a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-3*k)!/(n-4*k)!.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =0a(5) =-1a(6) =-2a(7) =-3a(8) =-2a(9) =1a(10) =6a(11) =13a(12) =16a(13) =9a(14) =-14a(15) =-59a(16) =-108a(17) =-119a(18) =-26a(19) =261a(20) =736a(21) =1177a(22) =1026a(23) =-731a(24) =-4964a(25) =-11079a(26) =-14978a(27) =-6299a(28) =30024a(29) =102841