Question: wrong taylor expansion result

taylor(1/(1+z^2), z = 1, 4)

The result is 

1/2-(1/2)*z-1+(1/4)*(z-1)^2+O((z-1)^4)

but in fact the result is 

1/2-(1/2)*(z-1)+(1/4)*(z-1)^2+O((z-1)^4)

my Maple is Maple 16,How to solve this problem?

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