Generating function
$$U_{144}(x, y) = \frac{1 - \sqrt{- 2 y \sqrt{4 x + 1} - 2 y + 1}}{2 y}$$
Explicit formula
$$T_{144}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 m - 1}{m}}}{k + m}&\text{if n=0} ,\ \\\frac{\left(-1\right)^{n - 1} k {\binom{k + 2 m - 1}{m}} {\binom{- k - m + 2 n - 1}{n - 1}}}{n} \end{cases} $$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
1 | 2 | 6 | 2 | 7 | 252 | 924 |
-1 | -1 | 0 | 1 | 7 | 378 | 1848 |
2 | 2 | 2 | 0 | 0 | 84 | 924 |
-5 | -5 | -6 | -5 | 0 | 0 | 0 |
14 | 14 | 18 | 2 | 14 | 0 | 0 |
-42 | -42 | -56 | -7 | -7 | -42 | 0 |
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #144?