Generating function
$$U_{1076}(x, y) = 2 x \left(y + 1\right)^{4} + \left(y + 1\right)^{2} \sqrt{4 x^{2} \left(y + 1\right)^{4} + 1}$$
Explicit formula
$$Tsqrt2(n, k) = \begin{cases}\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k even, where j =} \frac{n+k} {2},\\\frac {k \binom{n+j}{n} \binom{2n+2j}{n+j}} {\binom{2j}{j} {n+k}} &\text{if n+k odd, where j =} \frac{n+k+1} {2},\\\end{cases} $$$$T_{1076}(n, m, k) = k \operatorname{Tsqrt_{2}}{\left(n,k \right)} {\binom{2 k + 2 n}{m}}$$
1 | 2 | 1 | 0 | 0 | 0 | 0 |
2 | 8 | 12 | 8 | 2 | 0 | 0 |
2 | 12 | 3 | 4 | 3 | 12 | 2 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
-2 | -20 | -90 | -240 | -420 | -504 | -420 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
4 | 56 | 364 | 1456 | 4004 | 8008 | 12012 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #1076?