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 A059721 #24 Dec 30 2024 22:43:54
%S A059721 0,1,21,182,910,3255,9331,22876,49932,99645,185185,324786,542906,
%T A059721 871507,1351455,2034040,2982616,4274361,6002157,8276590,11228070,
%U A059721 15009071,19796491,25794132,33235300,42385525,53545401,67053546,83289682,102677835,125689655,152847856
%N A059721 Mean of first six positive powers of n, i.e., (n + n^2 + n^3 + n^4 + n^5 + n^6)/6.
%H A059721 Harry J. Smith, <a href="/A059721/b059721.txt">Table of n, a(n) for n = 0..1000</a>
%H A059721 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A059721 a(n) = (n^7 - n)/(6n - 6) = A053700(n)*n/6.
%F A059721 G.f.: x*(1+14*x+56*x^2+42*x^3+7*x^4)/(1-x)^7. [_Colin Barker_, May 08 2012]
%e A059721 a(2) = (2 + 4 + 8 + 16 + 32 + 64)/6 = 126/6 = 21.
%t A059721 Table[Total[n^Range[6]]/6,{n,0,30}] (* _Harvey P. Dale_, Jan 29 2011 *)
%o A059721 (PARI) a(n) = { if(n==1, 1, (n^7 - n)/(6*n - 6)) } \\ _Harry J. Smith_, Jun 28 2009
%Y A059721 Cf. A059722, A059723.
%K A059721 nonn,easy
%O A059721 0,3
%A A059721 _Henry Bottomley_, Feb 07 2001