Generating function
$$U_{107}(x, y) = \frac{x - 1}{x + y - 1}$$
Explicit formula
$$T_{107}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{k {\binom{m + n}{m}} {\binom{k + m - 1}{k}}}{m + n} \end{cases} $$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| 0 | 1 | 3 | 6 | 1 | 15 | 21 |
| 0 | 1 | 4 | 1 | 2 | 35 | 56 |
| 0 | 1 | 5 | 15 | 35 | 7 | 126 |
| 0 | 1 | 6 | 21 | 56 | 126 | 252 |
| 0 | 1 | 7 | 28 | 84 | 21 | 462 |
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