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A053540 a(n) = n*9^(n-1).

%I A053540 #48 Aug 15 2025 22:42:50
%S A053540 1,18,243,2916,32805,354294,3720087,38263752,387420489,3874204890,
%T A053540 38354628411,376572715308,3671583974253,35586121596606,
%U A053540 343151886824415,3294258113514384,31501343210481297,300189270593998242,2851798070642983299,27017034353459841780
%N A053540 a(n) = n*9^(n-1).
%H A053540 Vincenzo Librandi, <a href="/A053540/b053540.txt">Table of n, a(n) for n = 1..300</a>
%H A053540 Frank Ellermann, <a href="/A001792/a001792.txt">Illustration of binomial transforms</a>.
%H A053540 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-81).
%F A053540 From _Colin Barker_, Oct 17 2012: (Start)
%F A053540 a(n) = 18*a(n-1) - 81*a(n-2).
%F A053540 G.f.: x/(1-9*x)^2. (End)
%F A053540 E.g.f.: x*exp(9*x). - _G. C. Greubel_, May 16 2019
%F A053540 From _Amiram Eldar_, Oct 28 2020: (Start)
%F A053540 Sum_{n>=1} 1/a(n) = 9*log(9/8).
%F A053540 Sum_{n>=1} (-1)^(n+1)/a(n) = 9*log(10/9). (End)
%t A053540 f[n_]:=n*9^(n-1); f[Range[40]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011*)
%o A053540 (Magma) [n*9^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Jun 11 2011
%o A053540 (PARI) a(n)=n*9^(n-1) \\ _Charles R Greathouse IV_, Oct 07 2015
%o A053540 (Sage) [n*9^(n-1) for n in (1..20)] # _G. C. Greubel_, May 16 2019
%o A053540 (GAP) List([1..20], n-> n*9^(n-1)); # _G. C. Greubel_, May 16 2019
%Y A053540 Related to computing A023052.
%Y A053540 Cf. A001787, A053464, A053469.
%K A053540 nonn,easy
%O A053540 1,2
%A A053540 _Barry E. Williams_, Jan 15 2000
%E A053540 More terms from Larry Reeves (larryr(AT)acm.org), May 29 2001
%E A053540 Edited by _N. J. A. Sloane_ at the suggestion of _Reinhard Zumkeller_, Sep 16 2007