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

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =25a(5) =125a(6) =750a(7) =5250a(8) =42001a(9) =378009a(10) =3780090a(11) =41580990a(12) =498971881a(13) =6486634453a(14) =90812882342