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

Author

Peter Kagey, Feb 25 2020

Keywords

• nonn
• tabl

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)

Examples

			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
		

Links

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

Crossrefs

Cf. A008305.

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