Generating function
$$U_{860}(x, y) = \frac{2 \sqrt{3} \left(y + 1\right)^{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3 \sqrt{x \left(y + 1\right)}}$$
Explicit formula
$$T_{860}(n, m, k) = \frac{k {\binom{3 k + n}{m}} {\binom{k + 3 n - 1}{n}}}{k + 2 n}$$
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 4 | 6 | 4 | 1 | 0 | 0 |
| 3 | 15 | 3 | 3 | 15 | 3 | 0 |
| 12 | 72 | 18 | 24 | 18 | 72 | 12 |
| 55 | 385 | 1155 | 1925 | 1925 | 1155 | 385 |
| 273 | 2184 | 7644 | 15288 | 1911 | 15288 | 7644 |
| 1428 | 12852 | 51408 | 119952 | 179928 | 179928 | 119952 |
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