a(n) = A000166(n)*binomial(n+1,2).

Terms

a(0) =0a(1) =0a(2) =3a(3) =12a(4) =90a(5) =660a(6) =5565a(7) =51912a(8) =533988a(9) =6007320a(10) =73422855a(11) =969181620a(12) =13744757598a(13) =208462156812