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%I #17 Sep 08 2022 08:44:48
%S 1,1,-252,-6553,-65520,-390593,-1679552,-5764673,-16776960,-43046209,
%T -99998976,-214356833,-429977600,-815722529,-1475772672,-2562857857,
%U -4294901760,-6975626369,-11019698432,-16983038753,-25598951424
%N 2^n-n^8.
%H Vincenzo Librandi, <a href="/A024018/b024018.txt">Table of n, a(n) for n = 0..244</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (11,-54,156,-294,378,-336,204,-81,19,-2).
%F G.f.: (1 -10*x -209*x^2 -3883*x^3 -6907*x^4 +15493*x^5 +27029*x^6 +8303*x^7 +502*x^8 +x^9) / ((1-2*x)*(1-x)^9). - _Vincenzo Librandi_, Oct 08 2014
%F a(n) = 11*a(n-1) -54*a(n-2) +156*a(n-3) -294*a(n-4) +378*a(n-5) -336*a(n-6)+204*a(n-7) -81*a(n-8) +19*a(n-9) -2*a(n-10) for n>9. - _Vincenzo Librandi_, Oct 08 2014
%t Table[2^n - n^8, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 10 x - 209 x^2 - 3883 x^3 - 6907 x^4 + 15493 x^5 + 27029 x^6 + 8303 x^7 + 502 x^8 + x^9)/((1 - 2 x) (1 - x)^9), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 08 2014 *)
%o (Magma) [2^n-n^8: n in [0..25]]; // _Vincenzo Librandi_, Apr 30 2011
%o (Magma) I:=[1,1,-252,-6553,-65520,-390593,-1679552,-5764673,-16776960, -43046209]; [n le 10 select I[n] else 11*Self(n-1)-54*Self(n-2) +156*Self(n-3)-294*Self(n-4)+378*Self(n-5)-336*Self(n-6)+204*Self(n-7) -81*Self(n-8)+19*Self(n-9)-2*Self(n-10): n in [1..35]]; // _Vincenzo Librandi_, Oct 08 2014
%Y Cf. sequences of the form k^n-n^8: this sequence (k=2), A024031 (k=3), A024044 (k=4), A024057 (k=5), A024070 (k=6), A024083 (k=7), A024096 (k=8), A024109 (k=9), A024122 (k=10), A024135 (k=11), A024148 (k=12).
%K sign,easy
%O 0,3
%A _N. J. A. Sloane_.
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