An algebra problem by Budi Utomo

Algebra Level 4

(20160)(20161)+(20161)(20162)+(20162)(20163)++(20162015)(20162016)\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 ( a  b )\displaystyle {\ a \ \choose \ b \ } where a,ba, b are non-negative integers and bab \le a, find the smallest possible value of a+ba+b.

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

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