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a(n) = 0!*1!*2!*...*(n-1)! *(n^2)! *(n*(n-1))^2 / 2*n!*(n+1)!*...*(2*n-1)!
1

%I #7 Dec 18 2015 18:17:26

%S 0,4,756,1729728,140229804000,752239365180732000,

%T 419014989521191873479589920,34623595988556658225393154134784716800,

%U 571228532851873223553288547443139274046846826752000

%N a(n) = 0!*1!*2!*...*(n-1)! *(n^2)! *(n*(n-1))^2 / 2*n!*(n+1)!*...*(2*n-1)!

%C (Empirical) Number of n X n matrices containing a defective permutation of 1..n*n in strictly increasing order rowwise and columnwise, with one permutation value omitted and one repeated (see example)

%C Diagonal of A181204

%H R. H. Hardin, <a href="/A181200/b181200.txt">Table of n, a(n) for n=1..22</a>

%e Some solutions for 3X3

%e ..2..3..5....1..2..5....1..2..6....1..3..4....1..3..4....1..2..4....1..3..5

%e ..4..6..7....3..4..6....3..4..8....2..5..8....2..6..7....2..5..7....2..4..6

%e ..5..8..9....4..7..9....6..7..9....4..6..9....5..7..9....3..6..9....6..7..8

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 10 2010