%I #32 Feb 23 2026 23:06:15

%S 0,9,162,2187,26244,295245,3188646,33480783,344373768,3486784401,

%T 34867844010,345191655699,3389154437772,33044255768277,

%U 320275094369454,3088366981419735,29648323021629456,283512088894331673,2701703435345984178,25666182635786849691,243153309181138576020

%N a(n) = n*9^n.

%C a(n) is the number of positive integers of n+1 digits written with only one zero in base ten. - _Jamil Silva_, Feb 06 2026

%H Vincenzo Librandi, <a href="/A158749/b158749.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-81).

%F a(n) = n*9^n.

%F From _R. J. Mathar_, Mar 26 2009: (Start)

%F a(n) = 18*a(n-1) - 81*a(n-2) = A038299(n,1).

%F G.f.: 9*x/(1-9*x)^2. (End)

%F a(n) = A001019(n)*n. - _Omar E. Pol_, Mar 26 2009

%F From _Amiram Eldar_, Jul 20 2020: (Start)

%F Sum_{n>=1} 1/a(n) = log(9/8).

%F Sum_{n>=1} (-1)^(n+1)/a(n) = log(10/9). (End)

%F E.g.f.: 9*x*exp(9*x). - _Elmo R. Oliveira_, Sep 09 2024

%t Table[n 9^n, {n, 0, 20}] (* _Vincenzo Librandi_, Feb 25 2014 *)

%t LinearRecurrence[{18,-81},{0,9},30] (* _Harvey P. Dale_, Dec 27 2025 *)

%o (PARI) a(n) = n*9^n; \\ _Joerg Arndt_, Feb 23 2014

%o (Magma) [n*9^n: n in [0..20]]; // _Vincenzo Librandi_, Feb 25 2014

%Y Cf. A001019, A018215, A036289, A036290, A036291, A036292, A036293, A036294.

%Y Cf. A038299, A126431.

%K nonn,easy

%O 0,2

%A _Zerinvary Lajos_, Mar 25 2009