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) =2a(5) =6a(6) =16a(7) =36a(8) =211a(9) =1387a(10) =6511a(11) =23431a(12) =225721a(13) =2207921a(14) =14610597a(15) =71848141a(16) =958259121a(17) =12403693681a(18) =105819536881a(19) =659686502257