Generating function
$$U_{42}(x, y) = \frac{\left(y + 1\right)^{2}}{- x \left(y + 1\right) + 1}$$
Explicit formula
$$T_{42}(n, m, k) = {\binom{2 k + n}{m}} {\binom{k + n - 1}{n}}$$
| 1 | 2 | 1 | 0 | 0 | 0 | 0 |
| 1 | 3 | 3 | 1 | 0 | 0 | 0 |
| 1 | 4 | 6 | 4 | 1 | 0 | 0 |
| 1 | 5 | 1 | 1 | 5 | 1 | 0 |
| 1 | 6 | 15 | 2 | 15 | 6 | 1 |
| 1 | 7 | 21 | 35 | 35 | 21 | 7 |
| 1 | 8 | 28 | 56 | 7 | 56 | 28 |
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