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

Terms

a(0) =0a(1) =1a(2) =1a(3) =7a(4) =51a(5) =521a(6) =6665a(7) =102943a(8) =1864135a(9) =38742049a(10) =909090909a(11) =23775972551a(12) =685853880635