Generating function
$$U_{708}(x, y) = \frac{\sqrt{4 x + 1}}{\left(1 - y\right)^{2}}$$
Explicit formula
$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{708}(n, m, k) = \operatorname{Tsqrt}{\left(n,k \right)} {\binom{2 k + m - 1}{m}}$$
1 | 2 | 3 | 4 | 5 | 6 | 7 |
2 | 4 | 6 | 8 | 1 | 12 | 14 |
-2 | -4 | -6 | -8 | -10 | -12 | -14 |
4 | 8 | 12 | 16 | 20 | 24 | 28 |
-10 | -20 | -30 | -40 | -50 | -60 | -70 |
28 | 56 | 84 | 112 | 140 | 168 | 196 |
-84 | -168 | -252 | -336 | -420 | -504 | -588 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #708?