A173405 a(n) is the number of (2n) by (11n) (0,1)-matrices with row sum 11 and column sum 2.

1, 813689707488840, 66616980501713943527764656942096000, 7872210237152082461519795095323072380800492540574161420800, 221848107812451948017800051742871374872981904431531975133609486296113025373335680000

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{(11n)!}{2^{11n}}\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}}\frac{(2n)!}{% r_{0}!r_{1}!r_{2}!r_{3}!r_{4}!(2n-r_{0}-r_{1}-r_{2}-r_{3}-r_{4})!}\frac{% (-1)^{-4r_{1}-3r_{2}-2r_{3}-r_{4}+10n-5r_{0}}}{% (11n+4r_{1}+3r_{2}+2r_{3}+r_{4}-10n+5r_{0})!}\frac{(\allowbreak 10r_{0}+8r_{1}+6r_{2}+4r_{3}+2r_{4}+2n)!}{120^{2n}332% \,640^{r_{0}}3024^{r_{1}}84^{r_{2}}6^{r_{3}+r_{4}}5^{-r_{4}}

Crossrefs

Sequence in context: A298821 A159042 A129935 * A104835 A128446 A346569

Adjacent sequences: A173402 A173403 A173404 * A173406 A173407 A173408

Keyword

nonn

Author

Shanzhen Gao, Feb 17 2010

Status

approved