$$U_{664}(x, y) = \frac{\sqrt{4 x \left(y + 1\right) + 1}}{2} + \frac{1}{2}$$

$$T_{664}(n, m, k) = \begin{cases}{\binom{n}{m}}&\text{if n=0 } ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{n}{m}} {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$