$$U_{783}(x, y) = \frac{\left(- 4 y - 2 \sqrt{1 - 4 y} + 2\right) \sin^{2}{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{3 x y^{2}}$$

$$T_{783}(n, m, k) = \frac{k^{2} {\binom{2 k + 2 m}{m}} {\binom{2 k + 3 n - 1}{n}}}{\left(k + m\right) \left(k + n\right)}$$