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I would like to Maximize this fairly simple expression

Maximize[{2^(-1-n)*(1+k)^(-1-n)*(1+2k)^(-1+n)*(-1 - 2 k + n)*(-2 k + n),k<=n/2, k>=1},
         {n,k}, Integers]

However Mathematica just returns the query. What's the right way to do this?

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Try NMaximize.

Maximize[{2^(-1-n)(1+k)^(-1-n)(1+2k)^(-1+n)(-1 - 2 k + n)(-2 k + n),k<=n/2, k>=1},{n,k}]
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    $\begingroup$ What result do you get? $\endgroup$ – Dr. belisarius Apr 7 '14 at 19:36

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