Generating function
$$U_{791}(x, y) = \frac{3 x \left(- \sqrt{1 - \frac{y \left(8 - 8 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)}{3 x}} + 1 - \frac{y \left(4 - 4 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)}{3 x}\right)}{y^{2} \left(4 - 4 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)}$$
Explicit formula
$$T_{791}(n, m, k) = \frac{k {\binom{2 k + 2 m}{m}} {\binom{2 k + 2 m + 3 n - 1}{n}}}{k + m + n}$$
1 | 2 | 5 | 14 | 42 | 132 | 429 |
2 | 8 | 3 | 112 | 42 | 1584 | 6006 |
7 | 36 | 165 | 728 | 315 | 13464 | 57057 |
3 | 176 | 91 | 448 | 2142 | 10032 | 462462 |
143 | 91 | 51 | 27132 | 13965 | 701316 | 345345 |
728 | 4896 | 2907 | 163856 | 892584 | 473616 | 2459457 |
3876 | 27132 | 168245 | 99176 | 56511 | 3135132 | 170080911 |
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