%I #25 Sep 08 2022 08:45:29
%S 0,10,200,3000,40000,500000,6000000,70000000,800000000,9000000000,
%T 100000000000,1100000000000,12000000000000,130000000000000,
%U 1400000000000000,15000000000000000,160000000000000000
%N a(n) = n * 10^n.
%H Vincenzo Librandi, <a href="/A126431/b126431.txt">Table of n, a(n) for n = 0..100</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-100).
%F a(0)=0, a(1)=10; for n>1, a(n) = 20*a(n-1) - 100*a(n-2). - _Harvey P. Dale_, Mar 30 2012
%F G.f.: 10*x/(1 - 10*x)^2. - _Vincenzo Librandi_, Sep 09 2014
%F From _Amiram Eldar_, Jul 20 2020: (Start)
%F Sum_{n>=1} 1/a(n) = log(10/9).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = log(11/10). (End)
%p A126431 := proc(n) n*10^n ; end proc: # _Bruno Berselli_, Sep 09 2014
%t Table[n 10^n,{n,0,20}] (* or *) LinearRecurrence[{20,-100},{0,10},20] (* _Harvey P. Dale_, Mar 30 2012 *)
%t CoefficientList[Series[10 x/(1 - 10 x)^2, {x, 0, 20}], x] (* _Vincenzo Librandi_, Sep 09 2014 *)
%o (Magma) [n*10^n: n in [0..20]]; // _Vincenzo Librandi_, Sep 09 2014
%o (PARI) a(n)=n*10^n \\ _Charles R Greathouse IV_, Oct 07 2015
%K nonn,easy
%O 0,2
%A Jonathan R. Love (japanada11(AT)yahoo.ca), Mar 11 2007
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