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

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =1a(6) =2a(7) =6a(8) =25a(9) =123a(10) =731a(11) =5090a(12) =40595a(13) =364650a(14) =3641903a(15) =40026609a(16) =480029801a(17) =6237662582a(18) =87298953249