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%I #22 Feb 28 2023 17:38:20
%S 1,1,-124,-2179,-16368,-78093,-279872,-823415,-2096896,-4782457,
%T -9998976,-19485123,-35827712,-62740325,-105397120,-170826607,
%U -268369920,-410207601,-611957888,-893347451,-1278951424,-1798991389,-2490163584,-3396436839
%N a(n) = 2^n - n^7.
%H Vincenzo Librandi, <a href="/A024017/b024017.txt">Table of n, a(n) for n = 0..239</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (10,-44,112,-182,196,-140,64,-17,2).
%F G.f.: (1-9*x-90*x^2-1007*x^3+36*x^4+3585*x^5+ 2290*x^6 +231*x^7+3*x^8)/((1-2*x)*(1-x)^8). - _Vincenzo Librandi_, Oct 07 2014
%F a(n) = 10*a(n-1)-44*a(n-2)+112*a(n-3)-182*a(n-4)+196*a(n-5)-140*a(n-6)+64*a(n-7)-17*a(n-8)+2*a(n-9): n in [1..35]]; // _Vincenzo Librandi_, Oct 07 2014
%t Table[2^n - n^7, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 9 x - 90 x^2 - 1007 x^3 + 36 x^4 + 3585 x^5 + 2290 x^6 + 231 x^7 + 3 x^8)/((1 - 2 x) (1 - x)^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 07 2014 *)
%t LinearRecurrence[{10,-44,112,-182,196,-140,64,-17,2},{1,1,-124,-2179,-16368,-78093,-279872,-823415,-2096896},30] (* _Harvey P. Dale_, Feb 28 2023 *)
%o (Magma) [2^n-n^7: n in [0..25]]; // _Vincenzo Librandi_, Apr 30 2011
%o (Magma) I:=[1,1,-124,-2179,-16368,-78093,-279872,-823415,-2096896]; [n le 9 select I[n] else 10*Self(n-1)-44*Self(n-2)+112*Self(n-3)-182*Self(n-4)+196*Self(n-5)-140*Self(n-6)+64*Self(n-7)-17*Self(n-8)+2*Self(n-9): n in [1..35]]; // _Vincenzo Librandi_, Oct 07 2014
%Y Cf. sequences of the form k^n-n^7: this sequence (k=2), A024030 (k=3), A024043 (k=4), A024056 (k=5), A024069 (k=6), A024082 (k=7), A024095 (k=8), A024108 (k=9), A024121 (k=10), A024134 (k=11), A024147 (k=12).
%K sign,easy
%O 0,3
%A _N. J. A. Sloane_.
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