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A346492
Triangle read by rows: T(n,k) is the number of permutations of length n such that the minimum over maximum difference of elements in cycles is exactly k; 0 <= k < n.
0
1, 1, 1, 4, 0, 2, 15, 2, 1, 6, 76, 8, 8, 4, 24, 455, 40, 40, 45, 20, 120, 3186, 244, 246, 254, 270, 120, 720, 25487, 1729, 1728, 1757, 1849, 1890, 840, 5040, 229384, 13948, 13960, 14096, 14540, 14792, 15120, 6720, 40320
OFFSET
1,4
COMMENTS
First column is A002467.
EXAMPLE
The minimum over maximum difference of elements in cycles of the permutation (421)(53), written in cycle notation, is 2. The first cycle has maximum difference of 4-1=3, the second cycle has a maximum difference of 5-3=2, and the minimum of these is min(3,2) = 2.
The permutations whose minimum over maximum difference of elements in cycles is 0 are precisely those with a fixed point.
n\k | 0 1 2 3 4 5 6 7 8
----+--------------------------------------------------------
1 | 1
2 | 1 1
3 | 4 0 2
4 | 15 2 1 6
5 | 76 8 8 4 24
6 | 455 40 40 45 20 120
7 | 3186 244 246 254 270 120 720
8 | 25487 1729 1728 1757 1849 1890 840 5040
9 | 229384 13948 13960 14096 14540 14792 15120 6720 40320
CROSSREFS
Cf. A002467.
Sequence in context: A208748 A134895 A318468 * A145877 A373984 A283572
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Jul 19 2021
STATUS
approved