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 A136008 #37 Dec 07 2024 15:51:36
%S A136008 0,0,60,720,4080,15600,46620,117600,262080,531360,999900,1771440,
%T A136008 2985840,4826640,7529340,11390400,16776960,24137280,34011900,47045520,
%U A136008 63999600,85765680,113379420,148035360,191102400,244140000,308915100
%N A136008 a(n) = n^6 - n^2.
%H A136008 G. C. Greubel, <a href="/A136008/b136008.txt">Table of n, a(n) for n = 0..1000</a>
%H A136008 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A136008 G.f.: 60*x^2*(1 +5*x +5*x^2 +x^3)/(1-x)^7. - _Alexander R. Povolotsky_, Apr 01 2008
%F A136008 a(n) = A001014(n) - A000290(n). - _Omar E. Pol_, Dec 26 2008
%F A136008 From _Amiram Eldar_, Jan 12 2021: (Start)
%F A136008 Sum_{n>=2} 1/a(n) = 7/8 - Pi^2/6 + Pi*coth(Pi)/4.
%F A136008 Sum_{n>=2} (-1)^n/a(n) = -7/8 + Pi^2/12 + Pi*csch(Pi)/4 = -7/8 + A072691 + (1/4) * A090986. (End)
%F A136008 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). - _Wesley Ivan Hurt_, May 04 2021
%F A136008 From _G. C. Greubel_, Feb 07 2022: (Start)
%F A136008 a(n) = 6*binomial(n^2 + 1, 3).
%F A136008 E.g.f.: x^2*(30 +90*x +65*x^2 +15*x^3 +x^4)*exp(x). (End)
%t A136008 f[n_]:=n^6-n^2; f[Range[0,60]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 10 2011 *)
%t A136008 LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,0,60,720,4080,15600,46620},30] (* _Harvey P. Dale_, Dec 07 2024 *)
%o A136008 (Sage) [n^2*(n^4-1) for n in range(0,31)] # _Zerinvary Lajos_, Jul 16 2008
%o A136008 (Magma) [6*Binomial(n^2 +1, 3): n in [0..30]]; // _G. C. Greubel_, Feb 07 2022
%Y A136008 Cf. A000290, A001014, A013661, A072691, A090986.
%K A136008 easy,nonn
%O A136008 0,3
%A A136008 _Rolf Pleisch_, Mar 16 2008
%E A136008 Extended by _Ray Chandler_, Dec 13 2008