Generating function
$$U_{653}(x, y) = \frac{4 x \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y} + \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}}$$
Explicit formula
$$T_{653}(n, m, k) = \frac{\left(k + n\right) {\binom{k}{n}} {\binom{k + 3 m + n - 1}{m}}}{k + 2 m + n}$$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
1 | 2 | 7 | 3 | 143 | 728 | 3876 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
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