Generating function
$$U_{1286}(x, y) = \frac{y + 1}{\sqrt{- 4 x \left(y + 1\right)^{2} + 1}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1286}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(n,k + 2 n \right)} {\binom{k + 2 n}{m}}}{k + 2 n}$$
Data table
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
Export
expand_less