A116176 a(n) = 9^n * n*(n+1).
0, 18, 486, 8748, 131220, 1771470, 22320522, 267846264, 3099363912, 34867844010, 383546284110, 4142299868388, 44059007691036, 462619580755878, 4804126415541810, 49413871702715760, 504021491367700752
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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GAP
List([0..20], n-> 9^n*n*(n+1)); # G. C. Greubel, May 11 2019
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Magma
[(n^2+n)*9^n: n in [0..20]]; // Vincenzo Librandi, Feb 28 2013
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Mathematica
Table[(n^2 + n) 9^n, {n, 0, 20}] (* Vincenzo Librandi, Feb 28 2013 *) -
PARI
{a(n) = 9^n*n*(n+1)}; \\ G. C. Greubel, May 11 2019 -
Sage
[9^n*n*(n+1) for n in (0..20)] # G. C. Greubel, May 11 2019
Formula
G.f.: 18*x/(1-9*x)^3. - Vincenzo Librandi, Feb 28 2013
a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3). - Vincenzo Librandi, Feb 28 2013
a(n) = 18*A081139(n+1). - Bruno Berselli, Mar 01 2013
E.g.f.: 9*x*(2 + 9*x)*exp(9*x). - G. C. Greubel, May 11 2019
From Amiram Eldar, Jul 20 2020: (Start)
Sum_{n>=1} 1/a(n) = 1 - 8*log(9/8).
Sum_{n>=1} (-1)^(n+1)/a(n) = 10*log(10/9) - 1. (End)