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 A075668 #45 Apr 05 2025 04:56:48
%S A075668 1,2315,374445,17703664,394340375,5265954441,48574262275,338837482880,
%T A075668 1900477947429,8950536157375,36536761179281,132397570996560,
%U A075668 433806511149115,1303971065324669,3637715990646375,9507513902672896,23461050872397545,55013865421504275
%N A075668 Sum of next n 7th powers.
%H A075668 Kelvin Voskuijl, <a href="/A075668/b075668.txt">Table of n, a(n) for n = 1..10000</a>
%H A075668 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
%F A075668 a(n) = Sum_{i=n*(n-1)/2+1..n*(n-1)/2+n} i^7.
%F A075668 a(n) = (3*n^15 + 42*n^13 + 168*n^11 + 206*n^9 - 11*n^7 - 56*n^5 + 32*n^3)/384. - _Charles R Greathouse IV_, Sep 17 2009
%F A075668 G.f.: x*(x^14 +2299*x^13 +337525*x^12 +11989784*x^11 +154720571*x^10 +875467853*x^9 +2397170367*x^8 +3336829200*x^7 +2397170367*x^6 +875467853*x^5 +154720571*x^4 +11989784*x^3 +337525*x^2 +2299*x +1)/(x-1)^16. - _Colin Barker_, Jul 22 2012
%e A075668 a(1) = 1^7 = 1; a(2) = 2^7 + 3^7 = 2315; a(3) = 4^7 + 5^7 + 6^7 = 374445; a(4) = 7^7 + 8^7 + 9^7 + 10^7 = 17703664.
%t A075668 i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=7; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
%Y A075668 Cf. A001015 (7th powers).
%Y A075668 Cf. A006003 (for natural numbers), A072474 (for squares), A075664 - A075671 (for 3rd to 10th powers), A069876 (n-th powers).
%K A075668 nonn,easy
%O A075668 1,2
%A A075668 _Zak Seidov_, Sep 24 2002