A048091 Number of nonempty subsets of {1,2,...,n} in which exactly 1/6 of the elements are <= (n+3)/3.

0, 0, 0, 0, 0, 0, 0, 3, 4, 24, 84, 105, 280, 630, 756, 1527, 2937, 3465, 6930, 15015, 18304, 44044, 108164, 135219, 328944, 767244, 953360, 2152710, 4738410, 5848238, 12890614, 28583709, 35471919, 80628669, 184657869