Generating function
$$U_{831}(x, y) = \frac{1}{\left(1 - y\right)^{3} \left(- \frac{x}{1 - y} + 1\right)}$$
Explicit formula
$$T_{831}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{3 k + m + n - 1}{m}}$$
| 1 | 3 | 6 | 1 | 15 | 21 | 28 |
| 1 | 4 | 1 | 2 | 35 | 56 | 84 |
| 1 | 5 | 15 | 35 | 7 | 126 | 21 |
| 1 | 6 | 21 | 56 | 126 | 252 | 462 |
| 1 | 7 | 28 | 84 | 21 | 462 | 924 |
| 1 | 8 | 36 | 12 | 33 | 792 | 1716 |
| 1 | 9 | 45 | 165 | 495 | 1287 | 3003 |
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