

A319031


Triangle read by rows: T(n,k) is the number of permutations pi of [k] such that s(pi) avoids the pattern 12...n, where s is West's stacksorting map (1 <= k <= 2^(n1)1).


0



1, 1, 2, 1, 1, 2, 6, 10, 13, 10, 3, 1, 2, 6, 24, 78, 232, 631, 1498, 3017, 4934
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OFFSET

2,3


COMMENTS

We only consider k <= 2^(n1)1 because T(n,k) = 0 when k >= 2^(n1).
It appears that the rows T(n,1), ..., T(n,2^(n1)1) are unimodal.


LINKS



EXAMPLE

The only permutation pi of [3] such that s(pi) does not contain the pattern 123 is 231, so T(3,3) = 1.
Triangle begins:
1,
1, 2, 1,
1, 2, 6, 10, 13, 10, 3,
1, 2, 6, 24, 78, 232, 631, 1498, 3017, 4934, ...
(not all terms in the fourth row are known).


CROSSREFS



KEYWORD

nonn,tabf,more


AUTHOR



STATUS

approved



