$$U_{651}(x, y) = \frac{2 - 2 \sqrt{- \frac{x \left(\sqrt{4 y + 1} + 1\right)^{3}}{2} + 1}}{x \left(\sqrt{4 y + 1} + 1\right)^{2}}$$

$$T_{651}(n, m, k) = \begin{cases}1&\text{if n=0, m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + 2 m - 3 n - 1}{m - 1}}}{m}&\text{if n=0, m>0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k - n - 1}{n - 1}}}{n}&\text{if m=0, n>0} ,\ \\\frac{\left(-1\right)^{m + n - 2} k \left(k + 3 n\right) {\binom{- k - n - 1}{n - 1}} {\binom{- k + 2 m - 3 n - 1}{m - 1}}}{m n}&\text{if n>0,m>0} \end{cases} $$