Variable amount of nested sums

So I've been trying to code this equation where F can be any function with k inputs, ,..., are the same for the same subscript and I have m and k as input. I've been struggling to get the nested sums and the way i managed it, is by creating k-many symbolic expressions and iterating over them while summing up k times with symsum, similiar as shown below ( Fk(x) equivalent to F(cos(x) ) where x is our vector with k entries.

The problem is mv(i) take the values 1 to m and I'm not sure how to modify my function so that I can do something like Fk(θ(mv)) because Fk(theta(mv)) doesn't work or similiar stuff.

startsum = Fk(mv)

    for i = 1:k
        startsum = symsum(startsum, mv(i),1,m)
        
    end
end

Answer 1

[Walter Roberson]

See https://www.mathworks.com/matlabcentral/answers/623358-get-a-combination-of-unique-paths-for-given-pair-of-numbers#comment_1082638 where I show an implementation of what is sometimes called the "odometer" programming pattern.