Generating function
$$U_{52}(x, y) = \frac{- x + y + 1}{\left(1 - x\right)^{2}}$$
Explicit formula
$$T_{52}(n, m, k) = {\binom{k}{m}} {\binom{k + m + n - 1}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 2 | 0 | 0 | 0 | 0 | 0 |
| 1 | 3 | 0 | 0 | 0 | 0 | 0 |
| 1 | 4 | 0 | 0 | 0 | 0 | 0 |
| 1 | 5 | 0 | 0 | 0 | 0 | 0 |
| 1 | 6 | 0 | 0 | 0 | 0 | 0 |
| 1 | 7 | 0 | 0 | 0 | 0 | 0 |
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