Generating function
$$U_{1198}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3} \sqrt{4 x + 1}}{8 y^{3}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{1198}(n, m, k) = \frac{3 k \operatorname{Tsqrt}{\left(n,k \right)} {\binom{3 k + 2 m - 1}{m}}}{k + m}$$
Data table
3 6 15 42 126 396 1287
6 12 3 84 252 792 2574
-6 -12 -30 -84 -252 -792 -2574
12 24 60 168 504 1584 5148
-30 -60 -150 -420 -1260 -3960 -12870
84 168 420 1176 3528 11088 36036
-252 -504 -1260 -3528 -10584 -33264 -108108
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