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) =-224a(7) =1603a(8) =-12810a(9) =113589a(10) =-1109472a(11) =11852841a(12) =-137611110a(13) =1726238787a(14) =-23277264192a(15) =335861699355