$$U_{924}(x, y) = \left(x + 1\right) \left(2 y + \sqrt{4 y^{2} + 1}\right)$$

$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{924}(n, m, k) = \operatorname{Tsqrt_{2}}{\left(m,k \right)} {\binom{k}{n}}$$