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Sum[(2n+1)/(2n-1)*((2n-1)!!/(2n)!!)^2*(SetPrecision[1.6522295319699407/2,40])^n,{n,Infinity}]
Sum[(2n+1)/(2n-1)*((2n-1)!!/(2n)!!)^2*(SetPrecision[1.6522295319699407/2,40])^n,{n,Infinity}]
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