Generating function
$$U_{169}(x, y) = \frac{x}{2} + \frac{\left(x + 1\right) \sqrt{4 y + 1}}{2} + \frac{1}{2}$$
Explicit formula
$$T_{169}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{k}{n}} {\binom{- k + 2 m - 1}{m - 1}}}{m} \end{cases} $$
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 1 | 1 | -1 | 2 | -5 | 14 | -42 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
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