Generating function
$$U_{268}(x, y) = \frac{x}{2} + \frac{y}{2} + \frac{\sqrt{x^{2} + 2 x + y^{2} + y \left(2 - 2 x\right) + 1}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{268}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} {\binom{k - m - 1}{n}} {\binom{- k + m + n - 1}{m - 1}}}{m} \end{cases} $$
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | -1 | 1 | -1 | 1 | -1 | 1 |
| 0 | 1 | -3 | 6 | -1 | 15 | -21 |
| 0 | -1 | 6 | -2 | 5 | -105 | 196 |
| 0 | 1 | -1 | 5 | -175 | 49 | -1176 |
| 0 | -1 | 15 | -105 | 49 | -1764 | 5292 |
| 0 | 1 | -21 | 196 | -1176 | 5292 | -19404 |
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