Question: * 11. A particle performs a random walk on the integers starting at the origin. At discrete intervals of time, it takes a step of

* 11. A particle performs a random walk on the integers starting at the origin. At discrete intervals of time, it takes a step of unit size. The steps are independent and equally likely to be in the positive or negative direction. Determine the probability generating function of the time at which the particle first reaches the integer n (≥ 1).

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