a(n) = n! * Sum_{k=0..floor(n/4)} (-k/24)^k / (k! * (n-4*k)!).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =0a(5) =-4a(6) =-14a(7) =-34a(8) =71a(9) =1135a(10) =6091a(11) =22771a(12) =-87119a(13) =-1847559a(14) =-13769755a(15) =-70046339a(16) =390688481a(17) =10473961121a(18) =100030347361a(19) =643972996705