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Let S(n)=∑i=0n2i(ni)(n−i⌊n−i2⌋). S(n)=\sum_{i=0}^n 2^i{n\choose i}{n-i\choose \left\lfloor\frac{n-i}{2}\right\rfloor}. S(n)=i=0∑n2i(in)(⌊2n−i⌋n−i).
If S(2017)=(M2017)S(2017) = \dbinom{M}{2017} S(2017)=(2017M), find MMM.
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