Generating function
$$U_{287}(x, y) = \frac{\sqrt{3} \sqrt{x} - \sqrt{3 x - 16 y \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}}{4 y \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}$$
Explicit formula
$$T_{287}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{k + 2 m + 3 n - 1}{n}}}{k + 2 m + 2 n}$$
| 1 | 1 | 2 | 5 | 14 | 42 | 132 |
| 1 | 3 | 1 | 35 | 126 | 462 | 1716 |
| 3 | 12 | 5 | 21 | 882 | 3696 | 15444 |
| 12 | 55 | 26 | 1225 | 5712 | 26334 | 12012 |
| 55 | 273 | 14 | 714 | 3591 | 17787 | 868296 |
| 273 | 1428 | 7752 | 41895 | 223146 | 116886 | 602316 |
| 1428 | 7752 | 4389 | 24794 | 138138 | 756756 | 40756716 |
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