elementary symmetric polynomial

The coefficient of $x^{n-k}$ in the polynomial $(x+t_1) (x+t_2) \cdots (x+t_n)$ is called the $k^\mathrm{th}$ elementary symmetric polynomial in the $n$ variables $t_1, \dots, t_n$ . The elementary symmetric polynomials can also be constructed by taking the sum of all possible degree $k$ monomials in $t_1,\dots, t_n$ having distinct factors.

The first few examples are:

$n=1$ :

$n=2$ :

$n=3$ :