Infinite sum

Calculus Level pending

\[ \large \sum_{j=0}^\infty (3j+2)^3 x^{j+1} \]

If the series above converges and can be expressed as \( \dfrac{x(x^3 - ax^2 + bx + c)}{(x-1)^4} \) for a constant \(x\). Find the value of \(a\).

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