Generating function
$$U_{425}(x, y) = \frac{2 x y - x + \sqrt{x^{2} - 4 x y + 2 x + 1} - 1}{2 y - 2}$$
Explicit formula
$$T_{425}(n, m, k) = \begin{cases}0&\text{if n<2*k or m=0} ,\ \\- \frac{\left(-1\right)^{m - 1} k {\binom{- k + n - 1}{m - 1}} {\binom{k - m - 1}{n}}}{m} \end{cases} $$
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | -1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | -2 | 0 | 0 | 0 | 0 |
| 0 | -1 | 5 | -5 | 0 | 0 | 0 |
| 0 | 1 | -9 | 21 | -14 | 0 | 0 |
| 0 | -1 | 14 | -56 | 84 | -42 | 0 |
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