Generating function
$$U_{191}(x, y) = \frac{y - \sqrt{2 x y \sqrt{1 - 4 y} - 2 x y + y^{2}}}{2 x y}$$
Explicit formula
$$T_{191}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{k + 2 m + n - 1}{m}}}{k + m + n}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
1 | 2 | 5 | 14 | 42 | 132 | 429 |
2 | 6 | 18 | 56 | 18 | 594 | 2002 |
5 | 2 | 7 | 24 | 825 | 286 | 1001 |
14 | 7 | 28 | 105 | 385 | 14014 | 5096 |
42 | 252 | 1134 | 462 | 18018 | 68796 | 259896 |
132 | 924 | 462 | 20328 | 84084 | 336336 | 1319472 |
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #191?