(10^n-1) * (n+9) / 9.

Terms

a(0) =0a(1) =10a(2) =121a(3) =1332a(4) =14443a(5) =155554a(6) =1666665a(7) =17777776a(8) =188888887a(9) =1999999998a(10) =21111111109a(11) =222222222220