$$U_{769}(x, y) = \frac{- 2 x \left(4 y + 1\right) - \sqrt{- 4 x \left(4 y + 1\right) + 1} + 1}{2 x^{2} \left(4 y + 1\right)^{\frac{3}{2}}}$$

$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{769}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(m,k + 2 n \right)} {\binom{2 k + 2 n}{n}}}{k + n}$$