Generating function
$$U_{1086}(x, y) = \frac{\left(1 - \sqrt{1 - 4 y}\right)^{3} \left(- 2 x - \sqrt{1 - 4 x} + 1\right)^{2}}{32 x^{4} y^{3}}$$
Explicit formula
$$T_{1086}(n, m, k) = \frac{6 k^{2} {\binom{4 k + 2 n}{n}} {\binom{3 k + 2 m - 1}{m}}}{\left(2 k + n\right) \left(3 k + m\right)}$$
1 | 3 | 9 | 28 | 9 | 297 | 1001 |
4 | 12 | 36 | 112 | 36 | 1188 | 4004 |
14 | 42 | 126 | 392 | 126 | 4158 | 14014 |
48 | 144 | 432 | 1344 | 432 | 14256 | 48048 |
165 | 495 | 1485 | 462 | 1485 | 49005 | 165165 |
572 | 1716 | 5148 | 16016 | 5148 | 169884 | 572572 |
2002 | 6006 | 18018 | 56056 | 18018 | 594594 | 2004002 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #1086?