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 A052563 #21 Sep 08 2022 08:44:59
%S A052563 1,2,12,108,1296,19440,349920,7348320,176359680,4761711360,
%T A052563 142851340800,4714094246400,169707392870400,6618588321945600,
%U A052563 277980709521715200,12509131928477184000,600438332566904832000
%N A052563 E.g.f.: (1-x)/(1-3*x).
%C A052563 Laguerre transform of A052585. - _Paul Barry_, Aug 08 2008
%H A052563 G. C. Greubel, <a href="/A052563/b052563.txt">Table of n, a(n) for n = 0..375</a>
%H A052563 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=505">Encyclopedia of Combinatorial Structures 505</a>
%F A052563 E.g.f.: (-1+x)/(-1+3*x)
%F A052563 Recurrence: {a(0)=1, a(1)=2, (-3*n-3)*a(n)+a(n+1)=0}
%F A052563 a(n) = 2*3^(n-1)*n!.
%F A052563 a(n) = Sum_{k=0..n} binomial(n,k)(n!/k!)k!*A001045(k+1). - _Paul Barry_, Aug 08 2008
%p A052563 spec := [S,{S=Sequence(Prod(Union(Z,Z),Sequence(Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052563 With[{nn=20},CoefficientList[Series[(1-x)/(1-3x),{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, May 21 2014 *)
%o A052563 (PARI) x='x+O('x^30); Vec(serlaplace((1-x)/(1-3*x))) \\ _G. C. Greubel_, May 23 2018
%o A052563 (Magma) m:=25; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1-x)/(1-3*x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, May 23 2018
%K A052563 easy,nonn
%O A052563 0,2
%A A052563 encyclopedia(AT)pommard.inria.fr, Jan 25 2000