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A173445 a(n) is the number of (0,1) - matrices of size (2n)by(13n) with row sum 13 and column sum 2. 0
1, 825043888527957000, 503273760207613155429966482419001606580000, 1672873154003101614626125868425197066981858431932863917477140065600000, 3603605521974980862 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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.

LINKS

Table of n, a(n) for n=1..5.

FORMULA

a(n) = \frac{(13n)!}{2^{13n}}\sum_{r_{0} = 0}^{2n}\sum_{r_{1} = 0}^{2n - r_{0}}% \sum_{r_{2} = 0}^{2n - r_{0} - r_{1}}\sum_{r_{3} = 0}^{2n - r_{0} - r_{1} - r_{2}}% \sum_{r_{4} = 0}^{2n - r_{0} - r_{1} - r_{2} - r_{3}}% \sum_{r_{5} = 0}^{2n - r_{0} - r_{1} - r_{2} - r_{3} - r_{4}}\frac{(2n)!}{% r_{0}!r_{1}!r_{2}!r_{3}!r_{4}!r_{5}!(2n - r_{0} - r_{1} - r_{2} - r_{3} - r_{4} - r_{5})!% }\frac{( -1)^{ - 5r_{1} - 4r_{2} - 3r_{3} - 2r_{4} - r_{5} + 12n - 6r_{0}}}{% (13n + 5r_{1} + 4r_{2} + 3r_{3} + 2r_{4} + r_{5} - 12n + 6r_{0})!}$\bigskip $\frac{% (13r_{0} + 11r_{1} + 9r_{2} + 7r_{3} + 5r_{4} + 3r_{5} + (2n - r_{0} - r_{1} - r_{2} - r_{3} - r_{4} - r_{5}))!% }{% 13!^{r_{0}}11!^{r_{1}}(2!9!)^{r_{2}}(3!7!)^{r_{3}}(4!5!)^{r_{4}}(5!3!)^{r_{5}}6!^{2n - r_{0} - r_{1} - r_{2} - r_{3} - r_{4} - r_{5}}% }

CROSSREFS

Sequence in context: A172565 A172546 A256312 * A281390 A281301 A286481

Adjacent sequences:  A173442 A173443 A173444 * A173446 A173447 A173448

KEYWORD

nonn

AUTHOR

Shanzhen Gao, Feb 18 2010

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)