Generating function
$$U_{1034}(x, y) = \frac{\left(y + 1\right)^{3}}{\left(1 - x\right)^{2}}$$
Explicit formula
$$T_{1034}(n, m, k) = {\binom{3 k}{m}} {\binom{2 k + n - 1}{n}}$$
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 2 | 6 | 6 | 2 | 0 | 0 | 0 |
| 3 | 9 | 9 | 3 | 0 | 0 | 0 |
| 4 | 12 | 12 | 4 | 0 | 0 | 0 |
| 5 | 15 | 15 | 5 | 0 | 0 | 0 |
| 6 | 18 | 18 | 6 | 0 | 0 | 0 |
| 7 | 21 | 21 | 7 | 0 | 0 | 0 |
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