Generating function
$$U_{219}(x, y) = \frac{\left(y + 1\right) \left(- 2 x - \sqrt{1 - 4 x} + 1\right)}{2 x^{2}}$$
Explicit formula
$$T_{219}(n, m, k) = \frac{k {\binom{k}{m}} {\binom{2 k + 2 n}{n}}}{k + n}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 2 | 2 | 0 | 0 | 0 | 0 | 0 |
| 5 | 5 | 0 | 0 | 0 | 0 | 0 |
| 14 | 14 | 0 | 0 | 0 | 0 | 0 |
| 42 | 42 | 0 | 0 | 0 | 0 | 0 |
| 132 | 132 | 0 | 0 | 0 | 0 | 0 |
| 429 | 429 | 0 | 0 | 0 | 0 | 0 |
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