Pyramid #290
Generating function
$$U_{290}(x, y) = \frac{\sqrt{3} \sqrt{y} - \sqrt{- 16 x \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)} + 3 y}}{4 x \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}$$
Explicit formula
$$T_{290}(n, m, k) = \frac{k {\binom{k + 2 n}{n}} {\binom{k + 3 m + 2 n - 1}{m}}}{k + 2 m + 2 n}$$
Data table
1 1 3 12 55 273 1428
1 3 12 55 273 1428 7752
2 1 5 26 14 7752 4389
5 35 21 1225 714 41895 24794
14 126 882 5712 3591 223146 138138
42 462 3696 26334 17787 116886 756756
132 1716 15444 12012 868296 602316 40756716
Export
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