A024004 - OEIS

%I #31 Sep 08 2022 08:44:48

%S 1,0,-63,-728,-4095,-15624,-46655,-117648,-262143,-531440,-999999,

%T -1771560,-2985983,-4826808,-7529535,-11390624,-16777215,-24137568,

%U -34012223,-47045880,-63999999,-85766120,-113379903,-148035888,-191102975,-244140624,-308915775,-387420488,-481890303

%N a(n) = 1 - n^6.

%H Vincenzo Librandi, <a href="/A024004/b024004.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F From _G. C. Greubel_, May 11 2017: (Start)

%F G.f.: (1 - 7*x - 42*x^2 - 322*x^3 - 287*x^4 - 63*x^5)/(1 - x)^7.

%F E.g.f.: (1 - x - 31*x^2 - 90*x^3 - 65*x^4 - 15*x^5 - x^6)*exp(x). (End)

%F Sum_{k>=2} -1/a(k) = 11/12 - Pi*tanh(sqrt(3)*Pi/2)/(2*sqrt(3)) = A339529. - _Vaclav Kotesovec_, Dec 08 2020

%t Table[1-n^6,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 15 2011 *)

%o (Magma) [1-n^6: n in [0..50]]; // _Vincenzo Librandi_, Apr 29 2011

%o (Maxima) A024004(n):=1-n^6 $ makelist(A024004(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */

%o (Haskell)

%o a024004 = (1 -) . (^ 6)  -- _Reinhard Zumkeller_, Mar 11 2014

%o (PARI) for(n=0,50, print1(1-n^6, ", ")) \\ _G. C. Greubel_, May 11 2017

%Y Cf. A001014.

%Y a(n) = -A123866(n) for n > 0.

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_, corrected Mar 01 2007