A377597 Table read by antidiagonals: T(n,k) = (n*k)!/(n^k*k!), n >=1, k >= 0.

1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 15, 40, 6, 1, 1, 105, 2240, 1260, 24, 1, 1, 945, 246400, 1247400, 72576, 120, 1, 1, 10395, 44844800, 3405402000, 1743565824, 6652800, 720, 1, 1, 135135, 12197785600, 19799007228000, 162193467211776, 4940103168000, 889574400, 5040, 1

Offset

1,8

Comments

This is the number of permutations in S_{k*n} that consist of k disjoint n-cycles.

Links

Table of n, a(n) for n=1..45.

Example

The table begins:
n\k| 0  1     2          3               4                    5
---+-----------------------------------------------------------
 1 | 1  1     1          1               1                    1
 2 | 1  1     3         15             105                  945
 3 | 1  2    40       2240          246400             44844800
 4 | 1  6  1260    1247400      3405402000       19799007228000
 5 | 1 24 72576 1743565824 162193467211776 41363226782215962624
For example T(2,5) = (2*5)!/(2^5*5!) = 10!/(32*5!) = 945.

Crossrefs

Cf. A001147 (row 2), A052502 (row 3), A060706 (row 4), A052504 (row 5), A110468 (col 2).

Cf. A368213.

Sequence in context: A214742 A204124 A316674 * A101479 A136170 A245188

Adjacent sequences: A377594 A377595 A377596 * A377598 A377599 A377600

Keyword

nonn,tabl

Author

Peter Kagey, Nov 02 2024

Status

approved