%I
%S 7,16260,747558000,250071339672000,369820640830881240000,
%T 1796185853884657144990080000,23511842995969107700302647865600000,
%U 720289186703359375552628986978410240000000,46455761324619133018320834819622638940550400000000,5809177204262302555518772962193269714031251010176000000000
%N Number of 2n X 3n (0,1,2)matrices with every row sum 3 and column sum 2.
%D Zhonghua Tan, Shanzhen Gao, Kenneth Mathies, Joshua Fallon, Counting (0,1,2)Matrices, Congressus Numeratium, December 2008.
%F Let t(m,n)=6^{m} sum_{i=0}^{m}frac{3^{i}m!n!(2n2i)!}{i!(mi)!(ni)!2^{ni}}; then a(n) = t(2n,3n).
%F a(n) = (3n)!(2n)!288^(n) * Sum_{i=0..2n} (6n2i)!6^i/(i!(3ni)!(2ni)!).  _Shanzhen Gao_, Mar 02 2010
%e a(1) = 7:
%e 111 210 (6 ways)
%e 111 012
%p f:=proc(m,n) 6^(m)*add( (3^i*m!*n!*(2*n2*i)!)/ (i!*(mi)!*(ni)!*2^(ni)), i=0..m); end;
%Y Cf. A000681, A134646.
%K nonn
%O 1,1
%A _Shanzhen Gao_, Nov 05 2007
%E Corrected, edited and extended with Maple program by R. H. Hardin and _N. J. A. Sloane_, Oct 18 2009
