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 A052682 #22 Jun 04 2022 04:34:33
%S A052682 1,0,6,18,288,2520,41040,604800,11733120,236234880,5530291200,
%T A052682 138790713600,3855483878400,115075344384000,3716149018982400,
%U A052682 128239702246656000,4727462529613824000,185010460036706304000
%N A052682 Expansion of e.g.f. (1-x)/(1-x-3*x^2).
%H A052682 G. C. Greubel, <a href="/A052682/b052682.txt">Table of n, a(n) for n = 0..350</a>
%H A052682 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=630">Encyclopedia of Combinatorial Structures 630</a>
%F A052682 E.g.f.: (1-x)/(1 - x - 3*x^2).
%F A052682 Recurrence: a(0)=1, a(1)=0, a(n) = n*a(n-1) + 3*n*(n-1)*a(n-2).
%F A052682 a(n) = (n!/13)*Sum_{alpha=RootOf(-1+Z+3*Z^2)} (-1 + 7*alpha)*alpha^(-1-n).
%F A052682 a(n) = n!*A052533(n). - _R. J. Mathar_, Nov 27 2011
%p A052682 spec := [S,{S=Sequence(Prod(Z,Sequence(Z),Union(Z,Z,Z)))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052682 With[{nn=20},CoefficientList[Series[(1-x)/(1-x-3*x^2),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jul 15 2020 *)
%t A052682 a[n_]:= a[n]= If[n<2, 1-n, n*a[n-1] +3*n*(n-1)*a[n-2]];
%t A052682 Table[a[n], {n,0,40}] (* _G. C. Greubel_, Jun 04 2022 *)
%o A052682 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( (1-x)/(1-x-3*x^2) ))); // _G. C. Greubel_, Jun 04 2022
%o A052682 (SageMath) [factorial(n)*sum(binomial(n-k-1, n-2*k)*3^k for k in (0..n//2)) for n in (0..40)] # _G. C. Greubel_, Jun 04 2022
%Y A052682 Cf. A000142, A052533.
%K A052682 easy,nonn
%O A052682 0,3
%A A052682 encyclopedia(AT)pommard.inria.fr, Jan 25 2000