The number of partitions of [n] into a set of irreducible balanced subsets.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =2a(7) =2a(8) =4a(9) =5a(10) =14a(11) =19a(12) =64a(13) =89a(14) =305a(15) =489a(16) =1947a(17) =3122a(18) =13352a(19) =22777a(20) =111333a(21) =189016a(22) =1026737a(23) =1761266a(24) =11107110a(25) =18557581a(26) =131349930a(27) =218008848a(28) =1773125055a(29) =2850048230