I started with the right way but soon I lost it!... In terms of Zeta-Tranform, difference equation corresponding to the function is...
(1)
... where...
(2)
... so that the coefficients of the Taylor series are found symply expanding (1)...
... so that is...
(3)
... as awkward found...
Kind regards
From your original post:
So is the coefficient of in the series for f(x).
But the problem did not ask for a general form of the coefficient, it simply asked for the value of
,
which can be found without necessarily finding the general coefficient.