a(n) = Sum_{k=0..floor(n/4)} |Stirling1(n - 3*k,n - 4*k)|.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =4a(7) =7a(8) =11a(9) =18a(10) =33a(11) =64a(12) =122a(13) =227a(14) =428a(15) =838a(16) =1684a(17) =3396a(18) =6841a(19) =13912a(20) =28787a(21) =60398a(22) =127559a(23) =270687a(24) =579055a(25) =1251706a(26) =2730345a(27) =5994501a(28) =13238058a(29) =29436628