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A276974
Number T(n,k) of permutations of [n] where the minimal 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, 4, 1, 1, 0, 19, 3, 1, 1, 0, 103, 12, 3, 1, 1, 0, 651, 54, 10, 3, 1, 1, 0, 4702, 281, 42, 10, 3, 1, 1, 0, 38413, 1652, 203, 37, 10, 3, 1, 1, 0, 350559, 11017, 1086, 166, 37, 10, 3, 1, 1, 0, 3539511, 81665, 6564, 857, 151, 37, 10, 3, 1, 1, 0, 39196758, 669948, 44265, 4900, 726, 151, 37, 10, 3, 1, 1
OFFSET
0,8
LINKS
Per Alexandersson et al., d-regular partitions and permutations, MathOverflow, 2014
EXAMPLE
T(3,1) = 4: (1,2,3), (1,3,2), (1)(2,3), (1,2)(3).
T(3,2) = 1: (1,3)(2).
T(3,3) = 1: (1)(2)(3).
Triangle T(n,k) begins:
1;
0, 1;
0, 1, 1;
0, 4, 1, 1;
0, 19, 3, 1, 1;
0, 103, 12, 3, 1, 1;
0, 651, 54, 10, 3, 1, 1;
0, 4702, 281, 42, 10, 3, 1, 1;
0, 38413, 1652, 203, 37, 10, 3, 1, 1;
0, 350559, 11017, 1086, 166, 37, 10, 3, 1, 1;
0, 3539511, 81665, 6564, 857, 151, 37, 10, 3, 1, 1;
...
CROSSREFS
Columns k=0-1 give: A000007, A276975.
Row sums give A000142.
T(2n,n) = A138378(n) = A005493(n-1) for n>0.
Sequence in context: A276834 A016684 A324564 * A122777 A103524 A110916
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Sep 23 2016
STATUS
approved