Generating function
$$U_{476}(x, y) = \frac{\left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right)^{2} - \sqrt{4 x \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right) + \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right)^{4}}}{2 - \frac{8 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}}$$
Explicit formula
$$T_{476}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{k {\binom{k - n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\- \frac{\left(-1\right)^{m - 1} k \left(k - 3 n\right) {\binom{k - n - 1}{n - 1}} {\binom{- k + 3 m + 3 n - 1}{m - 1}}}{m n}&\text{if m>0 and n>0} \end{cases} $$
0 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 2 | -7 | 3 | -143 | 728 | -3876 |
1 | -5 | 25 | -13 | 7 | -3876 | 21945 |
-2 | 16 | -104 | 64 | -3876 | 23408 | -14168 |
5 | -55 | 44 | -3135 | 21175 | -13915 | 9009 |
-14 | 196 | -1862 | 15092 | -1127 | 80262 | -5550426 |
42 | -714 | 7854 | -714 | 584766 | -4493202 | 33112464 |
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