Generating function
$$U_{22}(x, y) = \frac{- y - \sqrt{- 4 x + y^{2} - 2 y + 1} + 1}{2 x}$$
Explicit formula
$$T_{22}(n, m, k) = \frac{k {\binom{k + 2 n}{n}} {\binom{k + m + 2 n - 1}{m}}}{k + 2 n}$$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 3 | 6 | 1 | 15 | 21 | 28 |
| 2 | 1 | 3 | 7 | 14 | 252 | 42 |
| 5 | 35 | 14 | 42 | 105 | 231 | 462 |
| 14 | 126 | 63 | 231 | 693 | 18018 | 42042 |
| 42 | 462 | 2772 | 12012 | 42042 | 126126 | 336336 |
| 132 | 1716 | 12012 | 6006 | 24024 | 816816 | 2450448 |
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