a(1)=0, a(2)=1; for n>2, a(n) = C(n,2)*(1+a(n-2)).

Terms

a(0) =0a(1) =1a(2) =3a(3) =12a(4) =40a(5) =195a(6) =861a(7) =5488a(8) =31032a(9) =247005a(10) =1706815a(11) =16302396a(12) =133131648a(13) =1483518127a(14) =13978823145a(15) =178022175360