Pyramid #287
Generating function
$$U_{287}(x, y) = \frac{\sqrt{3} \sqrt{x} - \sqrt{3 x - 16 y \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}}{4 y \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x}}{2} \right)}}{3} \right)}}$$
Explicit formula
$$T_{287}(n, m, k) = \frac{k {\binom{k + 2 m}{m}} {\binom{k + 2 m + 3 n - 1}{n}}}{k + 2 m + 2 n}$$
Data table
1 1 2 5 14 42 132
1 3 1 35 126 462 1716
3 12 5 21 882 3696 15444
12 55 26 1225 5712 26334 12012
55 273 14 714 3591 17787 868296
273 1428 7752 41895 223146 116886 602316
1428 7752 4389 24794 138138 756756 40756716
Export
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