Obtaining n^th order polynomial combinations in an array

Hi, I want to obtain an array consisting of all the possible combinations of polynomials upto n^(th) order. For example, for order 2, the array would look like

[1, x(1), x(2), x(3), x(4), x(5), x(6), x(1)*x(1), x(1)*x(2), x(1)*x(3), x(1)*x(4), x(1)*x(5), x(1)*x(6), x(2)*x(2), x(2)*x(3), x(2)*x(4), x(2)*x(5), x(2)*x(6), x(3)*x(3), x(3)*x(4), x(3)*x(5), x(3)*x(6), x(4)*x(4), x(4)*x(5), x(4)*x(6), x(5)*x(5),x(5)*x(6), x(6)*x(6)]

Whereas for order 3, it will look like

[1, x(1), x(2), x(3), x(4), x(5), x(6), x(1)*x(1), x(1)*x(2), x(1)*x(3), x(1)*x(4), x(1)*x(5), 
x(1)*x(6), x(2)*x(2), x(2)*x(3), x(2)*x(4), x(2)*x(5), x(2)*x(6), x(3)*x(3), x(3)*x(4), 
    x(3)*x(5), x(3)*x(6), x(4)*x(4), x(4)*x(5), x(4)*x(6), x(5)*x(5),x(5)*x(6), 
    x(6)*x(6), x(1)*x(1)*x(1), x(1)*x(1)*x(2), x(1)*x(1)*x(3), x(1)*x(1)*x(4), 
    x(1)*x(1)*x(5), x(1)*x(1)*x(6), x(1)*x(2)*x(2), x(1)*x(2)*x(3), x(1)*x(2)*x(4), 
    x(1)*x(2)*x(5), x(1)*x(2)*x(6), x(1)*x(3)*x(3), x(1)*x(3)*x(4), x(1)*x(3)*x(5), 
    x(1)*x(3)*x(6), x(1)*x(4)*x(4), x(1)*x(4)*x(5), x(1)*x(4)*x(6), x(1)*x(5)*x(5), 
    x(1)*x(5)*x(6), x(1)*x(6)*x(6), x(2)*x(2)*x(2), x(2)*x(2)*x(3), x(2)*x(2)*x(4), 
    x(2)*x(2)*x(5), x(2)*x(2)*x(6),x(2)*x(3)*x(3), x(2)*x(3)*x(4), x(2)*x(3)*x(5), x(2)*x(3)*x(6),  
    x(2)*x(4)*x(4), x(2)*x(4)*x(5), x(2)*x(4)*x(6),  x(2)*x(5)*x(5), x(2)*x(5)*x(6), x(2)*x(6)*x(6), 
    x(3)*x(3)*x(3),x(3)*x(3)*x(4), x(3)*x(3)*x(5), x(3)*x(3)*x(6), x(3)*x(4)*x(4), x(3)*x(4)*x(5), 
    x(3)*x(4)*x(6), x(3)*x(5)*x(5),  x(3)*x(5)*x(6), x(3)*x(6)*x(6), x(4)*x(4)*x(4),  x(4)*x(4)*x(5), 
    x(4)*x(4)*x(6), x(4)*x(5)*x(5),x(4)*x(5)*x(6), x(4)*x(6)*x(6), x(5)*x(5)*x(5), x(5)*x(5)*x(6), 
    x(5)*x(6)*x(6), x(6)*x(6)*x(6)]

So far, I am manually defining such arrays, but as you can see, it is very tedious. Is there a way to code this for any random order n? Thank you for all the help!

Answer 1

[KSSV]

REad about nchoosek

You may also refer to the below file exchange: https://in.mathworks.com/matlabcentral/fileexchange/9029-nmultichoosek