# Combinatorial Sum

Discrete Mathematics Level 4

$\sum_{r=1}^{n}r^3 {n \choose r} = 2^{n-3}\left(n^3+an^2+bn+c\right)$

Find the value of $$a^2+b^2+c^2$$ if the above equation is true for all integers $$r$$ and $$n$$.

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