Question: Expressing all possible answers in the simplest symbolic form


I need to express some discrete functions with domain in the natural numbers.

Is there a command like the 'AllSolutions' which is used for int?

As an example, how we can express all possible values of first derivative of chebyshev polynomial for various orders in terms of a piecewise function at origin ?

The following commands do not return a suitable answer, in this case!

f:=diff(ChebyshevT(n, r), r):

g:=simplify(eval(f, r = 0), symbolic) assuming(n::integer);

`assuming`([convert(g, piecewise, n)], [n::integer]);

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