factoring coefficients

Hello list,

Consider the function

(%i19) f(x) := (sin(x))^6;
                                           6
(%o19)                          f(x) := sin (x)

I take the sixth derivative of it and simplify it a bit, so that I have

(%i20) rat(trigreduce(diff(f(x), x, 6)));
(%o20)/R/         1458 cos(6 x) - 768 cos(4 x) + 30 cos(2 x)

This is already nice.  But to discover structure in the jth order derivatives,
it would be interesting to see the coefficients in this expression factored.
So
                      6
1458 should become 2 3 and so on.

Is this possible with Maxima?

Thanks,
Bart

PS: if by the way anybody knows a nice and general expression for the jth
order derivative of (sin(x))^n then I would be highly interested!