a(n) = floor( (10^n - 1) / (9*n) ).

Terms

a(0) =1a(1) =5a(2) =37a(3) =277a(4) =2222a(5) =18518a(6) =158730a(7) =1388888a(8) =12345679a(9) =111111111a(10) =1010101010a(11) =9259259259a(12) =85470085470a(13) =793650793650