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A075671 Sum of next n 10th powers.

%I A075671 #30 Jan 18 2025 11:22:57
%S A075671 1,60073,71280377,14843001474,1091618326275,39736919990851,
%T A075671 870012241054523,12967387960026452,143075291905145949,
%U A075671 1240006139651007925,8817026830146599701,53151169903167142598,278615540073819826527,1295610629596485350799,5430916505417064431575
%N A075671 Sum of next n 10th powers.
%H A075671 Harvey P. Dale, <a href="/A075671/b075671.txt">Table of n, a(n) for n = 1..1000</a>
%H A075671 <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (22, -231, 1540, -7315, 26334, -74613, 170544, -319770, 497420, -646646, 705432, -646646, 497420, -319770, 170544, -74613, 26334, -7315, 1540, -231, 22, -1).
%F A075671 a(n) = Sum_{i=n(n-1)/2+1..n(n-1)/2+n} i^10.
%F A075671 a(n) = (33n^21 + 825n^19 + 6336n^17 + 18546n^15 + 14289n^13 - 14187n^11 - 418n^9 + 20592n^7 - 10560n^5 - 4224n^3 + 2560n)/33792. - _Charles R Greathouse IV_, Sep 17 2009
%F A075671 G.f.: (x^20 +60051*x^19 +69959002*x^18 +13288708503*x^17 +781445555829*x^16 +19040717780376*x^15 +225625446425352*x^14 +1431958892640624*x^13 +5170348336132746*x^12 +11021721646301518*x^11 +14154518527431996*x^10 +11021721646301518*x^9 +5170348336132746*x^8 +1431958892640624*x^7 +225625446425352*x^6 +19040717780376*x^5 +781445555829*x^4 +13288708503*x^3 +69959002*x^2 +60051*x +1) / (x -1)^22. - _Colin Barker_, Dec 19 2012
%e A075671 a(1) = 1^10 = 1; a(2) = 2^10 + 3^10 = 60073; a(3) = 4^10 + 5^10 + 6^10 = 71280377; a(4) = 7^10 + 8^10 + 9^10 + 10^10 = 14843001474.
%t A075671 i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=10; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
%t A075671 With[{nn=20},Total/@TakeList[Range[(nn(nn+1))/2]^10,Range[nn]]] (* Requires Mathematica version 11 or later *) (* _Harvey P. Dale_, Mar 18 2018 *)
%Y A075671 Cf. A008454 (10th powers).
%Y A075671 Cf. A072474 (for squares), A075664 - A075670 (3rd to 9th powers), A069876 (n-th powers).
%K A075671 nonn,easy
%O A075671 1,2
%A A075671 _Zak Seidov_, Sep 24 2002
%E A075671 More terms from _Colin Barker_, Dec 19 2012