a(n) = ceiling((n+1/3)^n).

Terms

a(0) =2a(1) =6a(2) =38a(3) =353a(4) =4316a(5) =64535a(6) =1140539a(7) =23256804a(8) =537441242a(9) =13880477011a(10) =396218076728