OFFSET
1,2
COMMENTS
Equivalently, the number of directed Hamiltonian paths on the n X m rook graph.
Conjecture: T(n,m) mod n!*m! = 0. - Mikhail Kurkov, Feb 08 2019
The above conjecture is true since a path defines an ordering on the rows and columns by the order in which they are first visited by the path. Every permutation of rows and columns therefore gives a different path. - Andrew Howroyd, Feb 08 2021
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..96
Eric Weisstein's World of Mathematics, Hamiltonian Path
Eric Weisstein's World of Mathematics, Rook Graph
FORMULA
EXAMPLE
Array begins:
===========================================================
n\m| 1 2 3 4 5
---+-------------------------------------------------------
1 | 1, 2, 6, 24, 120, ...
2 | 2, 8, 60, 816, 17520, ...
3 | 6, 60, 1512, 83520, 8869680, ...
4 | 24, 816, 83520, 22394880, 13346910720, ...
5 | 120, 17520, 8869680, 13346910720, 50657369241600, ...
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 29 2016
STATUS
approved