Generating function
$$U_{51}(x, y) = \frac{x y - \sqrt{x^{2} y^{2} + y \left(- 2 x - 4\right) + 1} + 1}{2 y}$$
Explicit formula
$$T_{51}(n, m, k) = \frac{k {\binom{k + m}{n}} {\binom{k + 2 m - n - 1}{m}}}{k + m}$$
| 1 | 1 | 2 | 5 | 14 | 42 | 132 |
| 1 | 1 | 3 | 1 | 35 | 126 | 462 |
| 0 | 0 | 1 | 6 | 3 | 14 | 63 |
| 0 | 0 | 0 | 1 | 1 | 7 | 42 |
| 0 | 0 | 0 | 0 | 1 | 15 | 14 |
| 0 | 0 | 0 | 0 | 0 | 1 | 21 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
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