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A269565 Array read by antidiagonals: T(n,m) is the number of (directed) Hamiltonian paths in K_n X K_m. 4
1, 2, 2, 6, 8, 6, 24, 60, 60, 24, 120, 816, 1512, 816, 120, 720, 17520, 83520, 83520, 17520, 720, 5040, 550080, 8869680, 22394880, 8869680, 550080, 5040, 40320, 23839200, 1621680480, 13346910720, 13346910720, 1621680480, 23839200, 40320 (list; table; graph; refs; listen; history; text; internal format)
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

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

From Andrew Howroyd, Oct 20 2019: (Start)

T(n,m) = T(m,n).

T(n,1) = n!. (End)

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

Main diagonal is A096970.

Column 2 is A096121.

Cf. A286418, A269562.

Sequence in context: A142243 A269722 A091441 * A099490 A167878 A320139

Adjacent sequences:  A269562 A269563 A269564 * A269566 A269567 A269568

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Feb 29 2016

STATUS

approved

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Last modified January 29 10:34 EST 2020. Contains 331337 sequences. (Running on oeis4.)