a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-2*k)!/(n-3*k)!.

Terms

a(0) =1a(1) =1a(2) =1a(3) =0a(4) =-1a(5) =-2a(6) =-1a(7) =2a(8) =7a(9) =8a(10) =-1a(11) =-26a(12) =-49a(13) =-28a(14) =103a(15) =314a(16) =359a(17) =-344a(18) =-2113a(19) =-3682a(20) =-161a(21) =14684a(22) =36791a(23) =25762a(24) =-100297a(25) =-373456a(26) =-472241a(27) =587846a(28) =3877487a(29) =7149988