Generating function
$$U_{640}(x, y) = 2 x - \sqrt{4 x^{2} + \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{y}}{2} \right)}}{3} \right)}}{3 y}}$$
Explicit formula
$$T_{640}(n, m, k) = \begin{cases}\frac{\left(-1\right)^{- k + n} \left(-1\right)^{m - 1} \cdot 4^{n} k {\binom{\frac{k}{2} + \frac{n}{2} - 1}{n}} {\binom{- k - 2 m + n - 1}{m - 1}}}{m}&\text{if m>0} ,\ \\-1&\text{if m = 0, n = 0 } ,\ \\\frac{\left(-1\right)^{k - 1} \cdot 4^{n} k {\binom{- \frac{k}{2} + \frac{n}{2} - 1}{n - 1}}}{2 n}&\text{if m=0,n>0} \end{cases} $$
-1 | -1 | -3 | -12 | -55 | -273 | -1428 |
2 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #640?