How to sum the product between a matrix and 2 vectors

I need to solve a system of differential equation written as:

For each equation I should solve a summation like:

where K_Br is a matrix previously calculated and n is a vector as the solution of the differential equation system.

For example, for i=3:

I wrote the system of differential equation as:

function ndot = System_ni (t,n)
ndot = zeros(M,1);
ndot(1) = -n(1)*sum(K_Br(1,1:M)*n(1:M));
    for i = 2:M
        ndot(i) = 1/2*sum(K_Br(1:i-1,i-1:1)*n(i-1:1)*n(1:i-1))-n(i)*sum(K_Br(i,1:M)*n(1:M));
    end
end

but summation seems not to work.

Thank you in advance for any help.

[James Tursa]

It is not clear to me what is in your equation. Is the n indexing 1-based?

[Sara Crosetto]

I reported the initial equation wrong.

Actually, the equation is:

[VBBV]

@Sara Crosetto the terms in equation shown are dependent on another implicit summing variable i

You need two for loops instead of one for such summation to work.