Generating function
$$U_{490}(x, y) = \frac{\sqrt{3} \left(\sqrt{3} x \sqrt{y} - \sqrt{2 \sqrt{3} x \sqrt{y} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)} + \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}} + \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}\right)}{3 \sqrt{y}}$$
Explicit formula
$$T_{490}(n, m, k) = \begin{cases}0&\text{if n<2*k} ,\ \\\frac{2 \left(-1\right)^{n} k {\binom{- 2 k + 2 n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m} k {\binom{2 k - n - 1}{n}} {\binom{- k - 2 m + n - 1}{m - 1}}}{m} \end{cases} $$
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | -1 | -2 | -7 | -3 | -143 | -728 |
| -2 | 4 | 6 | 2 | 84 | 396 | 2002 |
| 5 | -15 | -15 | -5 | -21 | -99 | -5005 |
| -14 | 56 | 28 | 112 | 49 | 2352 | 12012 |
| 42 | -21 | 0 | -21 | -105 | -5292 | -2772 |
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