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A024019 2^n-n^9.

%I A024019 #17 Jul 08 2025 17:26:28
%S A024019 1,1,-508,-19675,-262128,-1953093,-10077632,-40353479,-134217472,
%T A024019 -387419977,-999998976,-2357945643,-5159776256,-10604491181,
%U A024019 -20661030400,-38443326607,-68719411200,-118587745425,-198359028224,-322687173491,-511998951424,-794277949429
%N A024019 2^n-n^9.
%H A024019 Vincenzo Librandi, <a href="/A024019/b024019.txt">Table of n, a(n) for n = 0..235</a>
%H A024019 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (12,-65,210,-450,672,-714,540,-285,100,-21,2).
%F A024019 G.f.: (1 -11*x -455*x^2 -13724*x^3 -58808*x^4 +20026*x^5 + 224356*x^6 +161740*x^7 +28759*x^8 +993*x^9 +3*x^10) / ((1-2*x)*(1-x)^10). - _Vincenzo Librandi_, Oct 08 2014
%F A024019 a(n) = 12*a(n-1) -65*a(n-2) +210*a(n-3) -450*a(n-4) +672*a(n-5) -714*a(n-6) +540*a(n-7) -285*a(n-8) +100*a(n-9) -21*a(n-10) +2*a(n-11) for n>10. - _Vincenzo Librandi_, Oct 08 2014
%t A024019 Table[2^n - n^8, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 11 x - 455 x^2 - 13724 x^3 - 58808 x^4 + 20026 x^5 + 224356 x^6 + 161740 x^7 + 28759 x^8 + 993 x^9 + 3 x^10)/((1 - 2 x) (1 - x)^10), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 08 2014 *)
%o A024019 (Magma) [2^n-n^9: n in [0..30]]; // _Vincenzo Librandi_, Apr 30 2011
%o A024019 (Magma) I:=[1,1,-508,-19675,-262128,-1953093,-10077632,-40353479, -134217472,-387419977,-999998976]; [n le 11 select I[n] else 12*Self(n -1)-65*Self(n-2)+210*Self(n-3)-450*Self(n-4)+672*Self(n-5)-714*Self(n -6)+540*Self(n-7)-285*Self(n-8)+100*Self(n-9)-21*Self(n-10)+2*Self(n -11): n in [1..35]]; // _Vincenzo Librandi_, Oct 08 2014
%Y A024019 Cf. sequences of the form k^n-n^9: this sequence (k=2), A024032 (k=3), A024045 (k=4), A024058 (k=5), A024071 (k=6), A024084 (k=7), A024097 (k=8), A024110 (k=9), A024123 (k=10), A024136 (k=11), A024149 (k=12).
%K A024019 sign,easy
%O A024019 0,3
%A A024019 _N. J. A. Sloane_