Generating function
$$U_{171}(x, y) = \frac{1}{x^{2} - 2 x + y \left(x - 1\right) + 1}$$
Explicit formula
$$T_{171}(n, m, k) = {\binom{k + m - 1}{m}} {\binom{2 k + m + n - 1}{n}}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 3 | 6 | 1 | 15 | 21 | 28 | 36 |
| 4 | 1 | 2 | 35 | 56 | 84 | 12 |
| 5 | 15 | 35 | 7 | 126 | 21 | 33 |
| 6 | 21 | 56 | 126 | 252 | 462 | 792 |
| 7 | 28 | 84 | 21 | 462 | 924 | 1716 |
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