A116166 a(n) = 8^n * n*(n+1).

0, 16, 384, 6144, 81920, 983040, 11010048, 117440512, 1207959552, 12079595520, 118111600640, 1133871366144, 10720238370816, 100055558127616, 923589767331840, 8444249301319680, 76561193665298432, 689050742987685888

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (24,-192,512).

Formula

G.f.: 16*x/(1-8*x)^3. - Vincenzo Librandi, Feb 28 2013

a(n) = 24*a(n-1) - 192*a(n-2) + 512*a(n-3). - Vincenzo Librandi, Feb 28 2013

a(n) = 16*A081138(n+1). - Bruno Berselli, Feb 28 2013

E.g.f.: 16*x*(1 + 4*x)*exp(8*x). - G. C. Greubel, May 11 2019

From Amiram Eldar, Jul 20 2020: (Start)

Sum_{n>=1} 1/a(n) = 1 - 7*log(8/7).

Sum_{n>=1} (-1)^(n+1)/a(n) = 9*log(9/8) - 1. (End)

Mathematica

Table[(n^2 + n) 8^n, {n, 0, 30}]  (* Harvey P. Dale, Mar 09 2011 *)
CoefficientList[Series[16 x/(1 - 8 x)^3, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 28 2013 *)

Prog

(Magma) [(n^2+n)*8^n: n in [0..30]]; // Vincenzo Librandi, Feb 28 2013
(PARI) a(n)=(n^2+n)*8^n \\ Charles R Greathouse IV, Feb 28 2013
(Sage) [8^n*n*(n+1) for n in (0..30)] # G. C. Greubel, May 11 2019
(GAP) List([0..30], n-> 8^n*n*(n+1)) # G. C. Greubel, May 11 2019

Crossrefs

Cf. A007758, A036289, A081138, A128796.

Sequence in context: A302962 A302805 A303466 * A034976 A114426 A189849

Adjacent sequences: A116163 A116164 A116165 * A116167 A116168 A116169

Keyword

nonn,easy

Author

Mohammad K. Azarian, Apr 08 2007

Status

approved