In[]:=
u=
b
3
y
+c+a
2
y
;​​(*{coefficientlist,maxdegree}*)​​coeffs={CoefficientList[u/y^Exponent[Series[u,y0],y],y],Exponent[u,y]}​​First[coeffs].(y^Range[Last[coeffs]-Length@First[coeffs]+1,Last[coeffs]])
Out[]=
c+
b
3
y
,0,a,2
Out[]=
c+
b
3
y
+a
2
y