From the game of Mousetrap.

Terms

a(0) =0a(1) =0a(2) =0a(3) =2a(4) =8a(5) =42a(6) =256a(7) =1810a(8) =14568a(9) =131642a(10) =1320128a(11) =14551074a(12) =174879880a(13) =2276108362a(14) =31894886208a(15) =478775722802