Random walk absorption

You have a row of n cells indexed 0..n-1. A token starts at cell s. Each step it moves left or right by one cell, each with probability 1/2, EXCEPT at the two ends which are absorbing: cell 0 and cell n-1 stop the walk. Return the expected number of steps until absorption, rounded to 6 decimal places. Constraints: 2 <= n <= 100000, 0 <= s <= n-1. (For an interior start the answer has the closed form s*(n-1-s).)