SeriesCoefficient

SeriesCoefficient[series, n] finds the coefficient of the nth-order term in a power series in the form generated by Series.

SeriesCoefficient[f, {x, x0, n}] finds the coefficient of (x-x0)^n in the expansion of f about the point x=x0.

Examples

Coefficient from a series:

SeriesCoefficient[Series[Sin[x], {x, 0, 5}], 3]
(* -1/6 *)

Direct computation:

SeriesCoefficient[Exp[x], {x, 0, 4}]
(* 1/24 *)

Please visit the official Wolfram Language Reference for more details.