Generating function
$$U_{1488}(x, y) = \frac{\left(\frac{x}{\left(1 - 4 y\right)^{\frac{3}{2}}} + 1\right)^{2}}{\sqrt{1 - 4 y}}$$
Explicit formula
$$TA_{984}(n, k) = \begin{cases}{4}^{n} \binom {n+j-1} {n} &\text{if k even, where j =} \frac {k} {2},\\\frac {\binom {n+j} {n} \binom {2n+2j} {n+j}} {\binom {2j} {j}}&\text{if k odd, where j =} \frac {k-1} {2},\end{cases} $$$$T_{1488}(n, m, k) = \operatorname{TA_{984}}{\left(m,k + 3 n \right)} {\binom{2 k}{n}}$$
1 | 2 | 6 | 20 | 70 | 252 | 924 |
2 | 16 | 96 | 512 | 2560 | 12288 | 57344 |
1 | 14 | 126 | 924 | 6006 | 36036 | 204204 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
Related
Export
Export as LaTeX
Export as Maxima
Confirm deletion
Are you sure, you want to delete Pyramid #1488?