A048088 Number of nonempty subsets of {1,2,...,n} in which exactly 2/5 of the elements are <= (n+3)/3.

0, 0, 0, 0, 1, 3, 12, 30, 60, 121, 217, 385, 700, 1260, 2521, 4960, 9460, 20020, 38500, 71071, 148161, 276549, 503685, 1071525, 2006508, 3681588, 8013256, 14981556, 27412041, 60042147, 111406614, 202871284, 447617884, 828004144