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%I #11 Mar 16 2021 04:35:34
%S 1,1,1,1,1,1,1,1,1,1,1,3,2,3,1,1,3,10,10,3,1,1,15,40,84,40,15,1,1,15,
%T 296,852,852,296,15,1,1,105,1576,11580,22368,11580,1576,105,1,1,105,
%U 15352,197640,822528,822528,197640,15352,105,1,1,945,104000,4314240,38772864,84961440,38772864,4314240,104000,945,1
%N Array read by antidiagonals: T(n,m) is the number of maximal matchings in the rook graph K_n X K_m.
%H Andrew Howroyd, <a href="/A341847/b341847.txt">Table of n, a(n) for n = 0..275</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentEdgeSet.html">Maximal 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 10 40 296 1576 ...
%e 3 | 1 3 10 84 852 11580 197640 ...
%e 4 | 1 3 40 852 22368 822528 38772864 ...
%e 5 | 1 15 296 11580 822528 84961440 12002446080 ...
%e 6 | 1 15 1576 197640 38772864 12002446080 5429866337280 ...
%e ...
%Y Rows n=1..4 are A133221(n+1), A281433, A341848, A341849.
%Y Main diagonal is A289198.
%Y Cf. A270227 (matchings), A297471, A341850 (maximum matchings).
%K nonn,tabl
%O 0,12
%A _Andrew Howroyd_, Feb 21 2021
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