Pyramid #488
Generating function
$$U_{488}(x, y) = \frac{- 4 x \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)} + \sqrt{3} \sqrt{y} - \sqrt{- 8 \sqrt{3} x \sqrt{y} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)} + 3 y}}{4 x^{2} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Explicit formula
$$T_{488}(n, m, k) = \frac{k {\binom{2 k + 2 n}{n}} {\binom{k + 3 m + n - 1}{m}}}{k + 2 m + n}$$
Data table
1 1 3 12 55 273 1428
2 4 14 6 286 1456 7752
5 15 6 275 1365 714 3876
14 56 252 1232 637 34272 189924
42 21 105 546 294 162792 92169
132 792 4356 24024 13464 767448 4441668
429 3003 18018 105105 612612 3594591 21273252
Export
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