Generating function
$$U_{1052}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right) \left(y + 1\right)^{3}}{2 x}$$
Explicit formula
$$T_{1052}(n, m, k) = \frac{k {\binom{3 k}{m}} {\binom{k + 2 n - 1}{n}}}{k + n}$$
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 2 | 6 | 6 | 2 | 0 | 0 | 0 |
| 5 | 15 | 15 | 5 | 0 | 0 | 0 |
| 14 | 42 | 42 | 14 | 0 | 0 | 0 |
| 42 | 126 | 126 | 42 | 0 | 0 | 0 |
| 132 | 396 | 396 | 132 | 0 | 0 | 0 |
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