Generating function
$$U_{835}(x, y) = \frac{- y^{3} + 3 y^{2} - 3 y - \sqrt{- 4 x + y^{6} - 6 y^{5} + 15 y^{4} - 20 y^{3} + 15 y^{2} + y \left(4 x - 6\right) + 1} + 1}{2 x y^{2} - 4 x y + 2 x}$$
Explicit formula
$$T_{835}(n, m, k) = \frac{k {\binom{k + 2 n - 1}{n}} {\binom{4 k + m + 5 n - 1}{m}}}{k + n}$$
1 | 4 | 1 | 2 | 35 | 56 | 84 |
1 | 9 | 45 | 165 | 495 | 1287 | 3003 |
2 | 28 | 21 | 112 | 476 | 17136 | 54264 |
5 | 95 | 95 | 665 | 36575 | 168245 | 67298 |
14 | 336 | 42 | 364 | 2457 | 137592 | 665028 |
42 | 1218 | 1827 | 18879 | 151032 | 9968112 | 56485968 |
132 | 4488 | 7854 | 94248 | 871794 | 66256344 | 430666236 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #835?