Generating function
$$U_{717}(x, y) = - \frac{\sqrt{4 y + 1}}{x \left(4 y + 1\right) - 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{717}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(m,k + 2 n \right)} {\binom{k + n}{n}}}{k + n}$$
1 | 2 | -2 | 4 | -10 | 28 | -84 |
1 | 6 | 6 | -4 | 6 | -12 | 28 |
1 | 10 | 30 | 2 | -10 | 12 | -20 |
1 | 14 | 70 | 140 | 7 | -28 | 28 |
1 | 18 | 126 | 420 | 630 | 252 | -84 |
1 | 22 | 198 | 924 | 2310 | 2772 | 924 |
1 | 26 | 286 | 1716 | 6006 | 12012 | 12012 |
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