a(n) = Stirling2(n, ceiling(n/2)).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =7a(5) =25a(6) =90a(7) =350a(8) =1701a(9) =6951a(10) =42525a(11) =179487a(12) =1323652a(13) =5715424a(14) =49329280a(15) =216627840a(16) =2141764053a(17) =9528822303a(18) =106175395755a(19) =477297033785