a(n) = Sum_{k=0..floor(n/4)} Stirling2(k,n - 4*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =0a(7) =0a(8) =0a(9) =1a(10) =1a(11) =0a(12) =0a(13) =1a(14) =3a(15) =1a(16) =0a(17) =1a(18) =7a(19) =6a(20) =1a(21) =1a(22) =15a(23) =25a(24) =10a(25) =2a(26) =31a(27) =90a(28) =65a(29) =16