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

Terms

a(0) =0a(1) =2a(2) =6a(3) =52a(4) =520a(5) =6666a(6) =102942a(7) =1864136a(8) =38742048a(9) =909090910a(10) =23775972550a(11) =685853880636