Generating function
$$U_{875}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{\sqrt{1 - 4 y}}}}{2} \right)}}{3} \right)}}{3 \sqrt{\frac{x}{\sqrt{1 - 4 y}}} \left(1 - 4 y\right)}$$
Explicit formula
$$TA_{984}(n, k) = \begin{cases}{4}^{n} \binom {n+j-1} {n} &\text{if k even, where j =} \frac {k} {2},\\\frac {\binom {n+j} {n} \binom {2n+2j} {n+j}} {\binom {2j} {j}}&\text{if k odd, where j =} \frac {k-1} {2},\end{cases} $$$$T_{875}(n, m, k) = \frac{k \operatorname{TA_{984}}{\left(m,2 k + n \right)} {\binom{k + 3 n - 1}{n}}}{k + 2 n}$$
1 | 4 | 16 | 64 | 256 | 1024 | 4096 |
1 | 6 | 30 | 140 | 630 | 2772 | 12012 |
3 | 24 | 144 | 768 | 3840 | 18432 | 86016 |
12 | 120 | 840 | 5040 | 27720 | 144144 | 720720 |
55 | 660 | 5280 | 35200 | 211200 | 1182720 | 6307840 |
273 | 3822 | 34398 | 252252 | 1639638 | 9837828 | 55747692 |
1428 | 22848 | 228480 | 1827840 | 12794880 | 81887232 | 491323392 |
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