Generating function
$$U_{19}(x, y) = - \frac{1}{x + y - 1}$$
Explicit formula
$$T_{19}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{k + m + n - 1}{m}}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 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 |
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