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 A014900 #35 Mar 31 2025 15:37:59
%S A014900 1,19,326,5546,94287,1602885,27249052,463233892,7874976173,
%T A014900 133874594951,2275868114178,38689757941038,657725884997659,
%U A014900 11181340044960217,190082780764323704,3231407272993502984,54933923640889550745,933876701895122362683,15875903932217080165630
%N A014900 a(1)=1, a(n) = 17*a(n-1) + n.
%H A014900 Vincenzo Librandi, <a href="/A014900/b014900.txt">Table of n, a(n) for n = 1..200</a>
%H A014900 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,-35,17).
%F A014900 a(1)=1, a(2)=19, a(3)=326, a(n) = 19*a(n-1) - 35*a(n-2) + 17*a(n-3). - _Vincenzo Librandi_, Oct 20 2012
%F A014900 From _Elmo R. Oliveira_, Mar 29 2025: (Start)
%F A014900 G.f.: x/((1-17*x)*(1-x)^2).
%F A014900 E.g.f.: exp(x)*(17*exp(16*x) - 16*x - 17)/256.
%F A014900 a(n) = (17^(n+1) - 16*n - 17)/256. (End)
%p A014900 a:=n->sum((17^(n-j)-1)/16,j=0..n): seq(a(n), n=1..16); # _Zerinvary Lajos_, Jan 05 2007
%p A014900 a:= n-> (Matrix([[1,0,1],[1,1,1],[0,0,17]])^n)[2,3]:
%p A014900 seq(a(n), n=1..16); # _Alois P. Heinz_, Aug 06 2008
%t A014900 LinearRecurrence[{19, -35, 17}, {1, 19, 326}, 20] (* _Vincenzo Librandi_, Oct 20 2012 *)
%t A014900 nxt[{n_,a_}]:={n+1,17a+n+1}; NestList[nxt,{1,1},20][[All,2]] (* _Harvey P. Dale_, Jun 19 2021 *)
%o A014900 (Magma) I:=[1, 19, 326]; [n le 3 select I[n] else 19*Self(n-1) - 35*Self(n-2) + 17*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 20 2012
%Y A014900 Row n=17 of A126885.
%K A014900 nonn,easy
%O A014900 1,2
%A A014900 _N. J. A. Sloane_, _Olivier Gérard_