Generating function
$$U_{792}(x, y) = \frac{1 - \sqrt{1 - \frac{y \left(8 - 8 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}\right)}{3 x}}}{2 y}$$
Explicit formula
$$T_{792}(n, m, k) = \frac{k {\binom{k + 2 m - 1}{m}} {\binom{2 k + 2 m + 3 n - 1}{n}}}{k + m + n}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
2 | 4 | 12 | 4 | 14 | 504 | 1848 |
7 | 18 | 66 | 26 | 105 | 4284 | 17556 |
3 | 88 | 364 | 16 | 714 | 3192 | 142296 |
143 | 455 | 204 | 969 | 4655 | 223146 | 10626 |
728 | 2448 | 11628 | 5852 | 297528 | 150696 | 756756 |
3876 | 13566 | 67298 | 3542 | 18837 | 997542 | 52332588 |
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