Generating function
$$U_{766}(x, y) = \frac{3 y \left(1 - \sqrt{- \frac{8 \sqrt{3} x \sin{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 \sqrt{y}} + 1}\right)^{3}}{32 x^{3} \sin^{2}{\left(\frac{\arcsin{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Explicit formula
$$T_{766}(n, m, k) = \frac{3 k \left(k + n\right) {\binom{3 k + 2 n}{n}} {\binom{k + 3 m + n - 1}{m}}}{\left(3 k + 2 n\right) \left(k + 2 m + n\right)}$$
1 | 1 | 3 | 12 | 55 | 273 | 1428 |
3 | 6 | 21 | 9 | 429 | 2184 | 11628 |
9 | 27 | 108 | 495 | 2457 | 12852 | 69768 |
28 | 112 | 504 | 2464 | 1274 | 68544 | 379848 |
9 | 45 | 225 | 117 | 63 | 34884 | 197505 |
297 | 1782 | 9801 | 54054 | 30294 | 1726758 | 9993753 |
1001 | 7007 | 42042 | 245245 | 1429428 | 8387379 | 49637588 |
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