OFFSET
0,2
REFERENCES
J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; citseerx. Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: -(x^6+120*x^5+1191*x^4+2416*x^3+1191*x^2+120*x+1) / (x-1)^7. - Colin Barker, Dec 21 2012
G.f.: polylog(-7, x)*(1-x)/x. See the g.f. of the rows of A008292 by Vladeta Jovovic, Sep 02 2002. - Wolfdieter Lang, May 10 2021
MATHEMATICA
q=7; lst={}; Do[AppendTo[lst, (n+1)^q-n^q], {n, 0, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jan 23 2009 *)
Table[(n+1)^7-n^7, {n, 0, 20}] (* Vincenzo Librandi, Nov 22 2011 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 127, 2059, 14197, 61741, 201811, 543607}, 30] (* Harvey P. Dale, Apr 17 2017 *)
Differences[Range[0, 50]^7] (* Harvey P. Dale, Jun 07 2023 *)
PROG
(Magma) [(n+1)^7-n^7: n in [0..30]]; // Vincenzo Librandi, Nov 22 2011
(PARI) a(n)=(n+1)^7-n^7 \\ Charles R Greathouse IV, Sep 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved