Generating function
$$U_{1417}(x, y) = \frac{1}{\left(1 - x\right)^{3} \left(- \frac{y}{1 - x} + 1\right)}$$
Explicit formula
$$T_{1417}(n, m, k) = {\binom{k + m - 1}{m}} {\binom{3 k + m + n - 1}{n}}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 6 | 1 | 15 | 21 | 28 | 36 | 45 |
| 1 | 2 | 35 | 56 | 84 | 12 | 165 |
| 15 | 35 | 7 | 126 | 21 | 33 | 495 |
| 21 | 56 | 126 | 252 | 462 | 792 | 1287 |
| 28 | 84 | 21 | 462 | 924 | 1716 | 3003 |
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