a(n) = Sum_{k=0..floor(n/2)} Stirling2(k,n - 2*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =0a(5) =1a(6) =1a(7) =1a(8) =3a(9) =2a(10) =7a(11) =7a(12) =16a(13) =26a(14) =41a(15) =92a(16) =128a(17) =317a(18) =478a(19) =1107a(20) =1977a(21) =4077a(22) =8547a(23) =16310a(24) =37775a(25) =71489a(26) =170660a(27) =339138a(28) =795833a(29) =1705058