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A132202 Number of 3n X 2n (0,1)-matrices with every row sum 2 and column sum 3. 3


%S 1,1860,90291600,31082452632000,46764764308702440000,

%T 229747284991066934931840000,3031982831164890119435183865600000,

%U 93453554057243260025029337978773248000000,6055976192395031960092036887782708145734400000000,760152286561053082358524425840024164536832608896000000000

%N Number of 3n X 2n (0,1)-matrices with every row sum 2 and column sum 3.

%D Gao, Shanzhen, and Matheis, Kenneth, Closed formulas and integer sequences arising from the enumeration of (0,1)-matrices with row sum two and some constant column sums. In Proceedings of the Forty-First Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 202 (2010), 45-53.

%F a(M,N)=2^(-M)*sum_{i=0..N} {(-1)^{i}M!N!(2M-2i)!}/{i!(M-i)!(N-i)!6^{N-i}}, for M=3n, N=2n.

%e 1 for 3X2:

%e 11

%e 11

%e 11

%e 1860 for 6X4.

%e 90291600 for 9X6.

%p f:=proc(m,n) 2^(-m)*add( ((-1)^(i)*m!*n!*(2*m-2*i)!)/ (i!*(m-i)!*(n-i)!*6^(n-i)), i=0..n); end;

%p [seq(f(3*n,2*n),n=0..10)];

%Y Cf. A134772, A134648.

%K nonn,easy

%O 1,2

%A _Shanzhen Gao_, Nov 05 2007

%E Edited and extended with Maple code by R. H. Hardin and _N. J. A. Sloane_, Oct 18 2009

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Last modified October 1 04:31 EDT 2022. Contains 357134 sequences. (Running on oeis4.)