Generating function
$$U_{774}(x, y) = \frac{\left(y + 1\right)^{3}}{\left(- x + y + 1\right)^{2}}$$
Explicit formula
$$T_{774}(n, m, k) = {\binom{k - n}{m}} {\binom{2 k + n - 1}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 | 0 | 0 | 0 |
| 3 | -3 | 3 | -3 | 3 | -3 | 3 |
| 4 | -8 | 12 | -16 | 2 | -24 | 28 |
| 5 | -15 | 3 | -5 | 75 | -105 | 14 |
| 6 | -24 | 6 | -12 | 21 | -336 | 504 |
| 7 | -35 | 105 | -245 | 49 | -882 | 147 |
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