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Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = largest permanent of any n X n (0,1) matrix with k 1's in each row and column.
1

%I #7 Aug 03 2016 12:20:59

%S 1,1,2,1,2,6,1,4,9,24,1,4,13,44,120,1,8,36,82,265,720,1,8,54,148,580,

%T 1854,5040,1,16,81,576,1313,4752,14833,40320,1,16,216,1056,2916,12108,

%U 43424,133496,362880,1,32,324,1968,14400,32826,127044,440192,1334961,3628800,1,32,486,3608,31800,86400,373208,1448640,4893072,14684570,39916800

%N Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = largest permanent of any n X n (0,1) matrix with k 1's in each row and column.

%D L. Hogben, ed., Handbook of Linear Algebra, pp. 31-6, 31-7.

%H G.-S. Cheon and I. M. Wanless, <a href="http://dx.doi.org/10.1016/j.laa.2005.02.030">An update on Minc's survey on open problems involving permanents</a>, Lin. Alg. Applic., 403 (2005), 314-342.

%e Triangle begins:

%e 1

%e 1,2

%e 1,2,6

%e 1,4,9,24

%e 1,4,13,44,120

%e 1,8,36,82,265,720

%e 1,8,54,148,580,1854,5040

%K nonn,tabl

%O 1,3

%A _N. J. A. Sloane_, Dec 17 2007