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

Terms

a(0) =1a(1) =1a(2) =1a(3) =-1a(4) =-5a(5) =-11a(6) =-7a(7) =31a(8) =139a(9) =245a(10) =-71a(11) =-1937a(12) =-5989a(13) =-6251a(14) =25945a(15) =144479a(16) =304843a(17) =-177899a(18) =-3517351a(19) =-11743505a(20) =-10097381a(21) =81902453a(22) =433558201a(23) =840235039a(24) =-1481279605a(25) =-15839941451a(26) =-48073840007a(27) =-8454966289a(28) =564429256219