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A052661 E.g.f. (2-3x)/((1-x)(1-x-x^2)). 1

%I #19 Nov 25 2023 13:22:49

%S 2,1,4,12,72,480,4320,45360,564480,7983360,127008000,2235340800,

%T 43110144000,902918016000,20399720140800,494300911104000,

%U 12783824621568000,351419178958848000,10230993181753344000

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

%H Harvey P. Dale, <a href="/A052661/b052661.txt">Table of n, a(n) for n = 0..417</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=608">Encyclopedia of Combinatorial Structures 608</a>

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

%F Recurrence: {a(1)=1, a(2)=4, a(0)=2, (n^3+6*n^2+11*n+6)*a(n)+(-2*n-6)*a(n+2)+a(n+3)=0}

%F (1+Sum(1/5*(-1+3*_alpha)*_alpha^(-1-n), _alpha =RootOf(-1+_Z+_Z^2)))*n!

%F a(n) = n!*A001611(n-1), n>0. - _R. J. Mathar_, Nov 27 2011

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

%t With[{nn=20},CoefficientList[Series[(2-3x)/((1-x)(1-x-x^2)),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 25 2023 *)

%K easy,nonn

%O 0,1

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

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Last modified May 21 15:47 EDT 2024. Contains 372738 sequences. (Running on oeis4.)