T6:=orthpoly::chebyshev1(6, t);
f:=x->arccos(x);
c:=k->2/PI*int(f(cos(x))*cos(k*x),x=0..PI);
c(0);
c(1);
c(2);
c(3);
c(n) assuming(n, Type::NonNegInt);
cc:=simplify(%);
simplify(cc) assuming(n, Type::Odd);
simplify(cc) assuming(n, Type::Even);