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 A134645 Number of 2n X 3n (0,1,2)-matrices with every row sum 3 and column sum 2. 2
 7, 16260, 747558000, 250071339672000, 369820640830881240000, 1796185853884657144990080000, 23511842995969107700302647865600000, 720289186703359375552628986978410240000000, 46455761324619133018320834819622638940550400000000, 5809177204262302555518772962193269714031251010176000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES Zhonghua Tan, Shanzhen Gao, Kenneth Mathies, Joshua Fallon, Counting (0,1,2)-Matrices, Congressus Numeratium, December 2008. LINKS Table of n, a(n) for n=1..10. FORMULA Let t(m,n)=6^{-m} sum_{i=0}^{m}frac{3^{i}m!n!(2n-2i)!}{i!(m-i)!(n-i)!2^{n-i}}; then a(n) = t(2n,3n). a(n) = (3n)!(2n)!288^(-n) * Sum_{i=0..2n} (6n-2i)!6^i/(i!(3n-i)!(2n-i)!). - Shanzhen Gao, Mar 02 2010 a(n) ~ sqrt(Pi) * 2^(n+1) * 3^(4*n + 1/2) * n^(6*n + 1/2) / exp(6*n-1). - Vaclav Kotesovec, Oct 21 2023 EXAMPLE a(1) = 7: 111 210 (6 ways) 111 012 MAPLE f:=proc(m, n) 6^(-m)*add( (3^i*m!*n!*(2*n-2*i)!)/ (i!*(m-i)!*(n-i)!*2^(n-i)), i=0..m); end; MATHEMATICA Table[(3*n)! * (2*n)! / 288^n * Sum[(6*n - 2*i)! * 6^i / (i! * (3*n - i)! * (2*n - i)!), {i, 0, 2*n}], {n, 1, 15}] (* Vaclav Kotesovec, Oct 21 2023 *) Table[(2/9)^n * (3*n)! * ((6*n - 1)/2)! * Hypergeometric1F1[-2*n, 1/2 - 3*n, 3/2] / Sqrt[Pi], {n, 1, 15}] (* Vaclav Kotesovec, Oct 21 2023 *) CROSSREFS Cf. A000681, A134646. Sequence in context: A344532 A280813 A203685 * A327840 A115997 A013786 Adjacent sequences: A134642 A134643 A134644 * A134646 A134647 A134648 KEYWORD nonn AUTHOR Shanzhen Gao, Nov 05 2007 EXTENSIONS Corrected, edited and extended with Maple program by R. H. Hardin and N. J. A. Sloane, Oct 18 2009 STATUS approved

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Last modified February 23 14:24 EST 2024. Contains 370283 sequences. (Running on oeis4.)