Generating function
$$U_{595}(x, y) = \left(1 - \frac{4 \sin^{2}{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{- x}}{2} \right)}}{3} \right)}}{3}\right) \left(y^{2} + 1\right)$$
Explicit formula
$$T_{595}(n, m, k) = \begin{cases}\left(\frac{\left(-1\right)^{m}}{2} + \frac{1}{2}\right) {\binom{k}{\frac{m}{2}}}&\text{if n==0} ,\ \\\frac{\left(-1\right)^{n - 1} k \left(\frac{\left(-1\right)^{m}}{2} + \frac{1}{2}\right) {\binom{k}{\frac{m}{2}}} {\binom{- k + 3 n - 1}{n - 1}}}{n}&\text{if n>0} \end{cases} $$
1 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 0 |
-2 | 0 | -2 | 0 | 0 | 0 | 0 |
7 | 0 | 7 | 0 | 0 | 0 | 0 |
-30 | 0 | -30 | 0 | 0 | 0 | 0 |
143 | 0 | 143 | 0 | 0 | 0 | 0 |
-728 | 0 | -728 | 0 | 0 | 0 | 0 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #595?