$$U_{544}(x, y) = \frac{4 \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{x} \sqrt{y}}$$

$$T_{544}(n, m, k) = \frac{k^{2} {\binom{k + 3 m - 1}{m}} {\binom{k + 3 n - 1}{n}}}{\left(k + 2 m\right) \left(k + 2 n\right)}$$