Generating function
$$U_{981}(x, y) = \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x \left(y + 1\right)}}{2} \right)}}{3} \right)}}{3}\right) \left(y + 1\right)^{2}$$
Explicit formula
$$T_{981}(n, m, k) = \begin{cases}{\binom{2 k + n}{m}}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{2 k + n}{m}} {\binom{- k + 3 n - 1}{n - 1}}}{n} \end{cases} $$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
1 | 3 | 3 | 1 | 0 | 0 | 0 |
-2 | -8 | -12 | -8 | -2 | 0 | 0 |
7 | 35 | 7 | 7 | 35 | 7 | 0 |
-3 | -18 | -45 | -6 | -45 | -18 | -3 |
143 | 1001 | 3003 | 5005 | 5005 | 3003 | 1001 |
-728 | -5824 | -20384 | -40768 | -5096 | -40768 | -20384 |
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