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Help on simplifying symbolic sum?

Dear All,

I want to syplify some symbolic sum, such like the following one:
2nSum[a[i]^2, {i,1,n}] - 2(Sum[a[i], {i,1,n}])^2

Is should be simplifyed to Sum[(a[i]-a[j])^2, {i,1,n}, {j,1,n}].

Could anybody give me some hints about how to do it? Thanks a lot!

Best wishes!


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