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A190048 Expansion of (8+6*x)/(1-x)^5 4

%I

%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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Last modified June 20 11:49 EDT 2021. Contains 345164 sequences. (Running on oeis4.)