a(n) = Sum_{k=0..floor(n/5)} Stirling1(n - 4*k,k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =-1a(7) =2a(8) =-6a(9) =24a(10) =-119a(11) =717a(12) =-5029a(13) =40270a(14) =-362606a(15) =3627037a(16) =-39903738a(17) =478892051a(18) =-6225994449a(19) =87167664184