OFFSET
1,7
COMMENTS
Rows are symmetric: T(n,k) = T(n,2n-k).
It appears that the sequence T(n,1),...,T(n,2n-1) is always unimodal. In fact, it appears that this sequence is always log-concave.
Row sums give A180874.
LINKS
Colin Defant, Michael Engen, and Jordan A. Miller, Stack-sorting, set partitions, and Lassalle's sequence, arXiv:1809.01340 [math.CO], 2018.
FORMULA
T(n,1) = T(n,2n-1) = 0 for n>1.
T(n,2) = T(n,2n-2) = A180874(n-1) for n>1.
EXAMPLE
The five uniquely sorted permutations of [5] are 21435, 31425, 32415, 32145, and 42135. Of these permutations, T(3,1) = 0 start with the entry 1, T(3,2) = 1 starts with 2, T(3,3) = 3 start with 3, T(3,4) = 1 starts with 4, and T(3,5) = 0 start with 5.
Triangle begins:
1,
0, 1, 0,
0, 1, 3, 1, 0,
0, 5, 13, 20, 13, 5, 0,
...
CROSSREFS
KEYWORD
nonn,tabf,more
AUTHOR
Colin Defant, Sep 06 2018
STATUS
approved