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

Author

Alois P. Heinz, Sep 25 2016

Keywords

• nonn
• tabl

Examples

			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;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..12, flattened
• Per Alexandersson et al., d-regular partitions and permutations, MathOverflow, 2014

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.