Generating function
$$U_{512}(x, y) = - \frac{\left(y + 1\right)^{3}}{x - \left(y + 1\right)^{2}}$$
Explicit formula
$$T_{512}(n, m, k) = {\binom{k - 2 n}{m}} {\binom{k + n - 1}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | -1 | 1 | -1 | 1 | -1 | 1 |
| 1 | -3 | 6 | -1 | 15 | -21 | 28 |
| 1 | -5 | 15 | -35 | 7 | -126 | 21 |
| 1 | -7 | 28 | -84 | 21 | -462 | 924 |
| 1 | -9 | 45 | -165 | 495 | -1287 | 3003 |
| 1 | -11 | 66 | -286 | 1001 | -3003 | 8008 |
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