A128803 a(n) = n*(n-1)*9^n.
0, 0, 162, 4374, 78732, 1180980, 15943230, 200884698, 2410616376, 27894275208, 313810596090, 3451916556990, 37280698815492, 396531069219324, 4163576226802902, 43237137739876290, 444724845324441840
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (27,-243,729).
Programs
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Magma
[(n^2-n)*9^n: n in [0..25]]; // Vincenzo Librandi, Feb 12 2013
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Magma
I:=[0,0,162]; [n le 3 select I[n] else 27*Self(n-1)-243*Self(n-2)+729*Self(n-3): n in [1..25]]; // Vincenzo Librandi, Feb 12 2013
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Mathematica
LinearRecurrence[{27, -243, 729}, {0, 0, 162}, 30] (* or *) CoefficientList[Series[162 x^2/(1 - 9 x)^3, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)
Formula
From Vincenzo Librandi, Feb 12 2013: (Start)
G.f.: 162*x^2/(1-9*x)^3.
a(n) = 27*a(n-1)-243*a(n-2)+729*a(n-3). (End)
a(n) = 162*A081139(n). - R. J. Mathar, Apr 26 2015
From Amiram Eldar, Jun 26 2025: (Start)
Sum_{n>=2} 1/a(n) = 1/9 - (8/9)*log(9/8).
Sum_{n>=2} (-1)^n/a(n) = (10/9)*log(10/9) - 1/9. (End)