Generating function
$$U_{1362}(x, y) = \frac{2 \sqrt{3} \sin{\left(\frac{\operatorname{asin}{\left(\frac{3 \sqrt{3} \sqrt{x} \left(1 - \sqrt{1 - 4 y}\right)^{3}}{16 y^{3}} \right)}}{3} \right)}}{3 \sqrt{x}}$$
Explicit formula
$$T_{1362}(n, m, k) = \frac{3 k {\binom{k + 3 n - 1}{n}} {\binom{3 k + 2 m + 6 n - 1}{m}}}{3 k + m + 6 n}$$
1 | 3 | 9 | 28 | 9 | 297 | 1001 |
1 | 9 | 54 | 273 | 126 | 5508 | 23256 |
3 | 45 | 405 | 285 | 17325 | 95634 | 49335 |
12 | 252 | 3024 | 273 | 206388 | 1381212 | 8457792 |
55 | 1485 | 22275 | 24552 | 222156 | 17494785 | 124230645 |
273 | 9009 | 162162 | 2111109 | 2225223 | 201675474 | 1630641012 |
1428 | 55692 | 1169532 | 17561544 | 21135114 | 2167309872 | 1966633032 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #1362?