Generating function
$$U_{562}(x, y) = \frac{x}{\left(1 - y\right)^{3}} + \frac{1}{1 - y}$$
Explicit formula
$$T_{562}(n, m, k) = {\binom{k}{n}} {\binom{k + m + 2 n - 1}{m}}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 3 | 6 | 1 | 15 | 21 | 28 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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