$$U_{303}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y} \left(1 - x\right)^{2}}$$

$$T_{303}(n, m, k) = \frac{k {\binom{k + 3 m - 1}{m}} {\binom{2 k + n - 1}{n}}}{k + 2 m}$$