Generating function
$$U_{84}(x, y) = \frac{- \sqrt{4 x + 1} - 1}{y \left(\sqrt{4 x + 1} + 1\right) - 2}$$
Explicit formula
$$T_{84}(n, m, k) = \begin{cases}{\binom{k + m - 1}{m}}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} \left(k + m\right) {\binom{k + m - 1}{m}} {\binom{- k - m + 2 n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| -1 | -1 | 0 | 2 | 5 | 9 | 14 |
| 2 | 2 | 1 | 0 | 0 | 2 | 7 |
| -5 | -5 | -3 | -1 | 0 | 0 | 0 |
| 14 | 14 | 9 | 4 | 1 | 0 | 0 |
| -42 | -42 | -28 | -14 | -5 | -1 | 0 |
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