$$U_{1477}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{\left(1 - y\right)^{3}}}}{2} \right)}}{3} \right)}}{3 \sqrt{\frac{x}{1 - y}} \left(1 - y\right)}$$

$$T_{1477}(n, m, k) = \frac{k {\binom{k + 3 n - 1}{n}} {\binom{3 k + m + 3 n - 1}{m}}}{k + 2 n}$$