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A052747 a(0) = a(1) = a(2) = 0; a(n) = n!/(n-2) for n > 2.

%I A052747 #31 Aug 20 2022 06:36:19
%S A052747 0,0,0,6,12,40,180,1008,6720,51840,453600,4435200,47900160,566092800,
%T A052747 7264857600,100590336000,1494484992000,23712495206400,400148356608000,
%U A052747 7155594141696000,135161222676480000,2688996956405760000,56200036388880384000,1231048416137379840000
%N A052747 a(0) = a(1) = a(2) = 0; a(n) = n!/(n-2) for n > 2.
%C A052747 A simple grammar.
%H A052747 Amiram Eldar, <a href="/A052747/b052747.txt">Table of n, a(n) for n = 0..450</a>
%H A052747 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=703">Encyclopedia of Combinatorial Structures 703</a>.
%F A052747 E.g.f.: log(-1/(-1+x))*x^2
%F A052747 Recurrence: {a(0)=0, a(1)=0, a(2)=0, a(3)=6, (n+2-n^2)*a(n)+(n-1)*a(n+1)}
%F A052747 Sum_{n>=3} 1/a(n) = 3 - e. - _Amiram Eldar_, Oct 07 2020
%F A052747 Sum_{n>=3} (-1)^(n+1)/a(n) = 3/e - 1. - _Amiram Eldar_, Aug 20 2022
%p A052747 spec := [S,{B=Cycle(Z),S=Prod(Z,Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052747 a[n_] := If[n < 3, 0, n!/(n-2)]; Array[a, 20, 0] (* _Amiram Eldar_, Oct 07 2020 *)
%o A052747 (PARI) a(n)=if(n>2,n!/(n-2),0) \\ _Charles R Greathouse IV_, Nov 20 2011
%Y A052747 Equals the square root of the second right hand column of A162990 for n=>3. [_Johannes W. Meijer_, Jul 21 2009]
%K A052747 easy,nonn
%O A052747 0,4
%A A052747 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052747 Better description from _Olivier Gérard_, Jun 13 2001