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CoefficientList[(((y=x^2+1)^#-x^#)/(y-x),x]&+O@x^(2#))[[3]]&
Try it online!Try it online!
CoefficientList[((y=x^2+1)^#-x^#)/(y-x),x]&
Try it online!
(((y=x^2+1)^#-x^#)/(y-x)+O@x^(2#))[[3]]&
