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
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