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

0, 1, 127, 2060, 14324, 63801, 216135, 607408, 1489744, 3293225, 6706775, 12780396, 23051412, 39697105, 65716399, 105142976, 163292480, 247046193, 365173839, 528697900, 751302100, 1049786441, 1444571447, 1960254000

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (7,-20,28,-14,-14,28,-20,7,-1).

Crossrefs

Cf. A152725 (6th powers).

Programs

Magma

m:=50; R:=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

Mathematica

k=0;lst={k};Do[k=n^7-k;AppendTo[lst,k],{n,1,5!}];lst
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 *)
Table[Total[(Times@@@Partition[Riffle[Range[n,1,-1],{1,-1},{2,-1,2}],2])^7],{n,0,30}] (* Harvey P. Dale, Mar 14 2023 *)

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

Formula

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

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

Extensions

Offset corrected by R. J. Mathar, Jul 08 2013