A048083 Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= (n+3)/3.

0, 0, 0, 2, 6, 9, 21, 45, 70, 154, 322, 525, 1125, 2325, 3921, 8301, 17061, 29491, 61915, 126763, 223210, 465746, 950818, 1698453, 3527109, 7184421, 12981421, 26855641, 54604081, 99589963, 205390163, 416990563, 766466053, 1576646941