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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 (list; table; graph; refs; listen; history; text; internal format)
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: A277529 A060338 A132795 * A085198 A339207 A199916

Adjacent sequences:  A277028 A277029 A277030 * A277032 A277033 A277034

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 25 2016

STATUS

approved

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Last modified October 19 21:59 EDT 2021. Contains 348095 sequences. (Running on oeis4.)