This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A123866 #50 Sep 08 2022 08:45:28
%S A123866 0,63,728,4095,15624,46655,117648,262143,531440,999999,1771560,
%T A123866 2985983,4826808,7529535,11390624,16777215,24137568,34012223,47045880,
%U A123866 63999999,85766120,113379903,148035888,191102975,244140624,308915775,387420488
%N A123866 a(n) = n^6 - 1.
%C A123866 a(n) mod 7 = 0 iff n mod 7 > 0: a(A008589(n))=6; a(A047304(n)) = 0; a(n) mod 7 = 6*(1-A082784(n)).
%C A123866 a(n) = A005563(n-1)*A059826(n) = A068601(n)*A001093(n). - _Reinhard Zumkeller_, Feb 02 2007
%H A123866 Vincenzo Librandi, <a href="/A123866/b123866.txt">Table of n, a(n) for n = 1..1000</a>
%H A123866 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A123866 G.f.: x^2*(63 + 287*x + 322*x^2 + 42*x^3 + 7*x^4 - x^5)/(1-x)^7. - _Colin Barker_, May 08 2012
%F A123866 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(1)=0, a(2)=63, a(3)=728, a(4)=4095, a(5)=15624, a(6)=46655, a(7)=117648. - _Harvey P. Dale_, Nov 18 2012
%F A123866 Sum_{n>=2} 1/a(n) = 11/12 - Pi*sqrt(3)*tanh(Pi*sqrt(3)/2)/6. - _Vaclav Kotesovec_, Feb 14 2015
%F A123866 E.g.f.: 1 + (-1 + x + 31*x^2 + 90*x^3 + 65*x^4 + 15*x^5 + x^6)*exp(x). - _G. C. Greubel_, Aug 08 2019
%F A123866 Product_{n>=2} (1 + 1/a(n)) = 6*Pi^2*sech(sqrt(3)*Pi/2)^2. - _Amiram Eldar_, Jan 20 2021
%p A123866 A123866:=n->n^6 - 1; seq(A123866(n), n=1..40); # _Wesley Ivan Hurt_, Feb 26 2014
%t A123866 Table[n^6-1,{n,40}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 15 2011 *)
%t A123866 LinearRecurrence[{7,-21,35,-35,21,-7,1}, {0,63,728,4095, 15624,46655, 117648}, 30] (* _Harvey P. Dale_, Nov 18 2012 *)
%o A123866 (Magma) [n^6 - 1: n in [1..30]]; // _Vincenzo Librandi_, May 01 2011
%o A123866 (Maxima) A123866(n):=n^6 -1 $ makelist(A123866(n),n,1,30); /* _Martin Ettl_, Nov 05 2012 */
%o A123866 (Haskell)
%o A123866 a123866 = (subtract 1) . (^ 6) -- _Reinhard Zumkeller_, Mar 11 2014
%o A123866 (PARI) a(n)=n^6-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A123866 (Sage) [n^6 -1 for n in (1..30)] # _G. C. Greubel_, Aug 08 2019
%o A123866 (GAP) List([1..30], n-> n^6 -1); # _G. C. Greubel_, Aug 08 2019
%Y A123866 Cf. A024004, A001014, A005563, A123865, A123867, A123868.
%K A123866 nonn,easy
%O A123866 1,2
%A A123866 _Reinhard Zumkeller_, Oct 16 2006