a(n) = (n*10^n - n + 9)/9.

Terms

a(0) =1a(1) =2a(2) =23a(3) =334a(4) =4445a(5) =55556a(6) =666667a(7) =7777778a(8) =88888889a(9) =1000000000a(10) =11111111111a(11) =122222222222