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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (18,-108,216).
Programs
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GAP
List([0..30], n-> 6^n*n*(n+1) ); # G. C. Greubel, May 10 2019
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Magma
[(n^2+n)*6^n: n in [0..30]]; // Vincenzo Librandi, Feb 28 2013
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Magma
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
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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 *) -
PARI
a(n)=(n^2+n)*6^n \\ Charles R Greathouse IV, Feb 28 2013
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Sage
[6^n*n*(n+1) for n in (0..30)] # G. C. Greubel, May 10 2019
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)