# An algebra problem by Budi Utomo

Algebra Level 4

$\small {2016 \choose 0}{2016 \choose 1} + {2016 \choose 1}{2016 \choose 2} + {2016 \choose 2}{2016 \choose 3} + \cdots + {2016 \choose 2015}{2016 \choose 2016}$

If the sum above can be expressed as $\displaystyle {\ a \ \choose \ b \ }$ where $a, b$ are non-negative integers and $b \le a$, find the smallest possible value of $a+b$.

Notation: $\displaystyle { \ M \ \choose \ N \ } = \dfrac {M!}{N!(M-N)!}$ denotes the binomial coefficient.

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