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%I #49 Jul 04 2023 08:44:13
%S 1,2,90,297200,116963796250,6736218287430460752,
%T 64051375889927380035549804336,
%U 108738182111446498614705217754614976371200,34812290428176298285394893936773707951192224124239796250,2188263032066768922535710968724036448759525154977348944382853301460850000
%N Number of 2n X 2n 0-1 matrices with n ones in each row and each column.
%C A diagonal of triangle in A008300.
%H Vladeta Jovovic, Nov 12 2006, <a href="/A058527/b058527.txt">Table of n, a(n) for n = 0..15</a>
%H A Conflitti, C. M. Da Fonseca, and R. Mamede, <a href="http://dx.doi.org/10.1016/j.laa.2011.07.043">The maximal length of a chain in the Bruhat order for a chain of binary matrices.</a>, Lin. Algebra Applic. (2011)
%H Alessandro Conflitti, C. M. da Fonseca and Ricardo Mamede, <a href="http://www.mat.uc.pt/preprints/ps/pre1125.ps">On the largest size of an antichain in the Bruhat order for A(2k, k)</a>.
%H Alessandro Conflitti, C. M. da Fonseca and Ricardo Mamede, <a href="http://dx.doi.org/10.1007/s11083-011-9241-1">On the Largest Size of an Antichain in the Bruhat Order for A(2k,k)</a>, ORDER, 2011, DOI: 10.1007/s11083-011-9241-1.
%H Jonathan Jedwab and Tabriz Popatia, <a href="http://people.math.sfu.ca/~jed/Papers/Jedwab%20Popatia.%20MOFS.%20Preprint.pdf">A new representation of mutually orthogonal frequency squares</a>, Simon Fraser University (Burnaby, BC, Canada, 2020).
%H M. A. Khojastepour and M. Farajzadeh-Tehrani, <a href="http://mysbfiles.stonybrook.edu/~mfarajzadeht/Conf2.pdf">Characterizing per Node Degrees of Freedom in an Interference Network</a>, 2014.
%H B. D. McKay, <a href="http://users.cecs.anu.edu.au/~bdm/data/semiregular.html">0-1 matrices with constant row and column sums</a>
%H Michael Penn, <a href="https://www.youtube.com/watch?v=G4QbuWB0EpY">A not so magic square...</a>, YouTube video, 2021.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dynamic_programming">Dynamic programming</a>
%Y Cf. A001499, A001501, A253316.
%Y Cf. A008300.
%K nonn
%O 0,2
%A _David desJardins_, Dec 22 2000
%E More terms (using dynamic programming in Python) from _Greg Kuperberg_, Feb 08 2001
%E More terms from _Vladeta Jovovic_, Nov 12 2006
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