Generating function
$$U_{44}(x, y) = \frac{1}{\left(1 - x\right) \left(1 - y\right)}$$
Explicit formula
$$T_{44}(n, m, k) = {\binom{k + m - 1}{m}} {\binom{k + n - 1}{n}}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
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