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 A132202 Number of 3n X 2n (0,1)-matrices with every row sum 2 and column sum 3. 4
 1, 1860, 90291600, 31082452632000, 46764764308702440000, 229747284991066934931840000, 3031982831164890119435183865600000, 93453554057243260025029337978773248000000, 6055976192395031960092036887782708145734400000000, 760152286561053082358524425840024164536832608896000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES Shanzhen Gao and Kenneth Matheis, 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. LINKS G. C. Greubel, Table of n, a(n) for n = 1..85 FORMULA a(n) = f(3*n, 2*n), where f(m, n) = 2^(-m) * Sum_{j=0..n} (-1)^j*n!*m!*(2*m-2*j)!/(j!*(m-j)!*(n-j)!*6^(n-j)). From G. C. Greubel, Oct 12 2023: (Start) a(n) = ((6*n)!/(288)^n)*Sum_{j=0..2*n} b(2*n,j)*b(3*n,j)*(-6)^j/(j!*b(2*j, j)*b(6*n,2*j)), where b(x,y) = binomomial(x,y). a(n) = (6*n)!/(288)^n * Hypergeometric1F1([-2*n], [1/2-3*n], -3/2). (End) 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 1 for 3X2: 11 11 11 1860 for 6X4. 90291600 for 9X6. MAPLE 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)]; MATHEMATICA Table[((6*n)!/(288)^n)*Hypergeometric1F1[-2*n, 1/2-3*n, -3/2], {n, 30}] (* G. C. Greubel, Oct 12 2023 *) PROG (Magma) B:=Binomial; A132202:= func< n | Factorial(6*n)/(288)^n*(&+[B(2*n, j)*B(3*n, j)*(-6)^j/(Factorial(j)*B(2*j, j)*B(6*n, 2*j)): j in [0..2*n]]) >; [A132202(n): n in [1..30]]; // G. C. Greubel, Oct 12 2023 (SageMath) b=binomial def A132202(n): return factorial(6*n)/(288)^n *simplify(hypergeometric([-2*n], [1/2-3*n], -3/2)) [A132202(n) for n in range(1, 31)] # G. C. Greubel, Oct 12 2023 CROSSREFS Cf. A134648, A134772. Sequence in context: A213868 A022062 A107526 * A054815 A295995 A237257 Adjacent sequences: A132199 A132200 A132201 * A132203 A132204 A132205 KEYWORD nonn,easy AUTHOR Shanzhen Gao, Nov 05 2007 EXTENSIONS Edited and extended with Maple code by R. H. Hardin and N. J. A. Sloane, Oct 18 2009 STATUS approved

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Last modified December 4 10:17 EST 2023. Contains 367560 sequences. (Running on oeis4.)