Out[11]:
\[\newcommand{\Bold}[1]{\mathbf{#1}}\begin{array}{lcl} \Gamma_{ \phantom{\, t} \, t \, r }^{ \, t \phantom{\, t} \phantom{\, r} } & = & -\frac{a^{4} - r^{4} - {\left(a^{4} + a^{2} r^{2}\right)} \sin\left({\theta}\right)^{2}}{a^{2} r^{4} + r^{6} - 2 \, r^{5} + {\left(a^{6} + a^{4} r^{2} - 2 \, a^{4} r\right)} \cos\left({\theta}\right)^{4} + 2 \, {\left(a^{4} r^{2} + a^{2} r^{4} - 2 \, a^{2} r^{3}\right)} \cos\left({\theta}\right)^{2}} \\ \Gamma_{ \phantom{\, t} \, t \, {\theta} }^{ \, t \phantom{\, t} \phantom{\, {\theta}} } & = & -\frac{2 \, a^{2} r \cos\left({\theta}\right) \sin\left({\theta}\right)}{a^{4} \cos\left({\theta}\right)^{4} + 2 \, a^{2} r^{2} \cos\left({\theta}\right)^{2} + r^{4}} \\ \Gamma_{ \phantom{\, t} \, r \, {\phi} }^{ \, t \phantom{\, r} \phantom{\, {\phi}} } & = & -\frac{{\left(a^{3} r^{2} + 3 \, a r^{4} - {\left(a^{5} - a^{3} r^{2}\right)} \cos\left({\theta}\right)^{2}\right)} \sin\left({\theta}\right)^{2}}{a^{2} r^{4} + r^{6} - 2 \, r^{5} + {\left(a^{6} + a^{4} r^{2} - 2 \, a^{4} r\right)} \cos\left({\theta}\right)^{4} + 2 \, {\left(a^{4} r^{2} + a^{2} r^{4} - 2 \, a^{2} r^{3}\right)} \cos\left({\theta}\right)^{2}} \\ \Gamma_{ \phantom{\, t} \, {\theta} \, {\phi} }^{ \, t \phantom{\, {\theta}} \phantom{\, {\phi}} } & = & -\frac{2 \, {\left(a^{5} r \cos\left({\theta}\right) \sin\left({\theta}\right)^{5} - {\left(a^{5} r + a^{3} r^{3}\right)} \cos\left({\theta}\right) \sin\left({\theta}\right)^{3}\right)}}{a^{6} \cos\left({\theta}\right)^{6} + 3 \, a^{4} r^{2} \cos\left({\theta}\right)^{4} + 3 \, a^{2} r^{4} \cos\left({\theta}\right)^{2} + r^{6}} \\ \Gamma_{ \phantom{\, r} \, t \, t }^{ \, r \phantom{\, t} \phantom{\, t} } & = & \frac{a^{2} r^{2} + r^{4} - 2 \, r^{3} - {\left(a^{4} + a^{2} r^{2} - 2 \, a^{2} r\right)} \cos\left({\theta}\right)^{2}}{a^{6} \cos\left({\theta}\right)^{6} + 3 \, a^{4} r^{2} \cos\left({\theta}\right)^{4} + 3 \, a^{2} r^{4} \cos\left({\theta}\right)^{2} + r^{6}} \\ \Gamma_{ \phantom{\, r} \, t \, {\phi} }^{ \, r \phantom{\, t} \phantom{\, {\phi}} } & = & -\frac{{\left(a^{3} r^{2} + a r^{4} - 2 \, a r^{3} - {\left(a^{5} + a^{3} r^{2} - 2 \, a^{3} r\right)} \cos\left({\theta}\right)^{2}\right)} \sin\left({\theta}\right)^{2}}{a^{6} \cos\left({\theta}\right)^{6} + 3 \, a^{4} r^{2} \cos\left({\theta}\right)^{4} + 3 \, a^{2} r^{4} \cos\left({\theta}\right)^{2} + r^{6}} \\ \Gamma_{ \phantom{\, r} \, r \, r }^{ \, r \phantom{\, r} \phantom{\, r} } & = & \frac{{\left(a^{2} r - a^{2}\right)} \sin\left({\theta}\right)^{2} + a^{2} - r^{2}}{a^{2} r^{2} + r^{4} - 2 \, r^{3} + {\left(a^{4} + a^{2} r^{2} - 2 \, a^{2} r\right)} \cos\left({\theta}\right)^{2}} \\ \Gamma_{ \phantom{\, r} \, r \, {\theta} }^{ \, r \phantom{\, r} \phantom{\, {\theta}} } & = & -\frac{a^{2} \cos\left({\theta}\right) \sin\left({\theta}\right)}{a^{2} \cos\left({\theta}\right)^{2} + r^{2}} \\ \Gamma_{ \phantom{\, r} \, {\theta} \, {\theta} }^{ \, r \phantom{\, {\theta}} \phantom{\, {\theta}} } & = & -\frac{a^{2} r + r^{3} - 2 \, r^{2}}{a^{2} \cos\left({\theta}\right)^{2} + r^{2}} \\ \Gamma_{ \phantom{\, r} \, {\phi} \, {\phi} }^{ \, r \phantom{\, {\phi}} \phantom{\, {\phi}} } & = & \frac{{\left(a^{4} r^{2} + a^{2} r^{4} - 2 \, a^{2} r^{3} - {\left(a^{6} + a^{4} r^{2} - 2 \, a^{4} r\right)} \cos\left({\theta}\right)^{2}\right)} \sin\left({\theta}\right)^{4} - {\left(a^{2} r^{5} + r^{7} - 2 \, r^{6} + {\left(a^{6} r + a^{4} r^{3} - 2 \, a^{4} r^{2}\right)} \cos\left({\theta}\right)^{4} + 2 \, {\left(a^{4} r^{3} + a^{2} r^{5} - 2 \, a^{2} r^{4}\right)} \cos\left({\theta}\right)^{2}\right)} \sin\left({\theta}\right)^{2}}{a^{6} \cos\left({\theta}\right)^{6} + 3 \, a^{4} r^{2} \cos\left({\theta}\right)^{4} + 3 \, a^{2} r^{4} \cos\left({\theta}\right)^{2} + r^{6}} \\ \Gamma_{ \phantom{\, {\theta}} \, t \, t }^{ \, {\theta} \phantom{\, t} \phantom{\, t} } & = & -\frac{2 \, a^{2} r \cos\left({\theta}\right) \sin\left({\theta}\right)}{a^{6} \cos\left({\theta}\right)^{6} + 3 \, a^{4} r^{2} \cos\left({\theta}\right)^{4} + 3 \, a^{2} r^{4} \cos\left({\theta}\right)^{2} + r^{6}} \\ \Gamma_{ \phantom{\, {\theta}} \, t \, {\phi} }^{ \, {\theta} \phantom{\, t} \phantom{\, {\phi}} } & = & \frac{2 \, {\left(a^{3} r + a r^{3}\right)} \cos\left({\theta}\right) \sin\left({\theta}\right)}{a^{6} \cos\left({\theta}\right)^{6} + 3 \, a^{4} r^{2} \cos\left({\theta}\right)^{4} + 3 \, a^{2} r^{4} \cos\left({\theta}\right)^{2} + r^{6}} \\ \Gamma_{ \phantom{\, {\theta}} \, r \, r }^{ \, {\theta} \phantom{\, r} \phantom{\, r} } & = & \frac{a^{2} \cos\left({\theta}\right) \sin\left({\theta}\right)}{a^{2} r^{2} + r^{4} - 2 \, r^{3} + {\left(a^{4} + a^{2} r^{2} - 2 \, a^{2} r\right)} \cos\left({\theta}\right)^{2}} \\ \Gamma_{ \phantom{\, {\theta}} \, r \, {\theta} }^{ \, {\theta} \phantom{\, r} \phantom{\, {\theta}} } & = & \frac{r}{a^{2} \cos\left({\theta}\right)^{2} + r^{2}} \\ \Gamma_{ \phantom{\, {\theta}} \, {\theta} \, {\theta} }^{ \, {\theta} \phantom{\, {\theta}} \phantom{\, {\theta}} } & = & -\frac{a^{2} \cos\left({\theta}\right) \sin\left({\theta}\right)}{a^{2} \cos\left({\theta}\right)^{2} + r^{2}} \\ \Gamma_{ \phantom{\, {\theta}} \, {\phi} \, {\phi} }^{ \, {\theta} \phantom{\, {\phi}} \phantom{\, {\phi}} } & = & -\frac{{\left({\left(a^{6} + a^{4} r^{2} - 2 \, a^{4} r\right)} \cos\left({\theta}\right)^{5} + 2 \, {\left(a^{4} r^{2} + a^{2} r^{4} - 2 \, a^{2} r^{3}\right)} \cos\left({\theta}\right)^{3} + {\left(a^{2} r^{4} + r^{6} + 2 \, a^{4} r + 4 \, a^{2} r^{3}\right)} \cos\left({\theta}\right)\right)} \sin\left({\theta}\right)}{a^{6} \cos\left({\theta}\right)^{6} + 3 \, a^{4} r^{2} \cos\left({\theta}\right)^{4} + 3 \, a^{2} r^{4} \cos\left({\theta}\right)^{2} + r^{6}} \\ \Gamma_{ \phantom{\, {\phi}} \, t \, r }^{ \, {\phi} \phantom{\, t} \phantom{\, r} } & = & -\frac{a^{3} \cos\left({\theta}\right)^{2} - a r^{2}}{a^{2} r^{4} + r^{6} - 2 \, r^{5} + {\left(a^{6} + a^{4} r^{2} - 2 \, a^{4} r\right)} \cos\left({\theta}\right)^{4} + 2 \, {\left(a^{4} r^{2} + a^{2} r^{4} - 2 \, a^{2} r^{3}\right)} \cos\left({\theta}\right)^{2}} \\ \Gamma_{ \phantom{\, {\phi}} \, t \, {\theta} }^{ \, {\phi} \phantom{\, t} \phantom{\, {\theta}} } & = & -\frac{2 \, a r \cos\left({\theta}\right)}{{\left(a^{4} \cos\left({\theta}\right)^{4} + 2 \, a^{2} r^{2} \cos\left({\theta}\right)^{2} + r^{4}\right)} \sin\left({\theta}\right)} \\ \Gamma_{ \phantom{\, {\phi}} \, r \, {\phi} }^{ \, {\phi} \phantom{\, r} \phantom{\, {\phi}} } & = & \frac{r^{5} + {\left(a^{4} r - a^{4}\right)} \cos\left({\theta}\right)^{4} - a^{2} r^{2} - 2 \, r^{4} + {\left(2 \, a^{2} r^{3} + a^{4} - a^{2} r^{2}\right)} \cos\left({\theta}\right)^{2}}{a^{2} r^{4} + r^{6} - 2 \, r^{5} + {\left(a^{6} + a^{4} r^{2} - 2 \, a^{4} r\right)} \cos\left({\theta}\right)^{4} + 2 \, {\left(a^{4} r^{2} + a^{2} r^{4} - 2 \, a^{2} r^{3}\right)} \cos\left({\theta}\right)^{2}} \\ \Gamma_{ \phantom{\, {\phi}} \, {\theta} \, {\phi} }^{ \, {\phi} \phantom{\, {\theta}} \phantom{\, {\phi}} } & = & \frac{a^{4} \cos\left({\theta}\right)^{5} + 2 \, {\left(a^{2} r^{2} - a^{2} r\right)} \cos\left({\theta}\right)^{3} + {\left(r^{4} + 2 \, a^{2} r\right)} \cos\left({\theta}\right)}{{\left(a^{4} \cos\left({\theta}\right)^{4} + 2 \, a^{2} r^{2} \cos\left({\theta}\right)^{2} + r^{4}\right)} \sin\left({\theta}\right)} \end{array}\]