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URL: https://oeis.org/A022523

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A022523
Nexus numbers (n + 1)^7 - n^7.
17
1, 127, 2059, 14197, 61741, 201811, 543607, 1273609, 2685817, 5217031, 9487171, 16344637, 26916709, 42664987, 65445871, 97576081, 141903217, 201881359, 281651707, 386128261, 521088541, 693269347, 910467559, 1181645977, 1517044201, 1928294551, 2428543027, 3032575309
OFFSET
0,2
REFERENCES
J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.
Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), pages 205-206.
LINKS
H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; citseerx. Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014
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
E.g.f.: exp(x)*(1 + 126*x + 903*x^2 + 1400*x^3 + 700*x^4 + 126*x^5 + 7*x^6). - Stefano Spezia, Oct 28 2025
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
First differences of A001015.
Column k=6 of array A047969.
Sequence in context: A181126 A228263 A228222 * A090029 A152726 A069092
KEYWORD
nonn,easy
STATUS
approved