A116164 a(n) = 6^n * n*(n+1).

0, 12, 216, 2592, 25920, 233280, 1959552, 15676416, 120932352, 906992640, 6651279360, 47889211392, 339578044416, 2377046310912, 16456474460160, 112844396298240, 767341894828032, 5179557790089216, 34733505180598272

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (18,-108,216).

Formula

G.f.: 12*x/(1-6*x)^3. - Vincenzo Librandi, Feb 28 2013

a(n) = 18*a(n-1) - 108*a(n-2) + 216*a(n-3). - Vincenzo Librandi, Feb 28 2013

a(n) = 12*A081136(n+1). - Bruno Berselli, Feb 28 2013

E.g.f.: 12*x*(1 + 3*x)*exp(6*x). - G. C. Greubel, May 10 2019

From Amiram Eldar, Jul 20 2020: (Start)

Sum_{n>=1} 1/a(n) = 1 - 5*log(6/5).

Sum_{n>=1} (-1)^(n+1)/a(n) = 7*log(7/6) - 1. (End)

Mathematica

Table[(n^2 + n) 6^n, {n, 0, 30}] (* or *) CoefficientList[Series[12 x/(1 - 6 x)^3, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 28 2013 *)

Prog

(Magma) [(n^2+n)*6^n: n in [0..30]]; /* or */ I:=[0, 12, 216]; [n le 3 select I[n] else 18*Self(n-1)-108*Self(n-2)+216*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 28 2013
(PARI) a(n)=(n^2+n)*6^n \\ Charles R Greathouse IV, Feb 28 2013
(Sage) [6^n*n*(n+1) for n in (0..30)] # G. C. Greubel, May 10 2019
(GAP) List([0..30], n-> 6^n*n*(n+1) ) # G. C. Greubel, May 10 2019

Crossrefs

Cf. A007758, A036289, A081136, A128796.

Sequence in context: A276245 A241225 A274956 * A268369 A091266 A119309

Adjacent sequences: A116161 A116162 A116163 * A116165 A116166 A116167

Keyword

nonn,easy

Author

Mohammad K. Azarian, Apr 08 2007

Status

approved