$$U_{1377}(x, y) = \frac{1}{\sqrt{- \frac{4 x}{1 - y} + 1}}$$

$$T_{1377}(n, m, k) = \begin{cases}1&\text{if n=0 , m=0 , k=0} ,\ \\4^{n} {\binom{\frac{k}{2} + n - 1}{n}} {\binom{m + n - 1}{m}}&\text{if k even} ,\ \\\frac{{\binom{\frac{k}{2} + n - \frac{1}{2}}{n}} {\binom{k + 2 n - 1}{\frac{k}{2} + n - \frac{1}{2}}} {\binom{m + n - 1}{m}}}{{\binom{k - 1}{\frac{k}{2} - \frac{1}{2}}}}&\text{if k odd} \end{cases} $$