Generating function
$$U_{1360}(x, y) = \left(y + 1\right)^{3} \sqrt{4 x \left(y + 1\right)^{2} + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1360}(n, m, k) = \operatorname{Tsqrt}{\left(n,k \right)} {\binom{3 k + 2 n}{m}}$$
1 | 3 | 3 | 1 | 0 | 0 | 0 |
2 | 1 | 2 | 2 | 1 | 2 | 0 |
-2 | -14 | -42 | -70 | -70 | -42 | -14 |
4 | 36 | 144 | 336 | 504 | 504 | 336 |
-10 | -110 | -550 | -1650 | -3300 | -4620 | -4620 |
28 | 364 | 2184 | 8008 | 20020 | 36036 | 48048 |
-84 | -1260 | -8820 | -38220 | -114660 | -252252 | -420420 |
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