Generating function
$$U_{222}(x, y) = \frac{- 2 x - \sqrt{1 - 4 x} + 1}{2 x^{2} \left(1 - y\right)}$$
Explicit formula
$$T_{222}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{k + m - 1}{m}}}{k + n}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| 14 | 14 | 14 | 14 | 14 | 14 | 14 |
| 42 | 42 | 42 | 42 | 42 | 42 | 42 |
| 132 | 132 | 132 | 132 | 132 | 132 | 132 |
| 429 | 429 | 429 | 429 | 429 | 429 | 429 |
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