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REFERENCES
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Shanzhen Gao, Sequences Arising from Integer Matrix Enumeration (in preparation) [From Shanzhen Gao, Feb 16 2010]
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.
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FORMULA
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\frac{1}{(7!)^{2n}}\sum_{\gamma =0}^{2n}\sum_{\alpha =0}^{\min \{2n-\gamma,\lfloor (7n-\gamma )/2\rfloor \}}\sum_{\beta =0}^{\min \{2n-\gamma -\alpha,\lfloor (7n-\gamma -2\alpha )/3\rfloor \}}\frac{% (-1)^{\beta +\gamma }105^{\alpha +\beta }21^{\gamma }(2n)!(7n)!(\allowbreak 14n-4\alpha -6\beta -2\gamma )!}{\alpha !\beta !\gamma !(2n-\alpha -\beta -\gamma )!(7n-2\alpha -3\beta -\gamma )!2^{7n-2\alpha -3\beta -\gamma }} [From Shanzhen Gao, Feb 16 2010]
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