Generating function
$$U_{399}(x, y) = \frac{\sqrt{\frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + \frac{\left(1 - \sqrt{1 - 4 y}\right)^{2}}{4 y^{2}}}}{2} + \frac{1 - \sqrt{1 - 4 y}}{4 y}$$
Explicit formula
$$T_{399}(n, m, k) = \begin{cases}1&\text{if m=0 and n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if n>0 } ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{k - n}{n}} {\binom{- k - m + n - 1}{m - 1}}}{m} \end{cases} $$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
-1 | -1 | -1 | -1 | -1 | -1 | -1 |
2 | 2 | 2 | 2 | 2 | 2 | 2 |
-5 | -5 | -5 | -5 | -5 | -5 | -5 |
14 | 14 | 14 | 14 | 14 | 14 | 14 |
-42 | -42 | -42 | -42 | -42 | -42 | -42 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #399?