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

Terms

a(0) =2a(1) =1a(2) =3a(3) =8a(4) =33a(5) =164a(6) =985a(7) =6894a(8) =55153a(9) =496376a(10) =4963761a(11) =54601370a(12) =655216441a(13) =8517813732a(14) =119249392249