Generating function
$$U_{1286}(x, y) = \frac{y + 1}{\sqrt{- 4 x \left(y + 1\right)^{2} + 1}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1286}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(n,k + 2 n \right)} {\binom{k + 2 n}{m}}}{k + 2 n}$$
1 | 1 | 0 | 0 | 0 | 0 | 0 |
2 | 6 | 6 | 2 | 0 | 0 | 0 |
6 | 30 | 60 | 60 | 30 | 6 | 0 |
20 | 140 | 420 | 700 | 700 | 420 | 140 |
70 | 630 | 2520 | 5880 | 8820 | 8820 | 5880 |
252 | 2772 | 13860 | 41580 | 83160 | 116424 | 116424 |
924 | 12012 | 72072 | 264264 | 660660 | 1189188 | 1585584 |
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