Generating function
$$U_{308}(x, y) = - \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{y^{2} \left(4 x - \frac{2 - 2 \sqrt{1 - 4 y}}{y}\right)}$$
Explicit formula
$$T_{308}(n, m, k) = \begin{cases}{\binom{k + n - 1}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - n\right) {\binom{k + n - 1}{n}} {\binom{- k - m + n - 1}{m - 1}}}{m} \end{cases} $$
| 1 | 1 | 2 | 5 | 14 | 42 | 132 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | -1 | -1 | -2 | -5 | -14 | -42 |
| 1 | -2 | -1 | -2 | -5 | -14 | -42 |
| 1 | -3 | 0 | -1 | -3 | -9 | -28 |
| 1 | -4 | 2 | 0 | -1 | -4 | -14 |
| 1 | -5 | 5 | 0 | 0 | -1 | -5 |
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