Generating function
$$U_{658}(x, y) = \frac{\frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3} - 1}{x \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right)^{2} - 1}$$
Explicit formula
$$T_{658}(n, m, k) = \begin{cases}{\binom{k + n - 1}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k + 2 n\right) {\binom{k + n - 1}{n}} {\binom{- k + 3 m - 2 n - 1}{m - 1}}}{m} \end{cases} $$
1 | 1 | -2 | 7 | -3 | 143 | -728 |
1 | 3 | -3 | 1 | -42 | 198 | -1001 |
1 | 5 | 0 | 5 | -25 | 126 | -66 |
1 | 7 | 7 | 0 | -7 | 49 | -294 |
1 | 9 | 18 | 3 | 0 | 9 | -84 |
1 | 11 | 33 | 22 | 0 | 0 | -11 |
1 | 13 | 52 | 65 | 13 | 0 | 0 |
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