Generating function
$$U_{359}(x, y) = \frac{- x - 2 y - \sqrt{x^{2} - 2 x + y \left(4 x - 4\right) + 1} + 1}{2 y^{2}}$$
Explicit formula
$$T_{359}(n, m, k) = \frac{k {\binom{2 k + 2 m}{m}} {\binom{k + m + n - 1}{n}}}{k + m}$$
| 1 | 2 | 5 | 14 | 42 | 132 | 429 |
| 1 | 4 | 15 | 56 | 21 | 792 | 3003 |
| 1 | 6 | 3 | 14 | 63 | 2772 | 12012 |
| 1 | 8 | 5 | 28 | 147 | 7392 | 36036 |
| 1 | 1 | 75 | 49 | 294 | 16632 | 9009 |
| 1 | 12 | 105 | 784 | 5292 | 33264 | 198198 |
| 1 | 14 | 14 | 1176 | 882 | 60984 | 396396 |
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