Generating function
$$U_{258}(x, y) = \frac{2 x y - y - \sqrt{- 4 x y + y^{2} + 2 y + 1} - 1}{2 x - 2}$$
Explicit formula
$$T_{258}(n, m, k) = \begin{cases}{\binom{k}{m}}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{m - n - 1} k {\binom{- k + m - 1}{n - 1}} {\binom{- k + m + n}{m}}}{n} \end{cases} $$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | -1 | 1 | -1 | 1 | -1 | 1 |
| 1 | -1 | 0 | 2 | -5 | 9 | -14 |
| 1 | -1 | 0 | 0 | 5 | -21 | 56 |
| 1 | -1 | 0 | 0 | 0 | 14 | -84 |
| 1 | -1 | 0 | 0 | 0 | 0 | 42 |
| 1 | -1 | 0 | 0 | 0 | 0 | 0 |
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