login
A277031
Number T(n,k) of permutations of [n] where the minimal cyclic distance between elements of the same cycle equals k (k=n for the identity permutation in S_n); triangle T(n,k), n>=0, 0<=k<=n, read by rows.
4
1, 0, 1, 0, 1, 1, 0, 5, 0, 1, 0, 20, 3, 0, 1, 0, 109, 10, 0, 0, 1, 0, 668, 44, 7, 0, 0, 1, 0, 4801, 210, 28, 0, 0, 0, 1, 0, 38894, 1320, 90, 15, 0, 0, 0, 1, 0, 353811, 8439, 554, 75, 0, 0, 0, 0, 1, 0, 3561512, 63404, 3542, 310, 31, 0, 0, 0, 0, 1, 0, 39374609, 517418, 23298, 1276, 198, 0, 0, 0, 0, 0, 1
OFFSET
0,8
LINKS
Per Alexandersson et al., d-regular partitions and permutations, MathOverflow, 2014
EXAMPLE
T(3,1) = 5: (1,2,3), (1,3,2), (1)(2,3), (1,2)(3), (1,3)(2).
T(3,3) = 1: (1)(2)(3).
Triangle T(n,k) begins:
1;
0, 1;
0, 1, 1;
0, 5, 0, 1;
0, 20, 3, 0, 1;
0, 109, 10, 0, 0, 1;
0, 668, 44, 7, 0, 0, 1;
0, 4801, 210, 28, 0, 0, 0, 1;
0, 38894, 1320, 90, 15, 0, 0, 0, 1;
0, 353811, 8439, 554, 75, 0, 0, 0, 0, 1;
0, 3561512, 63404, 3542, 310, 31, 0, 0, 0, 0, 1;
...
CROSSREFS
Columns k=0-1 give: A000007, A277032.
Row sums give A000142.
T(2n,n) = A255047(n) = A000225(n) for n>0.
Sequence in context: A354133 A060338 A132795 * A085198 A339207 A372959
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 25 2016
STATUS
approved