Generating function
$$U_{827}(x, y) = \frac{x y - 1}{x y + x - 1}$$
Explicit formula
$$T_{827}(n, m, k) = {\binom{n - 1}{m}} {\binom{k - m + n - 1}{- m + n}}$$
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 2 | 1 | 0 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 4 | 6 | 4 | 1 | 0 | 0 |
| 1 | 5 | 1 | 1 | 5 | 1 | 0 |
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