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A075669 Sum of next n 8th powers.

%I A075669 #42 Apr 05 2025 04:54:55
%S A075669 1,6817,2135777,165588738,5498750979,102697107715,1264908663011,
%T A075669 11373936899396,79985007371877,461856872635333,2269365182729029,
%U A075669 9747136491367430,37362375267437415,129917413702762791,415196000174767687,1232554282743058568,3428668198703973449
%N A075669 Sum of next n 8th powers.
%H A075669 Kelvin Voskuijl, <a href="/A075669/b075669.txt">Table of n, a(n) for n = 1..10000</a>
%H A075669 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18,-153,816,-3060,8568,-18564,31824,-43758,48620,-43758,31824,-18564,8568,-3060,816,-153,18,-1).
%F A075669 a(n) = Sum_{i=n*(n-1)/2+1..n*(n-1)/2+n} i^8.
%F A075669 a(n) = (45*n^17 + 780*n^15 + 3990*n^13 + 6900*n^11 + 1205*n^9 - 3240*n^7 + 1584*n^5 + 640*n^3 - 384*n)/11520. - _Charles R Greathouse IV_, Sep 17 2009
%F A075669 G.f.: x*(x^16 +6799*x^15 +2013224*x^14 +128186937*x^13 +2839367964*x^12 +27332724427*x^11 +129026301848*x^10 +319786366637*x^9 +431174080326*x^8 +319786366637*x^7 +129026301848*x^6 +27332724427*x^5 +2839367964*x^4 +128186937*x^3 +2013224*x^2 +6799*x +1)/(x -1)^18. - _Colin Barker_, Sep 06 2012
%e A075669 a(1) = 1^8 = 1; a(2) = 2^8 + 3^8 = 6817; a(3) = 4^8 + 5^8 + 6^8 = 2135777; a(4) = 7^8 + 8^8 + 9^8 + 10^8 = 165588738.
%t A075669 i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=8; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
%Y A075669 Cf. A001016 (8th powers).
%Y A075669 Cf. A006003 (for natural numbers), A072474 (for squares), A075664 - A075671 (for 3rd to 10th powers), A069876 (for n-th powers).
%K A075669 nonn,easy
%O A075669 1,2
%A A075669 _Zak Seidov_, Sep 24 2002