a(n) = Sum_{k=0..floor(n/5)} (-1)^k * (n-4*k)!/(n-5*k)!.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =0a(6) =-1a(7) =-2a(8) =-3a(9) =-4a(10) =-3a(11) =0a(12) =5a(13) =12a(14) =21a(15) =26a(16) =21a(17) =0a(18) =-43a(19) =-114a(20) =-195a(21) =-244a(22) =-195a(23) =42a(24) =581a(25) =1440a(26) =2421a(27) =2990a(28) =2157a(29) =-1644