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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..78.

Igor Pak, Periodic permutations and the Robinson-Schensted correspondence

Rémy Sigrist, C program for A343488

Index entries for sequences related to permutations

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

Cf. A000142, A324514.

Sequence in context: A253274 A337980 A343309 * A343270 A137303 A049084

Adjacent sequences:  A343485 A343486 A343487 * A343489 A343490 A343491

KEYWORD

nonn,tabf

AUTHOR

Rémy Sigrist, Apr 17 2021

STATUS

approved

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Last modified October 20 03:04 EDT 2021. Contains 348099 sequences. (Running on oeis4.)