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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.)