Generating function
$$U_{644}(x, y) = \frac{- \sqrt{4 y + 1} - 1}{x \sqrt{4 y + 1} + x - 2}$$
Explicit formula
$$T_{644}(n, m, k) = \begin{cases}{\binom{k + n - 1}{n}}&\text{if m==0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{k + n}{n}} {\binom{- k + 2 m - n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$
| 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 |
| 1 | 6 | 9 | 2 | 0 | 0 | -1 |
| 1 | 7 | 14 | 7 | 0 | 0 | 0 |
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