Generating function
$$U_{974}(x, y) = \frac{1}{\left(- x \left(4 y + 1\right)^{\frac{3}{2}} + 1\right)^{2}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{974}(n, m, k) = \operatorname{Tsqrt}{\left(m,3 n \right)} {\binom{2 k + n - 1}{n}}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 12 | 12 | -8 | 12 | -24 | 56 |
3 | 36 | 144 | 192 | 0 | 0 | 0 |
4 | 72 | 504 | 1680 | 2520 | 1008 | -336 |
5 | 120 | 1200 | 6400 | 19200 | 30720 | 2048 |
6 | 180 | 2340 | 17160 | 77220 | 216216 | 360360 |
7 | 252 | 4032 | 37632 | 225792 | 903168 | 2408448 |
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