First thing you should notice is you are assigning c in each iteration not its indices. In other words you are overwriting it. That is the reason why you only get the last iteration value. You need to assign the values to proper locations in the c.
Unfortunatly you cannot have a matrix with different number of columns in each row. You can use cell arrays but they are hard to work with for certain applications. Instead you can first initialize your c matrix as zeros, then assign the values to proper locations as follows;
n = input('Degree of polynomial: ');
c = zeros(n,n+1); %n rows n+1 columns of zeros
for k = 1:n
syms x y
z(k) = (x+y)^k;
coeff = coeffs(z(k));
c(k,1:k+1) = double(coeff); % proper rows and columns to assign the coefficients.
end
c =
1 1 0 0 0 0 0
1 2 1 0 0 0 0
1 3 3 1 0 0 0
1 4 6 4 1 0 0
1 5 10 10 5 1 0
1 6 15 20 15 6 1
The downside is you will have zeros in your matrix. So whenever you wanna get the nth order coefficient you need to call "c(n,1:n+1)"
