$$U_{1077}(x, y) = 2 x \left(y + 1\right)^{3} + \left(y + 1\right)^{2} \sqrt{4 x^{2} \left(y + 1\right)^{2} + 1}$$

$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{1077}(n, m, k) = k \operatorname{Tsqrt_{2}}{\left(n,k \right)} {\binom{2 k + n}{m}}$$