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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =3a(7) =4a(8) =5a(9) =6a(10) =9a(11) =14a(12) =21a(13) =30a(14) =41a(15) =60a(16) =93a(17) =146a(18) =225a(19) =336a(20) =509a(21) =798a(22) =1281a(23) =2060a(24) =3261a(25) =5154a(26) =8273a(27) =13536a(28) =22365a(29) =36806