  We introduce the notion of Differential Sequences of ordinary differential
equations. This is motivated by related studies based on evolution partial
differential equations. We discuss the Riccati Sequence in terms of symmetry
analysis, singularity analysis and identification of the complete symmetry
group for each member of the Sequence. The singularity analysis reveals
considerable structure for the values of the coefficients of the leading-order
terms and resonances of the different principal branches. Full proofs of the
symmetry properties are performed for differential equations defined by their
recursion properties and not given in explicit form.
