Generating function
$$U_{45}(x, y) = \frac{x y - \sqrt{x^{2} y^{2} - 2 x y - 4 x + 1} + 1}{2 x}$$
Explicit formula
$$T_{45}(n, m, k) = \frac{k {\binom{k + n}{m}} {\binom{k - m + 2 n - 1}{n}}}{k + n}$$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 2 | 3 | 1 | 0 | 0 | 0 | 0 |
| 5 | 1 | 6 | 1 | 0 | 0 | 0 |
| 14 | 35 | 3 | 1 | 1 | 0 | 0 |
| 42 | 126 | 14 | 7 | 15 | 1 | 0 |
| 132 | 462 | 63 | 42 | 14 | 21 | 1 |
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