We examine by singularity analysis an equation derived by reduction using Lie point symmetries from the Euler--Bernoulli Beam equation which is the Painlev\'{ e}--Ince Equation with additional terms. The equation possesses the same leading-order behaviour and resonances as the Painlev\'{ e}--Ince Equation and has a Right Painlev\'{ e} Series. However, it has no Left Painlev% \'{ e} Series. A conjecture for the existence of Left Painlev\'{ e} Series for ordinary differential equations is given.
Categories: nlin.SI math-ph math.CA math.MP