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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
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
Sequence in context: A344532 A280813 A203685 * A327840 A115997 A013786
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.)