This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A014918 #29 Jun 01 2025 17:54:05
%S A014918 1,13,121,985,7465,54121,380713,2620201,17736745,118513705,783641641,
%T A014918 5137206313,33435376681,216285092905,1391747554345,8914707307561,
%U A014918 56873575734313,361553445739561,2291192622439465,14478387422649385,91257714663971881,573870628752284713,3601169817124428841
%N A014918 a(1)=1, a(n) = n*6^(n-1) + a(n-1).
%H A014918 Vincenzo Librandi, <a href="/A014918/b014918.txt">Table of n, a(n) for n = 1..1000</a>
%H A014918 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13,-48,36).
%F A014918 From _Vincenzo Librandi_, Oct 23 2012: (Start)
%F A014918 a(n) = 12*a(n-1) - 36*a(n-2) + 1, a(1)=1, a(2)=13.
%F A014918 G.f.: x/((1-x)*(1-6*x)^2). (End)
%F A014918 From _Elmo R. Oliveira_, May 15 2025: (Start)
%F A014918 E.g.f.: exp(x)*(1 + exp(5*x)*(30*x - 1))/25.
%F A014918 a(n) = (6^n*(5*n - 1) + 1)/25.
%F A014918 a(n) = 13*a(n-1) - 48*a(n-2) + 36*a(n-3) for n > 3. (End)
%p A014918 a:=n->sum (6^n-6^j, j=0..n): seq(a(n)/5, n=1..31); # _Zerinvary Lajos_, Dec 14 2008
%t A014918 CoefficientList[Series[1/((1 - x)(1 - 6*x)^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 23 2012 *)
%t A014918 nxt[{n_,a_}]:={n+1,(n+1)*6^n+a}; Transpose[NestList[nxt,{1,1},20]][[2]] (* or *) LinearRecurrence[{13,-48,36},{1,13,121},20] (* _Harvey P. Dale_, Apr 08 2014 *)
%o A014918 (Magma) I:=[1, 13]; [n le 2 select I[n] else 12*Self(n-1)-36*Self(n-2)+1: n in [1..30]]; // _Vincenzo Librandi_, Oct 23 2012
%K A014918 nonn,easy
%O A014918 1,2
%A A014918 _Olivier Gérard_