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A036294 a(n) = n*8^n.

%I A036294 #20 Sep 09 2024 16:40:26
%S A036294 0,8,128,1536,16384,163840,1572864,14680064,134217728,1207959552,
%T A036294 10737418240,94489280512,824633720832,7146825580544,61572651155456,
%U A036294 527765581332480,4503599627370496,38280596832649216,324259173170675712,2738188573441261568,23058430092136939520
%N A036294 a(n) = n*8^n.
%H A036294 Vincenzo Librandi, <a href="/A036294/b036294.txt">Table of n, a(n) for n = 0..1000</a>
%H A036294 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-64).
%F A036294 From _Vincenzo Librandi_, Aug 09 2017: (Start)
%F A036294 G.f.: 8*x/(8*x-1)^2.
%F A036294 a(n) = 16*a(n-1) - 64*a(n-2) for n > 1. (End)
%F A036294 From _Amiram Eldar_, Jul 20 2020: (Start)
%F A036294 Sum_{n>=1} 1/a(n) = log(8/7).
%F A036294 Sum_{n>=1} (-1)^(n+1)/a(n) = log(9/8). (End)
%F A036294 From _Elmo R. Oliveira_, Sep 09 2024: (Start)
%F A036294 E.g.f.: 8*x*exp(8*x).
%F A036294 a(n) = n*A001018(n) = 8*A053539(n). (End)
%t A036294 Table[n 7^n, {n, 0, 30}] (* or *) LinearRecurrence[{16,-64},{0,8},31] (* _Vincenzo Librandi_, Aug 09 2017 *)
%o A036294 (Magma) [n*8^n: n in [0..20]]; // _Vincenzo Librandi_, Aug 09 2017
%Y A036294 Cf. A001018, A053539.
%K A036294 nonn,easy
%O A036294 0,2
%A A036294 _N. J. A. Sloane_