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 A167191 #21 Aug 08 2025 05:55:14
%S A167191 2664,20568,68592,161616,314520,542184,859488,1281312,1822536,2498040,
%T A167191 3322704,4311408,5479032,6840456,8410560,10204224,12236328,14521752,
%U A167191 17075376,19912080,23046744,26494248,30269472,34387296,38862600,43710264,48945168,54582192,60636216
%N A167191 a(n) = 4*n*(1 + 45*n + 620*n^2).
%C A167191 See A167190, where this sequence arises as the integer part of the quotient.
%H A167191 Vincenzo Librandi, <a href="/A167191/b167191.txt">Table of n, a(n) for n = 1..1000</a>
%H A167191 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A167191 G.f.: 24*x*(111+413*x+96*x^2)/(x-1)^4. - _R. J. Mathar_, Jan 27 2012
%F A167191 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jul 02 2012
%F A167191 E.g.f.: 4*x*(666 + 1905*x + 620*x^2)*exp(x). - _Elmo R. Oliveira_, Aug 07 2025
%t A167191 CoefficientList[Series[24*(111+413*x+96*x^2)/(x-1)^4,{x,0,40}],x] (* _Vincenzo Librandi_, Jul 02 2012 *)
%t A167191 LinearRecurrence[{4,-6,4,-1},{2664,20568,68592,161616},40] (* _Harvey P. Dale_, Jun 15 2014 *)
%o A167191 (Magma) I:=[2664, 20568, 68592, 161616]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jul 02 2012
%Y A167191 Cf. A167190.
%K A167191 nonn,easy
%O A167191 1,1
%A A167191 _A.K. Devaraj_, Oct 30 2009
%E A167191 Extended beyond a(6) by _R. J. Mathar_, Nov 17 2009