A321352 Triangle T(n,k) giving the number of permutations pi of {1,2,...,n} such that for all i, pi(i) is not in {i, i+1, ..., i+k-1} (mod n), with 0 <= k <= n - 1.

1, 2, 1, 6, 2, 1, 24, 9, 2, 1, 120, 44, 13, 2, 1, 720, 265, 80, 20, 2, 1, 5040, 1854, 579, 144, 31, 2, 1, 40320, 14833, 4738, 1265, 264, 49, 2, 1, 362880, 133496, 43387, 12072, 2783, 484, 78, 2, 1, 3628800, 1334961, 439792, 126565, 30818, 6208, 888, 125, 2, 1

Offset

1,2

Comments

This is A008305 with the rows reversed.

First column is A000142 (factorial numbers).

Second column is A000166 (derangements).

Third column is A000179 (ménage numbers).

Fourth column is A000183 (discordant permutations)

Links

Peter Kagey, Table of n, a(n) for n = 1..276 (first 23 rows, flattened)

Example

Table begins:
       1
       2,      1
       6,      2,     1
      24,      9,     2,     1
     120,     44,    13,     2,    1
     720,    265,    80,    20,    2,   1
    5040,   1854,   579,   144,   31,   2,  1
   40320,  14833,  4738,  1265,  264,  49,  2, 1
  362880, 133496, 43387, 12072, 2783, 484, 78, 2, 1

Crossrefs

Cf. A008305.

Cf. A000142, A000166, A000179, A000183, A004307, A189389, A184965.

Sequence in context: A069123 A134133 A157392 * A134134 A222005 A351442

Adjacent sequences: A321349 A321350 A321351 * A321353 A321354 A321355

Keyword

nonn,tabl

Author

Peter Kagey, Feb 25 2020

Status

approved