Generating function
$$U_{652}(x, y) = \frac{\sqrt{3} \left(\sqrt{4 x + 1} + 1\right) \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}}$$
Explicit formula
$$T_{652}(n, m, k) = \begin{cases}\frac{k {\binom{k + 3 m - 1}{m}}}{k + 2 m}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k^{2} {\binom{- k + 2 n - 1}{n - 1}} {\binom{k + 3 m - 1}{m}}}{n \left(k + 2 m\right)} \end{cases} $$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
-1 | -1 | -3 | -12 | -55 | -273 | -1428 |
2 | 2 | 6 | 24 | 11 | 546 | 2856 |
-5 | -5 | -15 | -6 | -275 | -1365 | -714 |
14 | 14 | 42 | 168 | 77 | 3822 | 19992 |
-42 | -42 | -126 | -504 | -231 | -11466 | -59976 |
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