

A332954


Triangle read by rows: T(n,k) is the number of permutations sigma of [n] such that sigma(j)/(j+k) > sigma(j+1)/(j+k+1) for 1 <= j <= n1.


3



1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 6, 3, 2, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 19, 8, 5, 3, 2, 1, 1, 1, 30, 13, 7, 5, 3, 2, 1, 1, 1, 60, 21, 12, 7, 5, 3, 2, 1, 1, 1, 108, 38, 17, 11, 7, 5, 3, 2, 1, 1, 1
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OFFSET

0,7


COMMENTS

Conjecture: T(2*n+4,n) = A052955(n+2). This is true for n <= 10.
T(n+1,k) is equal to the number of permutations sigma of [n] such that sigma(j)/(j+k) >= sigma(j+1)/(j+k+1) for 1 <= j <= n1.


LINKS



EXAMPLE

Triangle begins:
n\k  0 1 2 3 4 5 6 7 8 9 10 11
+
0  1;
1  1, 1;
2  1, 1, 1;
3  2, 1, 1, 1;
4  3, 2, 1, 1, 1;
5  6, 3, 2, 1, 1, 1;
6  9, 5, 3, 2, 1, 1, 1;
7  19, 8, 5, 3, 2, 1, 1, 1;
8  30, 13, 7, 5, 3, 2, 1, 1, 1;
9  60, 21, 12, 7, 5, 3, 2, 1, 1, 1;
10  108, 38, 17, 11, 7, 5, 3, 2, 1, 1, 1;
11  222, 64, 31, 16, 11, 7, 5, 3, 2, 1, 1, 1;


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



