Generating function
$$U_{1040}(x, y) = \frac{y + 1}{\left(1 - x\right)^{3}}$$
Explicit formula
$$T_{1040}(n, m, k) = {\binom{k}{m}} {\binom{3 k + n - 1}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 3 | 3 | 0 | 0 | 0 | 0 | 0 |
| 6 | 6 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 15 | 15 | 0 | 0 | 0 | 0 | 0 |
| 21 | 21 | 0 | 0 | 0 | 0 | 0 |
| 28 | 28 | 0 | 0 | 0 | 0 | 0 |
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