a(n) = n*(1 + n)*(10^n - 1)/18.

Terms

a(0) =0a(1) =1a(2) =33a(3) =666a(4) =11110a(5) =166665a(6) =2333331a(7) =31111108a(8) =399999996a(9) =4999999995a(10) =61111111105a(11) =733333333326