Generating function
$$U_{305}(x, y) = \frac{\sqrt{3} \left(1 - \sqrt{1 - 4 x}\right) \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 x \sqrt{y}}$$
Explicit formula
$$T_{305}(n, m, k) = \frac{k^{2} {\binom{k + 3 m - 1}{m}} {\binom{k + 2 n - 1}{n}}}{\left(k + 2 m\right) \left(k + n\right)}$$
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 |
132 | 132 | 396 | 1584 | 726 | 36036 | 188496 |
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