Generating function
$$U_{926}(x, y) = \frac{1 - \sqrt{- 32 x y^{2} - 16 x y \sqrt{4 y^{2} + 1} - 4 x + 1}}{4 x y + 2 x \sqrt{4 y^{2} + 1}}$$
Explicit formula
$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{926}(n, m, k) = \frac{k \operatorname{Tsqrt_{2}}{\left(m,k + 2 n \right)} {\binom{k + 2 n}{n}}}{k + 2 n}$$
1 | 2 | 2 | 0 | -2 | 0 | 4 |
1 | 6 | 18 | 32 | 30 | 0 | -28 |
2 | 20 | 100 | 320 | 700 | 1024 | 840 |
5 | 70 | 490 | 2240 | 7350 | 17920 | 32340 |
14 | 252 | 2268 | 13440 | 58212 | 193536 | 504504 |
42 | 924 | 10164 | 73920 | 396396 | 1655808 | 5549544 |
132 | 3432 | 44616 | 384384 | 2453880 | 12300288 | 50059152 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #926?