\[\frac{{2}^{\left(\left(-n\right) - 1\right)} \cdot \left(\left(\left(\left(\left(\left(-k\right) \cdot {\left(\left(\left(-\sqrt{\left({k}^{2} + 2 \cdot k\right) - 3}\right) + k\right) - 1\right)}^{n} + \sqrt{\left({k}^{2} + 2 \cdot k\right) - 3} \cdot {\left(\left(\left(-\sqrt{\left({k}^{2} + 2 \cdot k\right) - 3}\right) + k\right) - 1\right)}^{n}\right) + {\left(\left(\left(-\sqrt{\left({k}^{2} + 2 \cdot k\right) - 3}\right) + k\right) - 1\right)}^{n}\right) + k \cdot {\left(\left(\sqrt{\left({k}^{2} + 2 \cdot k\right) - 3} + k\right) - 1\right)}^{n}\right) + \sqrt{\left({k}^{2} + 2 \cdot k\right) - 3} \cdot {\left(\left(\sqrt{\left({k}^{2} + 2 \cdot k\right) - 3} + k\right) - 1\right)}^{n}\right) - {\left(\left(\sqrt{\left({k}^{2} + 2 \cdot k\right) - 3} + k\right) - 1\right)}^{n}\right)}{\sqrt{\left({k}^{2} + 2 \cdot k\right) - 3}}\]