Generating function
$$U_{849}(x, y) = \frac{1}{x y^{7} - 7 x y^{6} + 21 x y^{5} - x + y^{4} \left(1 - 35 x\right) + y^{3} \left(35 x - 4\right) + y^{2} \left(6 - 21 x\right) + y \left(7 x - 4\right) + 1}$$
Explicit formula
$$T_{849}(n, m, k) = {\binom{k + n - 1}{n}} {\binom{4 k + m - 3 n - 1}{m}}$$
| 1 | 4 | 1 | 2 | 35 | 56 | 84 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 1 | -2 | 1 | 0 | 0 | 0 | 0 |
| 1 | -5 | 1 | -1 | 5 | -1 | 0 |
| 1 | -8 | 28 | -56 | 7 | -56 | 28 |
| 1 | -11 | 55 | -165 | 33 | -462 | 462 |
| 1 | -14 | 91 | -364 | 1001 | -2002 | 3003 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #849?