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

1,2

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).

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.

Cf. A001787, A053464, A053469.

Sequence in context: A021064 A181379 A080629 * A080601 A333298 A016186

Adjacent sequences: A053537 A053538 A053539 * A053541 A053542 A053543

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