Pyramid #899
Generating function
$$U_{899}(x, y) = \frac{\left(1 - y\right) \left(2 - 2 \cos{\left(\frac{2 \arcsin{\left(\frac{3 \sqrt{3} \sqrt{x}}{2 \operatorname{abs}{\left(y - 1 \right)}} \right)}}{3} \right)}\right)}{3 x}$$
Explicit formula
$$T_{899}(n, m, k) = \frac{k {\binom{2 k + 3 n - 1}{n}} {\binom{k + m + 2 n - 1}{m}}}{k + n}$$
Data table
1 1 1 1 1 1 1
2 6 12 2 3 42 56
7 35 105 245 49 882 147
3 21 84 252 63 1386 2772
143 1287 6435 23595 70785 184041 429429
728 8008 48048 208208 728728 2186184 5829824
3876 50388 352716 176358 705432 23984688 71954064
Export
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