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%I #16 Sep 08 2022 08:44:52
%S 0,8,128,1536,16384,163840,1572864,14680064,134217728,1207959552,
%T 10737418240,94489280512,824633720832,7146825580544,61572651155456,
%U 527765581332480,4503599627370496,38280596832649216,324259173170675712,2738188573441261568,23058430092136939520
%N a(n) = n * 8^n.
%H Vincenzo Librandi, <a href="/A036294/b036294.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-64).
%F G.f.: 8*x / (8*x-1)^2. - _Vincenzo Librandi_, Aug 09 2017
%F a(n) = 16*a(n-1)-64*a(n-2). - _Vincenzo Librandi_, Aug 09 2017
%F From _Amiram Eldar_, Jul 20 2020: (Start)
%F Sum_{n>=1} 1/a(n) = log(8/7).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = log(9/8). (End)
%t Table[n 7^n, {n, 0, 30}] (* or *) LinearRecurrence[{16,-64},{0,8},31] (* _Vincenzo Librandi_, Aug 09 2017 *)
%o (Magma) [n*8^n: n in [0..20]]; // _Vincenzo Librandi_, Aug 09 2017
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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