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%I #30 Sep 08 2022 08:46:01
%S 1,9,46,175,551,1520,3811,8921,19922,43211,92363,196608,419295,897565,
%T 1926458,4135255,8854359,18875392,40024059,84417521,177221602,
%U 370688979,773342163,1610612736,3350668423,6964989333,14466833194,30021724351,62233946303
%N Expansion of 1/((1-2*x)*(1-3*x+3*x^2)*(1-4*x+6*x^2-4*x^3)).
%H Bruno Berselli, <a href="/A201458/b201458.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (9,-35,76,-98,72,-24).
%F G.f.: 1/((1-2*x)^2*(1-2*x+2*x^2)*(1-3*x+3*x^2)) = 1/((1-2*x+2*x^2)*(1-3*x+3*x^2)*(1-4*x+4*x^2)).
%F a(n) = 9*a(n-1)-35*a(n-2)+76*a(n-3)-98*a(n-4)+72*a(n-5)-24*a(n-6) for a(-5)=a(-4)=a(-3)=a(-2)=a(-1)=0, a(0)=1.
%F a(n) = 8*2^n*(n+1)+2*((1-i)^(n-1)+(1+i)^(n-1))+((3+i*sqrt(3))/2)^(n+4)+((3-i*sqrt(3))/2)^(n+4), where i=sqrt(-1).
%t CoefficientList[Series[1/((1-2*x)*(1-3*x+3*x^2)*(1-4*x+6*x^2-4*x^3)), {x, 0, 30}], x]
%t LinearRecurrence[{9,-35,76,-98,72,-24},{1,9,46,175,551,1520},30] (* _Harvey P. Dale_, Feb 01 2012 *)
%o (PARI) Vec(1/((1-2*x)*(1-3*x+3*x^2)*(1-4*x+6*x^2-4*x^3))+O(x^30))
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-3*x+3*x^2)*(1-4*x+6*x^2-4*x^3))));
%o (Maxima) makelist(coeff(taylor(1/((1-2*x)*(1-3*x+3*x^2)*(1-4*x+6*x^2-4*x^3)), x, 0, n), x, n), n, 0, 29);
%Y Cf. for type of g.f.: A099855, with 1/((1-2*x+2*x^2)*(1-4*x+4*x^2)); A000581, with 1/((1-x)^2*(1-x)^3*(1-x)^4).
%K nonn,easy
%O 0,2
%A _Bruno Berselli_, Dec 01 2011
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