OFFSET
1,5
COMMENTS
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.
LINKS
Colin Defant, Table of n, a(n) for n = 1..945
M. Bona, Symmetry and unimodality in t-stack-sortable permutations, J. Combin. Theory Ser. A, 98 (2002), 201-209.
M. Bona, A survey of stack-sorting disciplines, Electron. J. Combin., 9 (2003), Article #A1.
C. Defant, Counting 3-stack-sortable permutations, arXiv:1903.09138 [math.CO], 2019.
C. Defant, Preimages under the stack-sorting algorithm, arXiv:1511.05681 [math.CO], 2015-2018; Graphs Combin., 33 (2017), 103-122.
FORMULA
See the paper "Counting 3-Stack-Sortable Permutations" for a recurrence that generates this sequence.
EXAMPLE
T(5,1)=25 because there are 25 3-stack-sortable permutations of {1,2,3,4,5} with exactly 1 descent.
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Colin Defant, Mar 18 2019
STATUS
approved