Table[SeriesCoefficient[1/(1 - t), {t, 0, n}], {n, 1, 10}]

You can query specific coefficients of the series using SeriesCoefficient. What have you tried yourself?

Hi Roman,

the sequence which generates the function is just the Taylor serie. The general formula for the coefficients are the well known terms $\left.\frac{1}{n!}\frac{\partial}{\partial x} g(x)\right|_{x=0}$. You can calculate a bunch of those terms and than use FindSequenceFunction to find in a somewhat empirical way a more specific formula:

g[t_] := Exp[-2*t^2]
gterms = Table[(D[g[t], {t, n}]/n!) /. t -> 0, {n, 0, 20}]
(* or likewise: *)
gterms = Table[SeriesCoefficient[g[t], {t, 0, n}], {n, 0, 20}]
(* find a specific formula for the terms: *)
FindSequenceFunction[gterms, n]

resulting in:

Isn't Mathematica just great?!? Regards -- Henrik

Table[SeriesCoefficient[e^(-2t^2), {t, 0, n}], {n, 0, 10}]

It gives me table of values for each n but I want to get a formula for a_n depends on n.

Perhaps you can share your findings along with an example. Such as to make this discussion useful for future reference.