Generating function
$$U_{797}(x, y) = \frac{\left(1 - y\right) \left(2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}\right)}{3 x}$$
Explicit formula
$$T_{797}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{m + n - 1}{m}}}{k + n}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 2 | 2 | 2 | 2 | 2 | 2 |
7 | 14 | 21 | 28 | 35 | 42 | 49 |
3 | 9 | 18 | 3 | 45 | 63 | 84 |
143 | 572 | 143 | 286 | 5005 | 8008 | 12012 |
728 | 364 | 1092 | 2548 | 5096 | 91728 | 15288 |
3876 | 23256 | 81396 | 217056 | 488376 | 976752 | 1790712 |
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