Generating function
$$U_{975}(x, y) = \frac{1 - \sqrt{\sqrt{4 y + 1} \left(- 16 x y - 4 x\right) + 1}}{\sqrt{4 y + 1} \left(8 x y + 2 x\right)}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{975}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(m,3 n \right)} {\binom{k + 2 n - 1}{n}}}{k + n}$$
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 6 | 6 | -4 | 6 | -12 | 28 |
2 | 24 | 96 | 128 | 0 | 0 | 0 |
5 | 90 | 630 | 2100 | 3150 | 126 | -420 |
14 | 336 | 3360 | 17920 | 53760 | 86016 | 57344 |
42 | 1260 | 16380 | 120120 | 540540 | 1513512 | 2522520 |
132 | 4752 | 76032 | 709632 | 4257792 | 17031168 | 45416448 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #975?