P_n(3) (see A155100).

Terms

a(0) =1a(1) =3a(2) =10a(3) =60a(4) =560a(5) =6960a(6) =108160a(7) =2016960a(8) =43880960a(9) =1091055360a(10) =30518978560a(11) =948529167360