Generating function
$$U_{794}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3 \sqrt{x \left(y + 1\right)}}$$
Explicit formula
$$T_{794}(n, m, k) = \frac{k {\binom{n}{m}} {\binom{k + 3 n - 1}{n}}}{k + 2 n}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 0 |
3 | 6 | 3 | 0 | 0 | 0 | 0 |
12 | 36 | 36 | 12 | 0 | 0 | 0 |
55 | 22 | 33 | 22 | 55 | 0 | 0 |
273 | 1365 | 273 | 273 | 1365 | 273 | 0 |
1428 | 8568 | 2142 | 2856 | 2142 | 8568 | 1428 |
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