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A132202
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Number of 3n X 2n (0,1)-matrices with every row sum 2 and column sum 3.
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3
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1, 1860, 90291600, 31082452632000, 46764764308702440000, 229747284991066934931840000, 3031982831164890119435183865600000, 93453554057243260025029337978773248000000, 6055976192395031960092036887782708145734400000000, 760152286561053082358524425840024164536832608896000000000
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OFFSET
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1,2
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=1..10.
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FORMULA
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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.
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EXAMPLE
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1 for 3X2:
11
11
11
1860 for 6X4.
90291600 for 9X6.
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MAPLE
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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;
[seq(f(3*n, 2*n), n=0..10)];
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CROSSREFS
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Cf. A134772, A134648.
Sequence in context: A213868 A022062 A107526 * A054815 A295995 A237257
Adjacent sequences: A132199 A132200 A132201 * A132203 A132204 A132205
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KEYWORD
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nonn,easy
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AUTHOR
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Shanzhen Gao, Nov 05 2007
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EXTENSIONS
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Edited and extended with Maple code by R. H. Hardin and N. J. A. Sloane, Oct 18 2009
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STATUS
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approved
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