A048038 Number of nonempty subsets of {1,2,...,n} in which exactly 1/2 of the elements are <= (n+1)/3.

0, 1, 2, 3, 9, 14, 20, 55, 83, 119, 329, 494, 714, 2001, 3002, 4367, 12375, 18563, 27131, 77519, 116279, 170543, 490313, 735470, 1081574, 3124549, 4686824, 6906899, 20030009, 30045014, 44352164, 129024479, 193536719, 286097759