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a(n) = 0!*1!*2!*(3*n)!*3*n*(n-1) / ((n)!*(n+1)!*(n+2)!).
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%I #5 May 08 2022 23:58:36

%S 0,30,756,16632,360360,7876440,174594420,3926434512,89492111280,

%T 2064420294300,48134517631200,1133012491934400,26895067957892160,

%U 643240375326254160,15487976684184750900,375182135475713517600

%N a(n) = 0!*1!*2!*(3*n)!*3*n*(n-1) / ((n)!*(n+1)!*(n+2)!).

%C (Empirical) Number of n X 3 matrices containing a defective permutation of 1..3*n in strictly increasing order rowwise and columnwise, with one permutation value omitted and one repeated (see example).

%C Column 3 of A181204.

%H R. H. Hardin, <a href="/A181201/b181201.txt">Table of n, a(n) for n=1..50</a>

%e Some solutions for 4 X 3

%e ..1..3..4....1..4..6....1..4..6....1..2..8....1..2..7....1..2..8....1..2..3

%e ..2..6..9....2..5..7....2..7..9....3..4..9....2..5..9....2..5..9....2..6..7

%e ..7..8.10....3..9.11....3..8.11....5..7.11....3..8.11....3..6.11....5..8..9

%e .10.11.12....5.10.12....7.10.12....6..9.12....6.10.12....7.10.12...10.11.12

%Y Cf. A181204.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 10 2010