Generating function
$$U_{1318}(x, y) = \frac{4 y^{5} \left(- \frac{x \left(1 - \sqrt{1 - 4 y}\right)}{y} - \sqrt{- \frac{2 x \left(1 - \sqrt{1 - 4 y}\right)}{y} + 1} + 1\right)^{3}}{x^{6} \left(1 - \sqrt{1 - 4 y}\right)^{5}}$$
Explicit formula
$$T_{1318}(n, m, k) = \frac{3 k \left(k + n\right) {\binom{6 k + 2 n}{n}} {\binom{k + 2 m + n - 1}{m}}}{\left(3 k + n\right) \left(k + m + n\right)}$$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
6 | 12 | 3 | 84 | 252 | 792 | 2574 |
27 | 81 | 243 | 756 | 243 | 8019 | 27027 |
11 | 44 | 154 | 528 | 1815 | 6292 | 22022 |
429 | 2145 | 858 | 32175 | 117975 | 429429 | 156156 |
1638 | 9828 | 44226 | 18018 | 702702 | 2683044 | 10135944 |
6188 | 43316 | 21658 | 952952 | 3941756 | 15767024 | 61855248 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #1318?