Generating function
$$U_{1434}(x, y) = \frac{\left(y + 1\right)^{3}}{- x \left(y + 1\right)^{3} + 1}$$
Explicit formula
$$T_{1434}(n, m, k) = {\binom{3 k + 3 n}{m}} {\binom{k + n - 1}{n}}$$
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 6 | 15 | 2 | 15 | 6 | 1 |
| 1 | 9 | 36 | 84 | 126 | 126 | 84 |
| 1 | 12 | 66 | 22 | 495 | 792 | 924 |
| 1 | 15 | 105 | 455 | 1365 | 3003 | 5005 |
| 1 | 18 | 153 | 816 | 306 | 8568 | 18564 |
| 1 | 21 | 21 | 133 | 5985 | 20349 | 54264 |
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