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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

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OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (27,-243,729).

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)

MATHEMATICA

Table[(n^2 + n) 9^n, {n, 0, 20}] (* Vincenzo Librandi, Feb 28 2013 *)

PROG

(Magma) [(n^2+n)*9^n: n in [0..20]]; // Vincenzo Librandi, Feb 28 2013

(PARI) {a(n) = 9^n*n*(n+1)}; \\ G. C. Greubel, May 11 2019

(SageMath) [9^n*n*(n+1) for n in (0..20)] # G. C. Greubel, May 11 2019

(GAP) List([0..20], n-> 9^n*n*(n+1)); # G. C. Greubel, May 11 2019

CROSSREFS

Cf. A007758, A036289, A081139, A128796.

Sequence in context: A027405 A382404 A282477 * A035023 A180791 A384171

Adjacent sequences: A116173 A116174 A116175 * A116177 A116178 A116179

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian, Apr 08 2007

STATUS

approved

URL: https://oeis.org/A116176

⇱ A116176 - OEIS