Summation of Products of n Numbers taken m at a time with Repetitions/Inverse Formula/Examples

Examples of Summation of Products of n Numbers taken m at a time with Repetitions: Inverse Formula

Degree $1$

$S_1 = h_1$

Degree $2$

$S_2 = 2 h_2 - {h_1}^2$

Degree $3$

$S_3 = 3 h_3 - 3 h_1 h_2 + {h_1}^3$

Degree $4$

$S_4 = 4 h_4 - 4 h_1 h_3 - 2 {h_2}^2 + 4 {h_1}^2 h_1 - {h_1}^4$