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%I #19 Mar 18 2018 17:29:40
%S 1,60073,71280377,14843001474,1091618326275,39736919990851,
%T 870012241054523,12967387960026452,143075291905145949,
%U 1240006139651007925,8817026830146599701,53151169903167142598,278615540073819826527,1295610629596485350799,5430916505417064431575
%N Sum of next n 10th powers.
%H Harvey P. Dale, <a href="/A075671/b075671.txt">Table of n, a(n) for n = 1..1000</a>
%F a(1)=1; a(n)=sum(i^s, {i, n(n-1)/2+1, n(n-1)/2+1+n}).
%F a(n) = (33n^21 + 825n^19 + 6336n^17 + 18546n^15 + 14289n^13 - 14187n^11 - 418n^9 + 20592n^7 - 10560n^5 - 4224n^3 + 2560n)/33792
%F a(n) = n/33792*(33*n^20 + 825*n^18 + 6336*n^16 + 18546*n^14 + 14289*n^12 - 14187*n^10 - 418*n^8 + 20592*n^6 - 10560*n^4 - 4224*n^2 + 2560). - _Vladeta Jovovic_, Oct 03 2003
%F 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 s=10; a(1) = 1^s = 1; a(2) = 2^s + 3^s = 2^10 + 3^10 = 60073; a(3) = 4^s + 5^s + 6^s = 71280377, a(4) = 7^s + 8^s + 9^s + 10^3 = 14843001474.
%t i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=10; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
%t 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 Cf. A072474 (s=2), A075664 - A075670 (s=3-10), A075671 (s=n).
%K nonn,easy
%O 1,2
%A _Zak Seidov_, Sep 24 2002
%E Formula from _Charles R Greathouse IV_, Sep 17 2009
%E More terms from _Colin Barker_, Dec 19 2012
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