Generating function
$$U_{530}(x, y) = - \frac{1}{\left(1 - y\right)^{6} \left(x - \frac{1}{\left(1 - y\right)^{4}}\right)}$$
Explicit formula
$$T_{530}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{2 k + m - 4 n - 1}{m}}$$
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 1 | -2 | 1 | 0 | 0 | 0 | 0 |
| 1 | -6 | 15 | -2 | 15 | -6 | 1 |
| 1 | -1 | 45 | -12 | 21 | -252 | 21 |
| 1 | -14 | 91 | -364 | 1001 | -2002 | 3003 |
| 1 | -18 | 153 | -816 | 306 | -8568 | 18564 |
| 1 | -22 | 231 | -154 | 7315 | -26334 | 74613 |
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