$$U_{505}(x, y) = \frac{\sqrt{4 x + 1} + 1}{2 \left(1 - y\right)^{2}}$$

$$T_{505}(n, m, k) = \begin{cases}{\binom{2 k + m - 1}{m}}&\text{if n==0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + 2 n - 1}{n - 1}} {\binom{2 k + m - 1}{m}}}{n}&\text{if n>0} \end{cases} $$