Generating function
$$U_{424}(x, y) = \frac{2 x y - x - \sqrt{x^{2} - 4 x y + 2 x + 1} - 1}{2 y - 2}$$
Explicit formula
$$T_{424}(n, m, k) = \begin{cases}1&\text{if m=0,n=0} ,\ \\{\binom{k}{n}}&\text{if m=0} ,\ \\\frac{\left(-1\right)^{m - 1} k {\binom{- k + n - 1}{m - 1}} {\binom{k - m - 1}{n}}}{m} \end{cases} $$
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | -1 | -1 | -1 | -1 | -1 | -1 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | -1 | 2 | 0 | 0 | 0 | 0 |
| 0 | 1 | -5 | 5 | 0 | 0 | 0 |
| 0 | -1 | 9 | -21 | 14 | 0 | 0 |
| 0 | 1 | -14 | 56 | -84 | 42 | 0 |
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #424?