A052640 - OEIS

%I #15 Oct 10 2023 16:35:56

%S 0,1,2,18,144,1680,22320,352800,6330240,128096640,2877638400,

%T 71131737600,1917922406400,56024506137600,1762396334899200,

%U 59401108166400000,2135568241078272000,81575844571533312000

%N E.g.f. x*(1-x)/(1-2*x-x^2+x^3).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=586">Encyclopedia of Combinatorial Structures 586</a>

%F E.g.f.: -x*(-1+x)/(x^3-x^2-2*x+1)

%F Recurrence: {a(1)=1, a(0)=0, a(2)=2, (n^3+6*n^2+11*n+6)*a(n)+(-n^2-5*n-6)*a(n+1)+(-2*n-6)*a(n+2)+a(n+3)=0}

%F Sum(1/7*(-_alpha+_alpha^2+1)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))*n!

%F a(n) = n!*A077998(n-1), n>0. - _R. J. Mathar_, Nov 27 2011

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

%t With[{nn=20},CoefficientList[Series[-x*(-1+x)/(x^3-x^2-2*x+1),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Oct 10 2023 *)

%K easy,nonn

%O 0,3

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