Generating function
$$U_{518}(x, y) = - \frac{\left(y + 1\right)^{6}}{x - \left(y + 1\right)^{4}}$$
Explicit formula
$$T_{518}(n, m, k) = {\binom{2 k - 4 n}{m}} {\binom{k + n - 1}{n}}$$
| 1 | 2 | 1 | 0 | 0 | 0 | 0 |
| 1 | -2 | 3 | -4 | 5 | -6 | 7 |
| 1 | -6 | 21 | -56 | 126 | -252 | 462 |
| 1 | -1 | 55 | -22 | 715 | -2002 | 5005 |
| 1 | -14 | 105 | -56 | 238 | -8568 | 27132 |
| 1 | -18 | 171 | -114 | 5985 | -26334 | 100947 |
| 1 | -22 | 253 | -2024 | 1265 | -6578 | 29601 |
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