Generating function
$$U_{35}(x, y) = \frac{y + 1}{1 - x}$$
Explicit formula
$$T_{35}(n, m, k) = \begin{cases}1&\text{if m=0 and n=0} ,\ \\{\binom{k}{m}} {\binom{k + n - 1}{n}} \end{cases} $$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
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