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let's fix a positive integer n. for a nonnegative integer k, let ak be the number...

let's fix a positive integer n. for a nonnegative integer k, let ak be the number of ways to distribute k indistinguishable balls into n distinguishable bins so that an even number of balls are placed in each bin (allowing empty bins). The generating function for sequence ak is given as 1/F(x). Find F(x).

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