Generating function
$$U_{1297}(x, y) = \sqrt{\frac{2 x \left(- 2 y - \sqrt{1 - 4 y} + 1\right)}{y^{2}} + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1297}(n, m, k) = \begin{cases}1&\text{if n=0 , m=0 } ,\ \\\frac{2 n \operatorname{Tsqrt}{\left(n,k \right)} {\binom{2 m + 2 n - 1}{m}}}{m + 2 n} \end{cases} $$
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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