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A053540
a(n) = n*9^(n-1).
8
1, 18, 243, 2916, 32805, 354294, 3720087, 38263752, 387420489, 3874204890, 38354628411, 376572715308, 3671583974253, 35586121596606, 343151886824415, 3294258113514384, 31501343210481297, 300189270593998242, 2851798070642983299, 27017034353459841780
OFFSET
1,2
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)
MATHEMATICA
f[n_]:=n*9^(n-1); f[Range[40]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)
PROG
(Magma) [n*9^(n-1): n in [1..20]]; // Vincenzo Librandi, Jun 11 2011
(PARI) a(n)=n*9^(n-1) \\ Charles R Greathouse IV, Oct 07 2015
(Sage) [n*9^(n-1) for n in (1..20)] # G. C. Greubel, May 16 2019
(GAP) List([1..20], n-> n*9^(n-1)) # G. C. Greubel, May 16 2019
CROSSREFS
Related to computing A023052.
Sequence in context: A021064 A181379 A080629 * A080601 A333298 A016186
KEYWORD
nonn,easy
AUTHOR
Barry E. Williams, Jan 15 2000
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
STATUS
approved