$$U_{647}(x, y) = \frac{- x \sqrt{4 y + 1} - x - \sqrt{- 2 x \sqrt{4 y + 1} - 2 x + 1} + 1}{x^{2} \sqrt{4 y + 1} + x^{2}}$$

$$T_{647}(n, m, k) = \begin{cases}\frac{k {\binom{2 k + 2 n}{n}}}{k + n}&\text{if m==0 } ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{2 k + 2 n}{n}} {\binom{- k + 2 m - n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$