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 A052634 #23 Jun 03 2022 19:13:27
%S A052634 1,1,6,18,168,840,10800,75600,1249920,11249280,228614400,2514758400,
%T A052634 60833203200,790831641600,22230464256000,333456963840000,
%U A052634 10691545632768000,181756275757056000,6549628300959744000
%N A052634 Expansion of e.g.f. 1/((1-2*x^2)*(1-x)).
%H A052634 Vincenzo Librandi, <a href="/A052634/b052634.txt">Table of n, a(n) for n = 0..200</a>
%H A052634 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=580">Encyclopedia of Combinatorial Structures 580</a>
%F A052634 E.g.f.: 1/(-1+2*x^2)/(-1+x).
%F A052634 Recurrence: {a(1)=1, a(0)=1, a(2)=6, (12+2*n^3+12*n^2+22*n)*a(n) +(-2*n^2-10*n-12)*a(n+1) +(-n-3)*a(n+2) +a(n+3)=0}.
%F A052634 a(n) = (-1+Sum(1/2*(1+2*_alpha)*_alpha^(-1-n), with _alpha=RootOf(-1+2*_Z^2)))*n! .
%F A052634 a(n) = n!*[2^floor(n/2+1)-1].
%F A052634 a(n)=n!*A052551(n). - _R. J. Mathar_, Jun 03 2022
%p A052634 spec := [S,{S=Prod(Sequence(Prod(Z,Union(Z,Z))),Sequence(Z))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052634 With[{nn=20},CoefficientList[Series[1/((1-2x^2)(1-x)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 13 2014 *)
%K A052634 easy,nonn
%O A052634 0,3
%A A052634 encyclopedia(AT)pommard.inria.fr, Jan 25 2000