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A181201 a(n) = 0!*1!*2!*(3*n)!*3*n*(n-1) / ((n)!*(n+1)!*(n+2)!).

%I A181201 #5 May 08 2022 23:58:36
%S A181201 0,30,756,16632,360360,7876440,174594420,3926434512,89492111280,
%T A181201 2064420294300,48134517631200,1133012491934400,26895067957892160,
%U A181201 643240375326254160,15487976684184750900,375182135475713517600
%N A181201 a(n) = 0!*1!*2!*(3*n)!*3*n*(n-1) / ((n)!*(n+1)!*(n+2)!).
%C A181201 (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 A181201 Column 3 of A181204.
%H A181201 R. H. Hardin, <a href="/A181201/b181201.txt">Table of n, a(n) for n=1..50</a>
%e A181201 Some solutions for 4 X 3
%e A181201 ..1..3..4....1..4..6....1..4..6....1..2..8....1..2..7....1..2..8....1..2..3
%e A181201 ..2..6..9....2..5..7....2..7..9....3..4..9....2..5..9....2..5..9....2..6..7
%e A181201 ..7..8.10....3..9.11....3..8.11....5..7.11....3..8.11....3..6.11....5..8..9
%e A181201 .10.11.12....5.10.12....7.10.12....6..9.12....6.10.12....7.10.12...10.11.12
%Y A181201 Cf. A181204.
%K A181201 nonn
%O A181201 1,2
%A A181201 _R. H. Hardin_, Oct 10 2010