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%I #9 Mar 15 2021 17:53:30
%S 1,1,1,1,1,1,1,1,1,1,1,3,2,3,1,1,3,4,4,3,1,1,15,16,72,16,15,1,1,15,56,
%T 132,132,56,15,1,1,105,376,7020,2016,7020,376,105,1,1,105,1912,17280,
%U 44928,44928,17280,1912,105,1,1,945,17984,1920240,1551744,22615200,1551744,1920240,17984,945,1
%N Array read by antidiagonals: T(n,m) is the number of maximum matchings in the rook graph K_n X K_m.
%C In the case that both m and n are odd a single vertex is not covered, otherwise the maximum matchings are perfect matchings.
%H Andrew Howroyd, <a href="/A341850/b341850.txt">Table of n, a(n) for n = 0..527</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximumIndependentEdgeSet.html">Maximum Independent Edge Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>
%F T(n,m) = T(m,n).
%e Array begins:
%e ======================================================
%e n\m | 0 1 2 3 4 5 6
%e ----+-------------------------------------------------
%e 0 | 1 1 1 1 1 1 1 ...
%e 1 | 1 1 1 3 3 15 15 ...
%e 2 | 1 1 2 4 16 56 376 ...
%e 3 | 1 3 4 72 132 7020 17280 ...
%e 4 | 1 3 16 132 2016 44928 1551744 ...
%e 5 | 1 15 56 7020 44928 22615200 243319680 ...
%e 6 | 1 15 376 17280 1551744 243319680 61903180800 ...
%e ...
%Y Rows n=1..4 are A133221(n+1), A081919, A341851, A341852.
%Y Main diagonal is A289197.
%Y Cf. A270227 (matchings), A286070, A341847 (maximal matchings).
%K nonn,tabl
%O 0,12
%A _Andrew Howroyd_, Feb 21 2021
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