$$U_{547}(x, y) = \frac{y \left(3 x + \frac{8 \sqrt{3} \sin^{3}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y^{\frac{3}{2}}}\right)}{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$

$$T_{547}(n, m, k) = \begin{cases}{\binom{k}{n}}&\text{if m==0} ,\ \\\frac{\left(-1\right)^{m - 1} \left(k - 3 n\right) {\binom{k}{n}} {\binom{- k - 2 m + 3 n - 1}{m - 1}}}{m} \end{cases} $$