Power series/R/Fourth power/Fifth coefficient/Exercise

Let

$\sum _{n=0}^{\mathrm{\infty }}{a}_n{x}^n$

be an absolutely convergent power series. Determine the coefficients of the powers $x^0,x^1,x^2,x^3,x^4,x^5$ in the fourth power

$\sum _{n=0}^{\mathrm{\infty }}{c}_n{x}^n={\left(\sum _{n=0}^{\mathrm{\infty }}{a}_n{x}^n\right)}^4.$

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