$$U_{816}(x, y) = \frac{- 2 x \sqrt{1 - 4 y} - 4 y - \sqrt{16 y^{2} - 8 y + \sqrt{1 - 4 y} \left(16 x y - 4 x\right) + 1} + 1}{2 x^{2}}$$

$$TA_{984}(n, k) = \begin{cases}{4}^{n} \binom {n+j-1} {n} &\text{if k even, where j =} \frac {k} {2},\\\frac {\binom {n+j} {n} \binom {2n+2j} {n+j}} {\binom {2j} {j}}&\text{if k odd, where j =} \frac {k-1} {2},\end{cases} $$$$T_{816}(n, m, k) = \frac{k \operatorname{TA_{984}}{\left(m,n \right)} {\binom{2 k + 2 n}{n}}}{k + n}$$