Generating function
$$U_{519}(x, y) = \frac{x + \left(y + 1\right)^{6}}{\left(y + 1\right)^{4}}$$
Explicit formula
$$T_{519}(n, m, k) = {\binom{k}{n}} {\binom{2 k - 6 n}{m}}$$
| 1 | 2 | 1 | 0 | 0 | 0 | 0 |
| 1 | -4 | 1 | -2 | 35 | -56 | 84 |
| 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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