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 A016309 #29 Sep 08 2022 08:44:41
%S A016309 1,20,292,3824,47824,585536,7096384,85576448,1029436672,12368356352,
%T A016309 148510974976,1782675894272,21395375902720,256764101869568,
%U A016309 3081286768672768,36976146501533696,443717989683232768
%N A016309 Expansion of 1/((1-2*x)*(1-6*x)*(1-12*x)).
%H A016309 Vincenzo Librandi, <a href="/A016309/b016309.txt">Table of n, a(n) for n = 0..500</a>
%H A016309 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (20,-108,144)
%F A016309 a(n) = A071951(n+3, 3) = (24*12^n - 15*6^n + 2^n)/10. - _Wolfdieter Lang_, Nov 07 2003
%F A016309 a(n) = 18*a(n-1) - 72*a(n-2) + 2^n; a(n) = 20*a(n-1) - 108*a(n-2) + 144*a(n-3) for n > 2. - _Vincenzo Librandi_, Sep 02 2011
%F A016309 a(n) = det(|ps(i+3,j+2)|, 1 <= i,j <= n), where ps(n,k) are Legendre-Stirling numbers of the first kind (A129467). - _Mircea Merca_, Apr 06 2013
%t A016309 CoefficientList[Series[1/((1-2x)(1-6x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{20,-108,144},{1,20,292},30] (* _Harvey P. Dale_, Jul 26 2019 *)
%o A016309 (Magma) [(24*12^n-15*6^n+2^n)/10: n in [0..20]]; // _Vincenzo Librandi_, Sep 02 2011
%Y A016309 Cf. A089278, A089500.
%K A016309 nonn,easy
%O A016309 0,2
%A A016309 _N. J. A. Sloane_