[math-fun] Expansion of pi in factorial base

Has anyone seen the expansion of π to inverse-factorial base? More precisely, I’d like to know the first N coefficients c_n of oo π-3 = Sum c_k / k! k=1 where 0 <= c_k < k, for N not too small. Even better, does anyone know a nice algorithm for computing this inverse-factorial base expansion of a real number that avoids over/underflow (without using arbitrary-precision arithmetic)? —Dan