Binomial Summation

Probability Level 3

a=r=0n[1(nr)]. a = \displaystyle \sum_{r=0}^n \left [\dfrac1{\binom nr} \right ] .

Find the value of

r=0n[r(nr)] \sum_{r=0}^n \left [\dfrac r{\binom nr} \right ]

in terms of aa and nn.

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