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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.
3
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
KEYWORD
nonn,tabl
AUTHOR
Peter Kagey, Feb 25 2020
STATUS
approved