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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (24,-192,512).
Programs
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GAP
List([0..30], n-> 8^n*n*(n+1)); # G. C. Greubel, May 11 2019
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Magma
[(n^2+n)*8^n: n in [0..30]]; // Vincenzo Librandi, Feb 28 2013
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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 *) -
PARI
a(n)=(n^2+n)*8^n \\ Charles R Greathouse IV, Feb 28 2013
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Sage
[8^n*n*(n+1) for n in (0..30)] # G. C. Greubel, May 11 2019
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)