[newbie] help with simplification



Could anyone explain here which steps are needed to simplify the results 
of the following function

tpald(m):=product(1+4*s*(cos((k*%pi)/(2*m+1)))^2,k,1,m)-s^m;

I know e.g. that the result for m=2 should be 1+3s, for m=3 it should be 
1+5*s+6*s^2 ...
but I can't find the correct steps to make maxima give me those results

any help welcome

hugo