Generating function
$$U_{979}(x, y) = \frac{1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3}}{y + 1}$$
Explicit formula
$$T_{979}(n, m, k) = \begin{cases}{\binom{- k + n}{m}}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + n}{m}} {\binom{- k + 3 n - 1}{n - 1}}}{n} \end{cases} $$
1 | -1 | 1 | -1 | 1 | -1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
-2 | -2 | 0 | 0 | 0 | 0 | 0 |
7 | 14 | 7 | 0 | 0 | 0 | 0 |
-3 | -9 | -9 | -3 | 0 | 0 | 0 |
143 | 572 | 858 | 572 | 143 | 0 | 0 |
-728 | -364 | -728 | -728 | -364 | -728 | 0 |
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