# Analytical formula for the moments of SABR model?

Do analytical formulae exist for the central moments under the SABR model? Assuming dynamics for the forward rate $$\{F_t, t \geq 0\}$$ under a shifted SABR model. How do we derive $$\mathbb{E}[X(T)^n]$$ where $$X(T) = \log(F(T)/F(0))$$?

Reference to papers are appreciated.