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 A052720 #21 May 29 2022 03:18:54
%S A052720 0,0,0,0,0,0,720,30240,1088640,39916800,1556755200,65383718400,
%T A052720 2964061900800,144815595724800,7602818775552000,427447366714368000,
%U A052720 25646842002862080000,1636734826000834560000,110752389892723138560000
%N A052720 Expansion of e.g.f.: (1 - 4*x + 3*x^2)*(1 - 2*x - sqrt(1-4*x))/2 - x^2 + 2*x^3.
%H A052720 G. C. Greubel, <a href="/A052720/b052720.txt">Table of n, a(n) for n = 0..350</a>
%H A052720 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=676">Encyclopedia of Combinatorial Structures 676</a>
%F A052720 D-finite with recurrence: a(1)=0; a(2)=0; a(4)=0; a(3)=0; a(5)=0; a(6)=720; a(n+3) = (10+8*n)*a(n+2) + (22-27*n-19*n^2)*a(n+1) - (60-66*n+6*n^2+12*n^3)*a(n).
%F A052720 a(n) = n!*A003517(n-4). - _R. J. Mathar_, Oct 18 2013
%F A052720 From _G. C. Greubel_, May 28 2022: (Start)
%F A052720 G.f.: 6!*x^6*Hypergeometric2F0([3, 7/2], [], 4*x).
%F A052720 E.g.f.: (1/2)*(1 - 6*x + 9*x^2 - 2*x^3 - (1 - 4*x + 3*x^2)*sqrt(1-4*x)). (End)
%p A052720 spec := [S,{B=Union(Z,C),C=Prod(B,B),S=Prod(C,C,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052720 Table[If[n<6, 0, 6*(n-2)!*Binomial[n-4, 2]*CatalanNumber[n-3]], {n,0,30}] (* _G. C. Greubel_, May 28 2022 *)
%o A052720 (SageMath)
%o A052720 def A052720(n):
%o A052720 if (n<6): return 0
%o A052720 else: return 6*factorial(n-2)*binomial(n-4,2)*catalan_number(n-3)
%o A052720 [A052720(n) for n in (0..30)] # _G. C. Greubel_, May 28 2022
%Y A052720 Cf. A052711, A052712, A052713, A052714, A052715, A052716, A052717, A052718, A052719, A052721, A052722, A052723.
%Y A052720 Cf. A000108, A003517.
%K A052720 easy,nonn
%O A052720 0,7
%A A052720 encyclopedia(AT)pommard.inria.fr, Jan 25 2000