$$U_{645}(x, y) = \frac{1 - \sqrt{- 4 x y - 2 x \sqrt{4 y + 1} - 2 x + 1}}{x \sqrt{4 y + 1} + x}$$

$$T_{645}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 n - 1}{n}}}{k + n}&\text{if m==0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{k + 2 n}{n}} {\binom{- k + 2 m - 2 n - 1}{m - 1}}}{m}&\text{if m>0} \end{cases} $$