Generating function
$$U_{55}(x, y) = y + \frac{1}{\left(1 - x\right)^{2}}$$
Explicit formula
$$T_{55}(n, m, k) = {\binom{k}{m}} {\binom{2 k - 2 m + n - 1}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 3 | 0 | 0 | 0 | 0 | 0 | 0 |
| 4 | 0 | 0 | 0 | 0 | 0 | 0 |
| 5 | 0 | 0 | 0 | 0 | 0 | 0 |
| 6 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 0 | 0 | 0 | 0 | 0 | 0 |
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