Generating function
$$U_{312}(x, y) = \frac{- x y^{2} + 2 x y - x - 1}{y - 1}$$
Explicit formula
$$T_{312}(n, m, k) = {\binom{k}{n}} {\binom{k + m - 2 n - 1}{m}}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | -1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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