# Proof of a Ramanujan Statement [duplicate]

I recently came across the approximation $$\ln n! \approx n\ln n - n + \frac{1}{6}\ln(n(1+4n(1+2n)))+\frac{1}{2}\ln \pi$$ Supposedly this was written in Ramanujan's last notebook, but I can't seem to find it anywhere else, nevermind a proof for it. Does anyone know if it was ever proven, and if so where such a proof is?