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.

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

Alois P. Heinz, Rows n = 0..12, flattened

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.

Cf. A239145, A263757, A277031.

Sequence in context: A276834 A016684 A324564 * A122777 A103524 A110916

Adjacent sequences: A276971 A276972 A276973 * A276975 A276976 A276977

Keyword

nonn,tabl

Author

Alois P. Heinz, Sep 23 2016

Status

approved