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

Terms

a(0) =0a(1) =0a(2) =1a(3) =6a(4) =54a(5) =440a(6) =3975a(7) =38934a(8) =415324a(9) =4805856a(10) =60073245a(11) =807651350a(12) =11630179506a(13) =178681848696