Generating function
$$U_{1146}(x, y) = \frac{1}{\left(- \frac{x}{1 - y} + 1\right)^{3}}$$
Explicit formula
$$T_{1146}(n, m, k) = {\binom{3 k + n - 1}{n}} {\binom{m + n - 1}{m}}$$
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| 6 | 12 | 18 | 24 | 3 | 36 | 42 |
| 1 | 3 | 6 | 1 | 15 | 21 | 28 |
| 15 | 6 | 15 | 3 | 525 | 84 | 126 |
| 21 | 105 | 315 | 735 | 147 | 2646 | 441 |
| 28 | 168 | 588 | 1568 | 3528 | 7056 | 12936 |
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