Generating function
$$U_{868}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{\frac{x}{1 - y}}}{2} \right)}}{3} \right)}}{3 \sqrt{\frac{x}{1 - y}} \left(1 - y\right)^{3}}$$
Explicit formula
$$T_{868}(n, m, k) = \frac{k {\binom{k + 3 n - 1}{n}} {\binom{3 k + m + n - 1}{m}}}{k + 2 n}$$
1 | 3 | 6 | 1 | 15 | 21 | 28 |
1 | 4 | 1 | 2 | 35 | 56 | 84 |
3 | 15 | 45 | 105 | 21 | 378 | 63 |
12 | 72 | 252 | 672 | 1512 | 3024 | 5544 |
55 | 385 | 154 | 462 | 1155 | 2541 | 5082 |
273 | 2184 | 9828 | 3276 | 9009 | 216216 | 468468 |
1428 | 12852 | 6426 | 23562 | 70686 | 1837836 | 4288284 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #868?