A048041 Number of nonempty subsets of {1,2,...,n} in which exactly 1/4 of the elements are <= (n+1)/3.

0, 0, 0, 1, 2, 8, 20, 30, 63, 126, 182, 392, 844, 1270, 2800, 5995, 9020, 19595, 41951, 63518, 138866, 299411, 455966, 997640, 2154104, 3290520, 7201692, 15584085, 23878212, 52311408, 113406028, 174179258, 381766253, 828748052