Generating function
$$U_{336}(x, y) = \frac{- \sqrt{2 x \left(\sqrt{4 y + 1} + 1\right) + \frac{\left(\sqrt{4 y + 1} + 1\right)^{4}}{16}} + \frac{\left(\sqrt{4 y + 1} + 1\right)^{2}}{4}}{\sqrt{4 y + 1} + 1}$$
Explicit formula
$$T_{336}(n, m, k) = \begin{cases}0&\text{if n<k} ,\ \\- \frac{\left(-1\right)^{n - 1} k {\binom{- k + 2 n - 1}{n - 1}}}{n}&\text{if m=0} ,\ \\- \frac{\left(-1\right)^{m - 1} k \left(k - 3 n\right) {\binom{k - n - 1}{n - 1}} {\binom{- k + 2 m + 3 n - 1}{m - 1}}}{m n}&\text{if m>0} \end{cases} $$
0 | 0 | 0 | 0 | 0 | 0 | 0 |
-1 | 2 | -5 | 14 | -42 | 132 | -429 |
1 | -5 | 2 | -75 | 275 | -1001 | 364 |
-2 | 16 | -88 | 416 | -182 | 7616 | -31008 |
5 | -55 | 385 | -22 | 1122 | -53295 | 241395 |
-14 | 196 | -1666 | 11172 | -6517 | 347116 | -173558 |
42 | -714 | 714 | -54978 | 361284 | -213486 | 1169532 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #336?