cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Peter Kagey, Nov 02 2024

Keywords

Comments

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

Examples

			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.
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