$$U_{689}(x, y) = \frac{2 \sqrt{3} x \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}} + 1$$

$$T_{689}(n, m, k) = \frac{n {\binom{k}{n}} {\binom{3 m + n - 1}{m}}}{2 m + n}$$