Generating function
$$U_{706}(x, y) = \sqrt{4 x + 1} \left(y + 1\right)^{2}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{706}(n, m, k) = \operatorname{Tsqrt}{\left(n,k \right)} {\binom{2 k}{m}}$$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
2 | 4 | 2 | 0 | 0 | 0 | 0 |
-2 | -4 | -2 | 0 | 0 | 0 | 0 |
4 | 8 | 4 | 0 | 0 | 0 | 0 |
-10 | -20 | -10 | 0 | 0 | 0 | 0 |
28 | 56 | 28 | 0 | 0 | 0 | 0 |
-84 | -168 | -84 | 0 | 0 | 0 | 0 |
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