$$U_{777}(x, y) = \frac{4 \sin^{2}{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}{3 x \left(1 - y\right)}$$

$$T_{777}(n, m, k) = \frac{k {\binom{k + m - 1}{m}} {\binom{2 k + 3 n - 1}{n}}}{k + n}$$