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%I #14 Sep 08 2022 08:45:56
%S 8,46,150,370,770,1428,2436,3900,5940,8690,12298,16926,22750,29960,
%T 38760,49368,62016,76950,94430,114730,138138,164956,195500,230100,
%U 269100,312858,361746,416150,476470,543120,616528,697136,785400,881790,986790,1100898
%N Expansion of (8+6*x)/(1-x)^5
%C Equals the fifth right hand column of A175136.
%H Vincenzo Librandi, <a href="/A190048/b190048.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F G.f.: (8+6*x)/(1-x)^5.
%F a(n) = 8*binomial(n+4,4) + 6*binomial(n+3,4).
%F a(n) = A091894(4,0)*binomial(n+4,4) + A091894(4,1)*binomial(n+3,4).
%F a(n) = (7*n^4 +58*n^3 +173*n^2 +218*n +96)/12.
%p A190048 := proc(n) option remember; a(n):=(7*n^4+58*n^3+173*n^2+218*n+96)/12 end: seq(A190048(n),n=0..35);
%t LinearRecurrence[{5,-10,10,-5,1}, {8,46,150,370,770}, 30] (* or *) CoefficientList[Series[(8+6*x)/(1-x)^5, {x, 0, 50}], x] (* _G. C. Greubel_, Jan 10 2018 *)
%o (Magma) [(7*n^4+58*n^3+173*n^2+218*n+96)/12: n in [0..50]]; // _Vincenzo Librandi_, May 07 2011
%o (PARI) x='x+O('x^30); Vec((8+6*x)/(1-x)^5) \\ _G. C. Greubel_, Jan 10 2018
%o (PARI) for(n=0,50, print1((7*n^4 +58*n^3 +173*n^2 +218*n +96)/12, ", ")) \\ _G. C. Greubel_, Jan 10 2018
%Y Cf. A175136, A162148, A190049.
%Y Related to A000332 and A091894.
%K nonn,easy
%O 0,1
%A _Johannes W. Meijer_, May 06 2011
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