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 A052586 Expansion of e.g.f.: (1-x^3)/(1-x-x^3). 0

%I

%S 1,1,2,6,48,360,2880,30240,362880,4717440,68947200,1117670400,

%T 19639065600,373621248000,7671689625600,168689993472000,

%U 3954407288832000,98525417582592000,2599363724525568000

%N Expansion of e.g.f.: (1-x^3)/(1-x-x^3).

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=531">Encyclopedia of Combinatorial Structures 531</a>

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

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

%F Sum(1/31*(-2*_alpha+9*_alpha^2+6)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+_Z^3))*n!

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

%t With[{nn=20},CoefficientList[Series[(1-x^3)/(1-x-x^3),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 07 2020 *)

%K easy,nonn

%O 0,3

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

%E Definition clarified by _Harvey P. Dale_, Nov 07 2020

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Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)