Count Distinct Sets

Alice writes a permutation P1, P2, P3, … PN of [1, 2, 3, … N] that follows the condition: Pi > Pi/2 for all i = 2 to N, is assumed to be an ‘amusing’ permutation. Note that ‘/’ denotes integer division. Alice wrote down all ‘amusing’ permutations on a sheet of paper. For each number from i = 1 to N, she defines a set Si. A number j belongs to Si if number i was at jth position in at-least one