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a(0) = a(1) = a(2) = 0; a(n) = n!/(n-2) for n > 2.
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%I #31 Aug 20 2022 06:36:19

%S 0,0,0,6,12,40,180,1008,6720,51840,453600,4435200,47900160,566092800,

%T 7264857600,100590336000,1494484992000,23712495206400,400148356608000,

%U 7155594141696000,135161222676480000,2688996956405760000,56200036388880384000,1231048416137379840000

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

%C A simple grammar.

%H Amiram Eldar, <a href="/A052747/b052747.txt">Table of n, a(n) for n = 0..450</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=703">Encyclopedia of Combinatorial Structures 703</a>.

%F E.g.f.: log(-1/(-1+x))*x^2

%F 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 Sum_{n>=3} 1/a(n) = 3 - e. - _Amiram Eldar_, Oct 07 2020

%F Sum_{n>=3} (-1)^(n+1)/a(n) = 3/e - 1. - _Amiram Eldar_, Aug 20 2022

%p spec := [S,{B=Cycle(Z),S=Prod(Z,Z,B)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

%t a[n_] := If[n < 3, 0, n!/(n-2)]; Array[a, 20, 0] (* _Amiram Eldar_, Oct 07 2020 *)

%o (PARI) a(n)=if(n>2,n!/(n-2),0) \\ _Charles R Greathouse IV_, Nov 20 2011

%Y Equals the square root of the second right hand column of A162990 for n=>3. [_Johannes W. Meijer_, Jul 21 2009]

%K easy,nonn

%O 0,4

%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000

%E Better description from _Olivier GĂ©rard_, Jun 13 2001