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A152726 a(n) = n^7 - (n-1)^7 + (n-2)^7 - ... + ((-1)^n)*0^7. 10

%I

%S 0,1,127,2060,14324,63801,216135,607408,1489744,3293225,6706775,

%T 12780396,23051412,39697105,65716399,105142976,163292480,247046193,

%U 365173839,528697900,751302100,1049786441,1444571447,1960254000

%N a(n) = n^7 - (n-1)^7 + (n-2)^7 - ... + ((-1)^n)*0^7.

%H G. C. Greubel, <a href="/A152726/b152726.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (7,-20,28,-14,-14,28,-20,7,-1).

%F G.f.: x*(1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/((1+x)*(x-1)^8). - _R. J. Mathar_, Jul 08 2013

%F a(n) = (17*(-1)^n + 84*n^2 - 17 + 28*n^6 + 8*n^7 - 70*n^4)/16. - _R. J. Mathar_, Jul 08 2013

%t k=0;lst={k};Do[k=n^7-k;AppendTo[lst,k],{n,1,5!}];lst

%t LinearRecurrence[{7, -20, 28, -14, -14, 28, -20, 7, -1}, {0, 1, 127, 2060, 14324, 63801, 216135, 607408, 1489744}, 50] (* _G. C. Greubel_, Sep 01 2018 *)

%o (PARI) x='x+O('x^50); concat([0], Vec(x*(1+120*x+1191*x^2 +2416*x^3 +1191*x^4+120*x^5+x^6)/((1+x)*(x-1)^8))) \\ _G. C. Greubel_, Sep 01 2018

%o (MAGMA) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1+120*x+1191*x^2+2416*x^3+1191*x^4 +120*x^5+x^6)/( (1+x)*(x-1)^8))); // _G. C. Greubel_, Sep 01 2018

%Y Cf. A152725 (6th powers).

%K nonn,easy

%O 0,3

%A _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008

%E Offset corrected by _R. J. Mathar_, Jul 08 2013

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Last modified September 15 14:38 EDT 2019. Contains 327078 sequences. (Running on oeis4.)