A160767 - OEIS

%I #17 Sep 08 2022 08:45:45

%S 1,17,103,367,971,2131,4117,7253,11917,18541,27611,39667,55303,75167,

%T 99961,130441,167417,211753,264367,326231,398371,481867,577853,687517,

%U 812101,952901,1111267,1288603,1486367,1706071,1949281,2217617,2512753

%N Expansion of (1+12*x+28*x^2+12*x^3+x^4)/(1-x)^5.

%C Source: the De Loera et al. article and the Haws website listed in A160747.

%H G. C. Greubel, <a href="/A160767/b160767.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.: (1+12*x+28*x^2+12*x^3+x^4)/(1-x)^5.

%F a(n) = 9*n^4/4 +9*n^3/2 +23*n^2/4 +7*n/2 +1. - _R. J. Mathar_, Sep 11 2011

%F a(0)=1, a(1)=17, a(2)=103, a(3)=367, a(4)=971, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - _Harvey P. Dale_, Feb 28 2015

%F E.g.f.: (4 + 64*x + 140*x^2 + 72*x^3 + 9*x^4)*exp(x)/4. - _G. C. Greubel_, Apr 26 2018

%t CoefficientList[Series[(1+12x+28x^2+12x^3+x^4)/(1-x)^5,{x,0,40}],x] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,17,103,367,971},40] (* _Harvey P. Dale_, Dec 11 2014 *)

%o (PARI) for(n=0, 30, print1((9*n^4 +18*n^3 +23*n^2 +14*n +4)/4, ", ")) \\ _G. C. Greubel_, Apr 26 2018

%o (Magma) [(9*n^4 +18*n^3 +23*n^2 +14*n +4)/4: n in [0..30]]; // _G. C. Greubel_, Apr 26 2018

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 18 2009