Normal@Series[f[x], {x, x0, 7}]
From the above code, the expansion is:

How to convert Taylor series denominators to factorials (n!)as foll0ws?

expr = Normal@Series[f[x], {x, x0, 7}]
expr /. Rational[1, n_] :> 1/n!
The code shown above represents my personal attempt, though it proved unsuccessful.