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 A152725 #44 Jun 19 2025 13:22:44
%S A152725 0,1,63,666,3430,12195,34461,83188,178956,352485,647515,1124046,
%T A152725 1861938,2964871,4564665,6825960,9951256,14186313,19825911,27219970,
%U A152725 36780030,48986091,64393813,83642076,107460900,136679725,172236051,215184438
%N A152725 a(n) = n*(n+1)*(n^4 + 2*n^3 - 2*n^2 - 3*n + 3)/2.
%H A152725 G. C. Greubel, <a href="/A152725/b152725.txt">Table of n, a(n) for n = 0..5000</a>
%H A152725 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A152725 a(n) = n^6 - (n-1)^6 + (n-2)^6 - ... + ((-1)^n)*0^6.
%F A152725 G.f.: x*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1-x)^7. - _R. J. Mathar_, Jul 08 2013
%F A152725 a(n) = A050492(A000217(n)). - _Kelvin Voskuijl_, Jun 18 2025
%F A152725 E.g.f.: exp(x)*x*(2 + 61*x + 160*x^2 + 95*x^3 + 18*x^4 + x^5)/2. - _Stefano Spezia_, Jun 19 2025
%t A152725 k=0;lst={k};Do[k=n^6-k;AppendTo[lst,k],{n,1,5!}];lst
%t A152725 LinearRecurrence[{7,-21,35,-35,21,-7,1}, {0,1,63,666,3430,12195,34461}, 50] (* _G. C. Greubel_, Sep 01 2018 *)
%t A152725 CoefficientList[Series[-((x (1+56 x+246 x^2+56 x^3+x^4))/(-1+x)^7),{x,0,30}],x] (* _Harvey P. Dale_, Aug 03 2024 *)
%o A152725 (PARI) a(n)=n*(n+1)*(n^4+2*n^3-2*n^2-3*n+3)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A152725 (Magma) [n*(n+1)*(n^4+2*n^3-2*n^2-3*n+3)/2: n in [0..50]]; // _G. C. Greubel_, Sep 01 2018
%Y A152725 Cf. A062392, A062393 (for 5th powers), A011934, A152726 (for 7th powers).
%K A152725 nonn,easy
%O A152725 0,3
%A A152725 _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008
%E A152725 Offset set to 0 by _R. J. Mathar_, Aug 15 2010