$$ \Gamma^{ \class{red}{c} }_{\;\class{blue}{a}\class{green}{b}} ~=~ \frac{1}{2} \, g^{\class{red}{c}s} \, \left( \partial_{\class{blue}{a}} \, g_{\class{green}{b}s} ~+~ \partial_{\class{green}{b}} \, g_{\class{blue}{a}s} - \partial_s \, g_{\class{blue}{a}\class{green}{b}} \right) $$
