gravitational interaction of photons

Why do gravitational interactions of (CMB) photons with the cosmic large-scale structure such as gravitational lensing or the integrated Sachs-Wolfe effect conserve the Planckian shape of the photon energy distribution?

bonus question: What’s \(\sum_{i=0}^n{n\choose i}\) with the binomial coefficient \({n\choose i}=n!/i!/(n-i)!\)?