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

[matlabes (David carl)]

Normal@Series[f, {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.

[gianlucagorni]

Here is an attempt, using Inactive:

expr = Normal@Series[f[x], {x, x0, 7}]
expr /. Rational[1, n_] :> 
  1/Inactive[Factorial][SolveValues[n == k!, k, Integers][[1]]]