Generating function
$$U_{374}(x, y) = - \frac{\left(y + 1\right)^{2}}{x - y - 1}$$
Explicit formula
$$T_{374}(n, m, k) = {\binom{k - n}{m}} {\binom{k + n - 1}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | -1 | 1 | -1 | 1 | -1 | 1 |
| 1 | -2 | 3 | -4 | 5 | -6 | 7 |
| 1 | -3 | 6 | -1 | 15 | -21 | 28 |
| 1 | -4 | 1 | -2 | 35 | -56 | 84 |
| 1 | -5 | 15 | -35 | 7 | -126 | 21 |
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