Adomian polynomials of $y^3$

El-kalla polynomials of $y^3$

$A_0=y_0^3$

${\overline{A}}_0=y_0^3$

$A_1=3y_1{y}_0^2$

${\overline{A}}_1=3y_1{y}_0^2+3y_0{y}_1^2+y_1^3$

$A_2=3y_0{y}_1^2+3y_2{y}_0^2$

${\overline{A}}_2=3y_2{y}_0^2+6y_0{y}_1{y}_2+3y_0{y}_2^2+3y_2{y}_1^2+3y_1{y}_2^2+y_2^3$

$A_3=y_1^3+3y_3{y}_0^2+6y_0{y}_1{y}_2$

$\begin{array}{l}{\overline{A}}_3=3y_3{y}_0^2+6y_0{y}_1{y}_3+6y_0{y}_2{y}_3+3y_0{y}_3^2+3y_3{y}_1^2\\ +6y_1{y}_2{y}_3+3y_1{y}_3^2+3y_3{y}_2^2+3y_2{y}_3^2+y_3^3\end{array}$