Generating function
$$U_{1470}(x, y) = \frac{2 \sqrt{3} \left(y + 1\right)^{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{3 \sqrt{x}}$$
Explicit formula
$$T_{1470}(n, m, k) = \frac{k {\binom{3 k}{m}} {\binom{k + 3 n - 1}{n}}}{k + 2 n}$$
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 3 | 9 | 9 | 3 | 0 | 0 | 0 |
| 12 | 36 | 36 | 12 | 0 | 0 | 0 |
| 55 | 165 | 165 | 55 | 0 | 0 | 0 |
| 273 | 819 | 819 | 273 | 0 | 0 | 0 |
| 1428 | 4284 | 4284 | 1428 | 0 | 0 | 0 |
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