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A152726 a(n) = n^7 - (n-1)^7 + (n-2)^7 - ... + ((-1)^n)*0^7. 10
0, 1, 127, 2060, 14324, 63801, 216135, 607408, 1489744, 3293225, 6706775, 12780396, 23051412, 39697105, 65716399, 105142976, 163292480, 247046193, 365173839, 528697900, 751302100, 1049786441, 1444571447, 1960254000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

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

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 *)

PROG

(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

(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

CROSSREFS

Cf. A152725 (6th powers).

Sequence in context: A228222 A022523 A090029 * A069092 A024005 A258808

Adjacent sequences:  A152723 A152724 A152725 * A152727 A152728 A152729

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Dec 11 2008

EXTENSIONS

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

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)