a(n) = 1 + ((1+(-1)^(n-1))*(n-1)!)/(n+1).

Terms

a(0) =2a(1) =1a(2) =2a(3) =1a(4) =9a(5) =1a(6) =181a(7) =1a(8) =8065a(9) =1a(10) =604801a(11) =1a(12) =68428801a(13) =1a(14) =10897286401a(15) =1a(17) =1a(19) =1a(21) =1a(23) =1a(25) =1a(27) =1a(29) =1