1,246,6045,33655,58007,
%U 33655,6045,246,1,1,375,14049,119737,327269,327269,119737,14049,375,1
%N Triangle read by rows: T(n,k) is the number of 3-stack-sortable permutations of [n] with k descents (0 <= k <= n-1).
%C Bona has proven that the polynomial Sum_{k=0..n-1} T(n,k)*x^k is always symmetric and unimodal. He has conjectured that it has only real roots.
%H Colin Defant, <a href="/A324916/b324916.txt">Table of n, a(n) for n = 1..945</a>
%H M. Bona, <a href="https://doi.org/10.1006/jcta.2001.3235">Symmetry and unimodality in t-stack-sortable permutations</a>, J. Combin. Theory Ser. A, 98 (2002), 201-209.
%H M. Bona, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v9i2a1">A survey of stack-sorting disciplines</a>, Electron. J. Combin., 9 (2003), Article #A1.
%H C. Defant, <a href="https://arxiv.org/abs/1903.09138">Counting 3-stack-sortable permutations</a>, arXiv:1903.09138 [math.CO], 2019.
%H C. Defant, <a href="https://arxiv.org/abs/1511.05681">Preimages under the stack-sorting algorithm</a>, arXiv:1511.05681 [math.CO], 2015-2018; Graphs Combin., 33 (2017), 103-122.
%F See the paper "Counting 3-Stack-Sortable Permutations" for a recurrence that generates this sequence.
%e T(5,1)=25 because there are 25 3-stack-sortable permutations of {1,2,3,4,5} with exactly 1 descent.
%Y Row sums give A134664.
%K nonn,tabl
%O 1,5
%A _Colin Defant_, Mar 18 2019
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