Generating function
$$U_{790}(x, y) = \frac{3 x \left(1 - \sqrt{1 - \frac{16 y \left(1 - \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)^{2}}{9 x^{2}}}\right)}{y \left(4 - 4 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)}$$
Explicit formula
$$T_{790}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{2 k + 4 m + 3 n - 1}{n}}}{k + 2 m + n}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
2 | 6 | 2 | 7 | 252 | 924 | 3432 |
7 | 33 | 15 | 665 | 2898 | 12474 | 53196 |
3 | 182 | 102 | 539 | 273 | 13398 | 641784 |
143 | 102 | 665 | 4025 | 230202 | 1260336 | 666666 |
728 | 5814 | 42504 | 28665 | 1812384 | 10885644 | 62730096 |
3876 | 33649 | 2691 | 1982295 | 13634544 | 88666578 | 550606056 |
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