Generating function
$$U_{294}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{3 \sqrt{x} \left(1 - y\right)}$$
Explicit formula
$$T_{294}(n, m, k) = \frac{k {\binom{k + m - 1}{m}} {\binom{k + 3 n - 1}{n}}}{k + 2 n}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| 12 | 12 | 12 | 12 | 12 | 12 | 12 |
| 55 | 55 | 55 | 55 | 55 | 55 | 55 |
| 273 | 273 | 273 | 273 | 273 | 273 | 273 |
| 1428 | 1428 | 1428 | 1428 | 1428 | 1428 | 1428 |
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