A053540 a(n) = n*9^(n-1).
1, 18, 243, 2916, 32805, 354294, 3720087, 38263752, 387420489, 3874204890, 38354628411, 376572715308, 3671583974253, 35586121596606, 343151886824415, 3294258113514384, 31501343210481297, 300189270593998242, 2851798070642983299, 27017034353459841780
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..300
- Frank Ellermann, Illustration of binomial transforms.
- Index entries for linear recurrences with constant coefficients, signature (18,-81).
Programs
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GAP
List([1..20], n-> n*9^(n-1)); # G. C. Greubel, May 16 2019
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Magma
[n*9^(n-1): n in [1..20]]; // Vincenzo Librandi, Jun 11 2011
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Mathematica
f[n_]:=n*9^(n-1); f[Range[40]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)
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PARI
a(n)=n*9^(n-1) \\ Charles R Greathouse IV, Oct 07 2015
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Sage
[n*9^(n-1) for n in (1..20)] # G. C. Greubel, May 16 2019
Formula
From Colin Barker, Oct 17 2012: (Start)
a(n) = 18*a(n-1) - 81*a(n-2).
G.f.: x/(1-9*x)^2. (End)
E.g.f.: x*exp(9*x). - G. C. Greubel, May 16 2019
From Amiram Eldar, Oct 28 2020: (Start)
Sum_{n>=1} 1/a(n) = 9*log(9/8).
Sum_{n>=1} (-1)^(n+1)/a(n) = 9*log(10/9). (End)
Extensions
More terms from Larry Reeves (larryr(AT)acm.org), May 29 2001
Edited by N. J. A. Sloane at the suggestion of Reinhard Zumkeller, Sep 16 2007