symbolic summation of derivatives of a function

I would like to generate a symbolic sum of the first "n" derivatives of a function.

For example, f = 1/(1-x^4)

sum(f^(n),n=0..3)

The response from Maple is not as expected.  The first term is:  -1/(4*(x-1)) and the subsequent terms are less recognizable.

If I use "seq" with the same syntax, I end up with a list that includes the function and the first 3 derivatives.

I have also tried:

sum(diff(f,x$n),n=0..3)

and get the same result as with "sum".

Any help would be greatly appreciated.

Regards,

Frank