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 A021514 #26 Aug 02 2025 20:27:06
%S A021514 1,20,273,3208,35069,368988,3800761,38676176,390782997,3931986916,
%T A021514 39464899409,395519441304,3960417893485,39635522209004,
%U A021514 396543288909417,3966561311533792,39672383714545733,396764460934414452,3967888352659017985,39680345988222812840
%N A021514 Expansion of 1/((1-x)(1-3x)(1-6x)(1-10x)).
%H A021514 Vincenzo Librandi, <a href="/A021514/b021514.txt">Table of n, a(n) for n = 0..200</a>
%H A021514 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (20,-127,288,-180).
%F A021514 a(n) = (10^(n+4) - 7*6^(n+4) + 20*3^(n+4) - 28)/2520. [_Yahia Kahloune_, Jun 19 2013]
%F A021514 a(0)=1, a(1)=20; for n>1, a(n) = 16*(n-1) -60*a(n-2) +(3^n -1)/2. - _Vincenzo Librandi_, Jul 10 2013
%F A021514 a(0)=1, a(1)=20, a(2)=273, a(3)=3208; for n>3, a(n) = 20*a(n-1) -127*a(n-2) +288*a(n-3) -180*a(n-4). - _Vincenzo Librandi_, Jul 10 2013
%t A021514 CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 6 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 10 2013 *)
%t A021514 LinearRecurrence[{20,-127,288,-180},{1,20,273,3208},20] (* _Harvey P. Dale_, Feb 13 2022 *)
%o A021514 (PARI) Vec(1/((1-x)*(1-3*x)*(1-6*x)*(1-10*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o A021514 (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-10*x)))); // _Vincenzo Librandi_, Jul 10 2013
%o A021514 (Magma) I:=[1, 20, 273, 3208]; [n le 4 select I[n] else 20*Self(n-1)-127*Self(n-2)+288*Self(n-3)-180*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 10 2013
%K A021514 nonn,easy
%O A021514 0,2
%A A021514 _N. J. A. Sloane_