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A343488
Irregular table T(n, k), n >= 0, k = 1..max(1, n), read by rows; T(n, k) is the number of permutations s of { 1..n } such that p(s) = k where p(s) is the least m > 0 such that, working in Z/nZ, s(i) + m = s(i + m) for i = 1..n.
1
1, 1, 2, 0, 3, 0, 3, 4, 4, 0, 16, 5, 0, 0, 0, 115, 6, 12, 42, 0, 0, 660, 7, 0, 0, 0, 0, 0, 5033, 8, 24, 0, 352, 0, 0, 0, 39936, 9, 0, 153, 0, 0, 0, 0, 0, 362718, 10, 40, 0, 0, 3830, 0, 0, 0, 0, 3624920, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39916789, 12, 60, 372, 1872, 0, 45636, 0, 0, 0, 0, 0, 478953648
OFFSET
0,3
COMMENTS
We set the row for n = 0 to [1] by convention.
The number p(s) can be interpreted as the period of the permutation s.
FORMULA
T(n, 1) = max(n, 1).
T(n, n) = A324514(n).
Sum_{k = 1..max(1, n)} T(n, k) = n!.
EXAMPLE
Table begins:
0: [1]
1: [1]
2: [2, 0]
3: [3, 0, 3]
4: [4, 4, 0, 16]
5: [5, 0, 0, 0, 115]
6: [6, 12, 42, 0, 0, 660]
7: [7, 0, 0, 0, 0, 0, 5033]
8: [8, 24, 0, 352, 0, 0, 0, 39936]
9: [9, 0, 153, 0, 0, 0, 0, 0, 362718]
10: [10, 40, 0, 0, 3830, 0, 0, 0, 0, 3624920]
PROG
(C) See Links section.
CROSSREFS
Sequence in context: A337980 A373148 A343309 * A343270 A137303 A049084
KEYWORD
nonn,tabf
AUTHOR
Rémy Sigrist, Apr 17 2021
STATUS
approved