a(n) = n*a(n-1) + (1/2)*(1+(-1)^n), a(0)=0.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =13a(5) =65a(6) =391a(7) =2737a(8) =21897a(9) =197073a(10) =1970731a(11) =21678041a(12) =260136493a(13) =3381774409a(14) =47344841727a(15) =710172625905