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.

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

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

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.

Cf. A239145, A263757, A276974.

Sequence in context: A354133 A060338 A132795 * A085198 A339207 A372959

Adjacent sequences: A277028 A277029 A277030 * A277032 A277033 A277034

Keyword

nonn,tabl

Author

Alois P. Heinz, Sep 25 2016

Status

approved