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

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =2a(7) =12a(8) =18a(9) =63a(10) =168a(11) =224a(12) =504a(13) =1014a(14) =1270a(15) =2420a(16) =4620a(17) =5742a(18) =12012a(19) =27027a(20) =35035a(21) =84119a(22) =199304a(23) =260064a(24) =601664a(25) =1339464a(26) =1720944a(27) =3755844a(28) =8093214a(29) =10329750