$$U_{765}(x, y) = \frac{\left(1 - \sqrt{- 4 x \left(1 - \frac{4 \sin^{2}{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right) + 1}\right)^{3}}{8 x^{3} \left(1 - \frac{4 \sin^{2}{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{- y}}{2} \right)}}{3} \right)}}{3}\right)^{2}}$$

$$TLeftA_{271825}(n, k) = \begin{cases}1&\text{if n = 0},\\\frac {k {(-1)}^{n-1}} {n} {\binom{3n-k-1}{n-1}} &\text{if n > 0},\\\end{cases} $$$$T_{765}(n, m, k) = \frac{3 k \operatorname{TLeftA_{271825}}{\left(m,k + n \right)} {\binom{3 k + 2 n}{n}}}{3 k + 2 n}$$