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%I #12 May 19 2019 06:21:27
%S -1,-4,14,-49,158,-538,1877,-6688,24026,-86557,311882,-1123270,
%T 4043813,-14554252,52377062,-188485501,678287318,-2440910842,
%U 8784002237,-31610714104,113756642690,-409373197645,1473201178034,-5301572184286,19078633788629
%N Expansion of (2*x+1)*(4*x^2+8*x+1) / ((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)).
%H G. C. Greubel, <a href="/A110686/b110686.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 (-6,-10,-3,8,6,6).
%F a(n) = -6*a(n-1) - 10*a(n-2) - 3*a(n-3) + 8*a(n-4) + 6*a(n-5) + 6*a(n-6) for n>5. - _Colin Barker_, May 19 2019
%p seriestolist(series((2*x+1)*(4*x^2+8*x+1)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)), x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: tessum(infty)-4basekforsumseq[ + 'i - .25'j + .25'k - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e], Sumtype is set to: sum[Y[15]] = sum[ * ], Fortype is set to: 1A.
%t CoefficientList[Series[(2*x + 1)*(4*x^2 + 8*x + 1)/((x - 1)*(3*x^2 + 3*x + 1)*(2*x^3 + 2*x^2 + 4*x + 1)), {x, 0, 50}], x] (* _G. C. Greubel_, Sep 06 2017 *)
%o (PARI) Vec((2*x+1)*(4*x^2+8*x+1)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y Cf. A110683, A110684, A110685.
%K sign,easy
%O 0,2
%A _Creighton Dement_, Aug 02 2005
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