Generating function
$$U_{31}(x, y) = \frac{y}{\left(1 - x\right)^{3}} + \frac{1}{1 - x}$$
Explicit formula
$$T_{31}(n, m, k) = {\binom{k}{m}} {\binom{k + 2 m + n - 1}{n}}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 3 | 0 | 0 | 0 | 0 | 0 |
| 1 | 6 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 15 | 0 | 0 | 0 | 0 | 0 |
| 1 | 21 | 0 | 0 | 0 | 0 | 0 |
| 1 | 28 | 0 | 0 | 0 | 0 | 0 |
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