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A036293 a(n) = n*7^n.

%I A036293 #29 Sep 09 2024 16:40:23
%S A036293 0,7,98,1029,9604,84035,705894,5764801,46118408,363182463,2824752490,
%T A036293 21750594173,166095446412,1259557135291,9495123019886,71213422649145,
%U A036293 531726889113616,3954718737782519,29311444762388082,216579008522089717,1595845325952240020,11729463145748964147
%N A036293 a(n) = n*7^n.
%H A036293 Vincenzo Librandi, <a href="/A036293/b036293.txt">Table of n, a(n) for n = 0..1000</a>
%H A036293 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-49).
%F A036293 From _Harvey P. Dale_, Aug 08 2011: (Start)
%F A036293 a(n) = 14*a(n-1) - 49*a(n-2) with a(0)=0 and a(1)=7.
%F A036293 G.f.: (7*x)/(7*x-1)^2. (End)
%F A036293 From _Amiram Eldar_, Jul 20 2020: (Start)
%F A036293 Sum_{n>=1} 1/a(n) = log(7/6).
%F A036293 Sum_{n>=1} (-1)^(n+1)/a(n) = log(8/7). (End)
%F A036293 From _Elmo R. Oliveira_, Sep 09 2024: (Start)
%F A036293 E.g.f.: 7*x*exp(7*x).
%F A036293 a(n) = n*A000420(n). (End)
%t A036293 Table[n 7^n,{n,0,30}] (* or *) LinearRecurrence[{14,-49},{0,7},31] (* _Harvey P. Dale_, Aug 08 2011 *)
%o A036293 (Magma) [n*7^n: n in [0..20]] ; // _Vincenzo Librandi_, Aug 09 2011
%Y A036293 Cf. A000420.
%K A036293 nonn,easy
%O A036293 0,2
%A A036293 _N. J. A. Sloane_