Generating function
$$U_{1297}(x, y) = \sqrt{\frac{2 x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{y^{2}} + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1297}(n, m, k) = \begin{cases}1&\text{if n=0 , m=0 } ,\ \\\frac{2 n \operatorname{Tsqrt}{\left(n,k \right)} {\binom{2 m + 2 n - 1}{m}}}{m + 2 n} \end{cases} $$
Data table
1 0 0 0 0 0 0
2 4 1 28 84 264 858
-2 -8 -28 -96 -330 -1144 -4004
4 24 108 440 1716 6552 24752
-10 -80 -440 -2080 -9100 -38080 -155040
28 280 1820 9800 47600 217056 949620
-84 -1008 -7560 -45696 -244188 -1206576 -5653032
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