n! * Sum[k=1..ceiling(n/2), 1/k].

Terms

a(0) =1a(1) =2a(2) =9a(3) =36a(4) =220a(5) =1320a(6) =10500a(7) =84000a(8) =828576a(9) =8285760a(10) =97796160a(11) =1173553920a(12) =16145775360a(13) =226040855040