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 A052569 #20 Sep 25 2019 17:01:09
%S A052569 1,1,2,12,48,240,2160,15120,120960,1451520,14515200,159667200,
%T A052569 2395008000,31135104000,435891456000,7846046208000,125536739328000,
%U A052569 2134124568576000,44816615940096000,851515702861824000
%N A052569 E.g.f. 1/((1-x)(1-x^3)).
%H A052569 Robert Israel, <a href="/A052569/b052569.txt">Table of n, a(n) for n = 0..448</a>
%H A052569 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=512">Encyclopedia of Combinatorial Structures 512</a>
%F A052569 E.g.f.: 1/(-1+x)/(-1+x^3)
%F A052569 Recurrence: {a(1)=1, a(0)=1, a(2)=2, (-14*n-n^3-7*n^2-8)*a(n)+(-2-n)*a(n+1)+a(n+3)-a(n+2)=0}
%F A052569 (1/3*n+2/3+Sum(1/9*(-1+_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2+_Z+1)))*n!
%F A052569 a(n) = n!*A008620(n). - _R. J. Mathar_, Nov 27 2011
%p A052569 spec := [S,{S=Prod(Sequence(Prod(Z,Z,Z)),Sequence(Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p A052569 # Alternative:
%p A052569 f:= gfun:-rectoproc({ a(1)=1, a(0)=1, a(2)=2, (-14*n-n^3-7*n^2-8)*a(n)+(-2-n)*a(n+1)+a(n+3)-a(n+2)=0},a(n),remember):
%p A052569 map(f, [$0..30]); # _Robert Israel_, Sep 25 2019
%t A052569 With[{nn=20},CoefficientList[Series[1/((1-x)(1-x^3)),{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Aug 25 2012 *)
%K A052569 easy,nonn
%O A052569 0,3
%A A052569 encyclopedia(AT)pommard.inria.fr, Jan 25 2000