A158749 a(n) = n*9^n.

0, 9, 162, 2187, 26244, 295245, 3188646, 33480783, 344373768, 3486784401, 34867844010, 345191655699, 3389154437772, 33044255768277, 320275094369454, 3088366981419735, 29648323021629456, 283512088894331673, 2701703435345984178, 25666182635786849691, 243153309181138576020

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (18,-81).

Formula

a(n) = n*9^n.

From R. J. Mathar, Mar 26 2009: (Start)

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

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

a(n) = A001019(n)*n. - Omar E. Pol, Mar 26 2009

From Amiram Eldar, Jul 20 2020: (Start)

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

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

E.g.f.: 9*x*exp(9*x). - Elmo R. Oliveira, Sep 09 2024

Mathematica

Table[n 9^n, {n, 0, 20}] (* Vincenzo Librandi, Feb 25 2014 *)

Prog

(PARI) a(n) = n*9^n; \\ Joerg Arndt, Feb 23 2014
(Magma) [n*9^n: n in [0..20]]; // Vincenzo Librandi, Feb 25 2014

Crossrefs

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

Cf. A038299, A126431.

Sequence in context: A319197 A209962 A084874 * A300843 A133681 A157553

Adjacent sequences: A158746 A158747 A158748 * A158750 A158751 A158752

Keyword

nonn,easy

Author

Zerinvary Lajos, Mar 25 2009

Status

approved