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Expansion of 2*(1 -4*x +14*x^2 +4*x^3 +9*x^4)/(1-x)^5.
1

%I #18 Apr 20 2024 11:35:00

%S 2,2,18,98,338,882,1922,3698,6498,10658,16562,24642,35378,49298,66978,

%T 89042,116162,149058,188498,235298,290322,354482,428738,514098,611618,

%U 722402,847602,988418,1146098,1321938,1517282,1733522,1972098,2234498

%N Expansion of 2*(1 -4*x +14*x^2 +4*x^3 +9*x^4)/(1-x)^5.

%D Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

%H G. C. Greubel, <a href="/A173785/b173785.txt">Table of n, a(n) for n = 0..1000</a>

%H Clark Kimberling, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Kimberling/kimberling26.html">Complementary Equations</a>, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

%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.: 2*(1 -4*x +14*x^2 +4*x^3 +9*x^4)/(1-x)^5.

%F a(n) = 2*(n^2 - n + 1)^2.

%F a(n) = 2*A058031(n).

%F E.g.f.: 2*(1 + 4*x^2 + 4*x^3 + x^4)*exp(x). - _G. C. Greubel_, Jul 07 2021

%p a:= n-> 2*(n^2-n+1)^2:

%p seq (a(n), n=0..40);

%t Table[2*(1-n+n^2)^2, {n,0,40}] (* _G. C. Greubel_, Jul 07 2021 *)

%t LinearRecurrence[{5,-10,10,-5,1},{2,2,18,98,338},50] (* _Harvey P. Dale_, Apr 20 2024 *)

%o (Sage) [2*(1-n+n^2)^2 for n in (0..40)] # _G. C. Greubel_, Jul 07 2021

%o (PARI) a(n)=2*(n^2-n+1)^2 \\ _Charles R Greathouse IV_, Oct 21 2022

%Y Cf. A058031.

%K nonn,easy

%O 0,1

%A _Michel Lagneau_, Feb 24 2010

%E Edited by _Alois P. Heinz_, Feb 16 2012