%I #21 Sep 08 2022 08:44:48
%S 1,0,-15,-80,-255,-624,-1295,-2400,-4095,-6560,-9999,-14640,-20735,
%T -28560,-38415,-50624,-65535,-83520,-104975,-130320,-159999,-194480,
%U -234255,-279840,-331775,-390624,-456975,-531440,-614655,-707280,-809999,-923520,-1048575,-1185920,-1336335,-1500624
%N a(n) = 1 - n^4.
%H Vincenzo Librandi, <a href="/A024002/b024002.txt">Table of n, a(n) for n = 0..630</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = -A123865(n) for n>0.
%F From _G. C. Greubel_, May 11 2017: (Start)
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F G.f.: (1 - 5*x - 5*x^2 - 15*x^3)/(1 - x)^5.
%F E.g.f.: (1 - x - 7*x^2 - 6*x^3 - x^4)*exp(x). (End)
%F Sum_{k>=2} -1/a(k) = A256919 = 7/8 - Pi*coth(Pi)/4. - _Vaclav Kotesovec_, Dec 08 2020
%t Table[1 - n^4, {n, 0, 50}] (* _Bruno Berselli_, Jun 12 2015 *)
%t CoefficientList[Series[(1 - 5*x - 5*x^2 - 15*x^3)/(1 - x)^5, {x, 0, 50}], x] (* _G. C. Greubel_, May 11 2017 *)
%o (Magma) [1-n^4: n in [0..50]]; // _Vincenzo Librandi_, Apr 29 2011
%o (PARI) x='x+O('x^50); Vec((1 - 5*x - 5*x^2 - 15*x^3)/(1 - x)^5) \\ _G. C. Greubel_, May 11 2017
%Y Cf. A123865.
%K sign,easy
%O 0,3
%A _N. J. A. Sloane_
%E Corrected by _T. D. Noe_, Nov 08 2006