$$U_{1027}(x, y) = \frac{\left(x + 1\right)^{3} \left(- 2 y - \sqrt{1 - 4 y} + 1\right)^{2}}{4 y^{4}}$$

$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{1027}(n, m, k) = k \operatorname{Tsqrt_{2}}{\left(n,k \right)} {\binom{3 k + 3 n}{m}}$$