$$U_{376}(x, y) = \frac{- 4 x y + x + 1}{\sqrt{1 - 4 y}}$$

$$T_{376}(n, m, k) = \begin{cases}1&\text{if n=0 and m=0} ,\ \\\frac{\left(-1\right)^{n - 1} \cdot 4^{m} k {\binom{- k + n - 1}{n - 1}} {\binom{\frac{k}{2} + m - n - 1}{m}}}{n}&\text{if n>0} ,\ \\\frac{\left(-1\right)^{m - 1} \cdot 4^{m} k {\binom{- \frac{k}{2} + \frac{n}{2} - 1}{m - 1}}}{2 m}&\text{if m>0} \end{cases} $$