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%I #35 Aug 20 2022 06:31:56
%S 0,0,0,0,24,60,240,1260,8064,60480,518400,4989600,53222400,622702080,
%T 7925299200,108972864000,1609445376000,25406244864000,426824913715200,
%U 7602818775552000,143111882833920000,2838385676206080000,59157933040926720000,1292600836944248832000
%N E.g.f.: x^3*log(1/(1-x)).
%C Previous name was: A simple grammar.
%H Amiram Eldar, <a href="/A052759/b052759.txt">Table of n, a(n) for n = 0..450</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=716">Encyclopedia of Combinatorial Structures 716</a>.
%F E.g.f.: x^3*log(-1/(-1+x)).
%F Recurrence: a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=24, (-n^2+2*n+3)*a(n)+(-2+n)*a(n+1) = 0.
%F a(n) = n! / (n-3) (n > 3). - _Olivier Gérard_, Jun 13 2001
%F Sum_{n>=4} 1/a(n) = 11/2 - 2*e. - _Amiram Eldar_, Oct 07 2020
%F Sum_{n>=4} (-1)^n/a(n) = 3/2 - 4/e. - _Amiram Eldar_, Aug 20 2022
%p spec := [S,{B=Cycle(Z),S=Prod(B,Z,Z,Z)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t Join[{0, 0, 0, 0}, Table[n!/(n - 3), {n, 4, 30}]] (* _Vincenzo Librandi_, Jul 08 2015 *)
%o (PARI) a(n) = if (n <= 3, 0, n!/(n-3)); \\ _Michel Marcus_, Jul 08 2015
%o (Magma) [n le 3 select 0 else Factorial(n)/(n-3): n in [0..30]]; // _Vincenzo Librandi_, Jul 08 2015
%K nonn,easy
%O 0,5
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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