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%I #21 Sep 08 2022 08:44:48
%S 1,1,-12,-73,-240,-593,-1232,-2273,-3840,-6049,-8976,-12593,-16640,
%T -20369,-22032,-17857,0,47551,157168,393967,888576,1902671,3960048,
%U 8108767,16445440,33163807,66651888,133686287,267820800,536163631,1072931824
%N 2^n-n^4.
%H Vincenzo Librandi, <a href="/A024014/b024014.txt">Table of n, a(n) for n = 0..240</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (7,-20,30,-25,11,-2).
%F G.f.: (1-6*x+x^2+x^3+26*x^4+x^5) / ((1-2*x)*(1-x)^5). - _Vincenzo Librandi_, Oct 06 2014
%F a(n) = 7*a(n-1) -20*a(n-2) +30*a(n-3) -25*a(n-4) +11*a(n-5) -2*a(n-6) for n>5. - _Vincenzo Librandi_, Oct 06 2014
%F E.g.f.: exp(2*x) - (x + 7*x^2 + 6*x^3 + x^4)* exp(x). - _Robert Israel_, Oct 06 2014
%p seq(2^n-n^4, n=0..100); # _Robert Israel_, Oct 06 2014
%t Table[2^n-n^4,{n,0,100}]
%t CoefficientList[Series[(1 - 6 x + x^2 + x^3 + 26 x^4 + x^5)/((1 - 2 x) (1 - x)^5), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 06 2014 *)
%o (Magma) [2^n-n^4: n in [0..30]]; // _Vincenzo Librandi_, Apr 29 2011
%o (Magma) I:=[1,1,-12,-73,-240,-593]; [n le 6 select I[n] else 7*Self(n-1)-20*Self(n-2)+30*Self(n-3)-25*Self(n-4)+11*Self(n-5)-2*Self(n-6): n in [1..35]]; // _Vincenzo Librandi_, Oct 06 2014
%Y Cf. A024012, A024013.
%Y Cf. sequences of the form k^n-n^4: this sequence (k=2), A024027 (k=3), A024040 (k=4), A024053 (k=5), A024066 (k=6), A024079 (k=7), A024092 (k=8), A024105 (k=9), A024118 (k=10), A024131 (k=11), A024144 (k=12).
%K sign,easy
%O 0,3
%A _N. J. A. Sloane_.