Editing Ideal gas Helmholtz energy function

From equations 
:<math>Q_{NVT}=\frac{1}{N!} \left( \frac{V}{\Lambda^{3}}\right)^N</math>
and 
:<math>A=-k_B T \ln Q_{NVT}</math>
one has
:<math>A=-k_BT\left(\ln \frac{1}{N!} + N\ln\frac{V}{\Lambda^{3}}\right)</math>
::<math>=-k_BT\left(-\ln N! + N\ln\frac{VN}{\Lambda^3N}\right)</math>
::<math>=-k_BT\left(-\ln N! + N\ln\frac{N}{\Lambda^3 \rho}\right)</math>
using [[Stirling's approximation]]
:<math>=-k_BT\left( -N\ln N +N + N\ln N - N\ln \Lambda^3 \rho \right)</math>
one arrives at 

<math>A=Nk_BT\left(\ln \Lambda^3 \rho -1 \right)</math>