$\large{a_{n+1} = 2a_n - n^2 + n}$

Define a sequence $a_n$ that satisfy the recurrence relation as described above, with $a_1 = 3$. Find the value of $\dfrac{ |a_{20} - a_{15} | }{18133}$.

**Bonus**: Generalize this for all values of $a_n$.

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