Generating function
$$U_{1296}(x, y) = \sqrt{\frac{x \left(1 - \sqrt{1 - 4 y}\right)^{3}}{2 y^{3}} + 1}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1296}(n, m, k) = \frac{3 n \operatorname{Tsqrt}{\left(n,k \right)} {\binom{2 m + 3 n - 1}{m}}}{m + 3 n}$$
nan | 0 | 0 | 0 | 0 | 0 | 0 |
2 | 6 | 18 | 56 | 18 | 594 | 2002 |
-2 | -12 | -54 | -220 | -858 | -3276 | -12376 |
4 | 36 | 216 | 1092 | 5040 | 22032 | 93024 |
-10 | -120 | -900 | -5440 | -29070 | -143640 | -672980 |
28 | 420 | 3780 | 26600 | 161700 | 892584 | 4604600 |
-84 | -1512 | -15876 | -127512 | -869400 | -5307120 | -29926260 |
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