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\sum_(n=0)^(\infty ) (((1 - 2 n - 4 ) \Gamma (-1 + ((1)/(4) + n + n^(2))/(n + 1)))/((1 + 2 n) (n + 1) \Gamma (1 + n) \Gamma (-n + ((1)/(4) + n + n^(2))/(n + 1))))
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