Generating function
$$U_{18}(x, y) = \frac{1 - \sqrt{y \left(- 4 x - 4\right) + 1}}{2 y}$$
Explicit formula
$$T_{18}(n, m, k) = \frac{k {\binom{k + m}{n}} {\binom{k + 2 m - 1}{m}}}{k + m}$$
| 1 | 1 | 2 | 5 | 14 | 42 | 132 |
| 1 | 2 | 6 | 2 | 7 | 252 | 924 |
| 0 | 1 | 6 | 3 | 14 | 63 | 2772 |
| 0 | 0 | 2 | 2 | 14 | 84 | 462 |
| 0 | 0 | 0 | 5 | 7 | 63 | 462 |
| 0 | 0 | 0 | 0 | 14 | 252 | 2772 |
| 0 | 0 | 0 | 0 | 0 | 42 | 924 |
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