Generating function
$$U_{618}(x, y) = - \frac{\sqrt{4 x + \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right)^{2}}}{2} - \frac{2 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3} + \frac{1}{2}$$
Explicit formula
$$T_{618}(n, m, k) = \begin{cases}0&\text{if n < k} ,\ \\- \frac{k {\binom{k - n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\- \frac{\left(-1\right)^{m - 1} k \left(k - 2 n\right) {\binom{k - n - 1}{n - 1}} {\binom{- k + 3 m + 2 n - 1}{m - 1}}}{m n} \end{cases} $$
0 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 1 | -3 | 12 | -55 | 273 | -1428 |
1 | -3 | 12 | -55 | 273 | -1428 | 7752 |
-2 | 1 | -5 | 26 | -14 | 7752 | -4389 |
5 | -35 | 21 | -1225 | 714 | -41895 | 24794 |
-14 | 126 | -882 | 5712 | -3591 | 223146 | -138138 |
42 | -462 | 3696 | -26334 | 17787 | -116886 | 756756 |
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