Pyramid #766
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
$$T_{766}(n, m, k) = \frac{3 k \left(k + n\right) {\binom{3 k + 2 n}{n}} {\binom{k + 3 m + n - 1}{m}}}{\left(3 k + 2 n\right) \left(k + 2 m + n\right)}$$
Data table
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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