$$U_{534}(x, y) = \frac{\sqrt{3} \left(1 - \sqrt{1 - 4 y}\right) \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{3 \sqrt{x} y}$$

$$T_{534}(n, m, k) = \frac{k^{2} {\binom{k + 2 m - 1}{m}} {\binom{k + 3 n - 1}{n}}}{\left(k + m\right) \left(k + 2 n\right)}$$