Generating function
$$U_{339}(x, y) = \frac{\left(x + y + 1\right)^{2}}{y + 1}$$
Explicit formula
$$T_{339}(n, m, k) = {\binom{2 k}{n}} {\binom{k - n}{m}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | -1 | 1 | -1 | 1 | -1 | 1 |
| 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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