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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (18,-81).
Crossrefs
Programs
-
Magma
[n*9^n: n in [0..20]]; // Vincenzo Librandi, Feb 25 2014
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Mathematica
Table[n 9^n, {n, 0, 20}] (* Vincenzo Librandi, Feb 25 2014 *) -
PARI
a(n) = n*9^n; \\ Joerg Arndt, Feb 23 2014
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