cp's OEIS Frontend

A052559 Expansion of e.g.f. (1-x)/(1 - 2*x - x^2 + x^3).

%I A052559 #25 Sep 08 2022 08:44:59
%S A052559 1,1,6,36,336,3720,50400,791280,14232960,287763840,6466521600,
%T A052559 159826867200,4309577395200,125885452492800,3960073877760000,
%U A052559 133473015067392000,4798579092443136000,183299247820136448000
%N A052559 Expansion of e.g.f. (1-x)/(1 - 2*x - x^2 + x^3).
%H A052559 G. C. Greubel, <a href="/A052559/b052559.txt">Table of n, a(n) for n = 0..395</a>
%H A052559 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=501">Encyclopedia of Combinatorial Structures 501</a>
%F A052559 E.g.f.: (1-x)/(1 - 2*x - x^2 + x^3).
%F A052559 a(n) = 2*n*a(n-1) + n*(n-1)*a(n-2) - n*(n-1)*(n-2)*a(n-3), with a(0)=1, a(1)=1, a(2)=6.
%F A052559 a(n) = Sum((-1/7)*(-2*_alpha+_alpha^2-1)*_alpha^(-1-n), _alpha = RootOf(_Z^3-_Z^2-2*_Z+1))*n!.
%F A052559 a(n) = n!*A077998(n). - _R. J. Mathar_, Nov 27 2011
%p A052559 spec := [S,{S=Sequence(Prod(Z,Union(Z,Sequence(Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052559 With[{nn=20},CoefficientList[Series[(1-x)/(1-2x-x^2+x^3),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 14 2018 *)
%o A052559 (PARI) my(x='x+O('x^30)); Vec(serlaplace( (1-x)/(1-2*x-x^2+x^3) )) \\ _G. C. Greubel_, May 06 2019
%o A052559 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (1-x)/(1-2*x-x^2+x^3) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, May 06 2019
%o A052559 (Sage) m = 30; T = taylor((1-x)/(1-2*x-x^2+x^3), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # _G. C. Greubel_, May 06 2019
%K A052559 easy,nonn
%O A052559 0,3
%A A052559 encyclopedia(AT)pommard.inria.fr, Jan 25 2000