a(n) = Sum_{k=0..floor(n/3)} Stirling1(n - 2*k,k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =1a(4) =-1a(5) =2a(6) =-5a(7) =21a(8) =-109a(9) =671a(10) =-4772a(11) =38591a(12) =-350036a(13) =3520830a(14) =-38903271a(15) =468490350a(16) =-6107642906a(17) =85704534787