Generating function
$$U_{49}(x, y) = \frac{x^{2} - 2 x - \sqrt{x^{4} - 4 x^{3} + 6 x^{2} - 4 x + y \left(4 x - 4\right) + 1} + 1}{2 y}$$
Explicit formula
$$T_{49}(n, m, k) = \begin{cases}\frac{k {\binom{k + 2 m - 1}{m}} {\binom{k + 3 m + n - 1}{n}}}{k + m}&\text{if m=0} ,\ \\\frac{k {\binom{k + 2 m - 1}{m}} {\binom{k + 3 m + n - 1}{n}}}{k + m} \end{cases} $$
1 | 1 | 2 | 5 | 14 | 42 | 132 |
1 | 4 | 14 | 5 | 182 | 672 | 2508 |
1 | 1 | 56 | 275 | 1274 | 5712 | 2508 |
1 | 2 | 168 | 11 | 637 | 34272 | 17556 |
1 | 35 | 42 | 3575 | 2548 | 162792 | 96558 |
1 | 56 | 924 | 1001 | 86632 | 651168 | 4441668 |
1 | 84 | 1848 | 25025 | 259896 | 2279088 | 17766672 |
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #49?