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

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =6a(5) =35a(6) =226a(7) =1645a(8) =13454a(9) =122661a(10) =1236018a(11) =13656951a(12) =164290182a(13) =2138379243a(14) =29949509226a(15) =449188719525