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%I #35 Jun 07 2023 16:12:34
%S 1,127,2059,14197,61741,201811,543607,1273609,2685817,5217031,9487171,
%T 16344637,26916709,42664987,65445871,97576081,141903217,201881359,
%U 281651707,386128261,521088541,693269347,910467559,1181645977,1517044201,1928294551,2428543027
%N Nexus numbers (n+1)^7-n^7.
%D J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.
%H Vincenzo Librandi, <a href="/A022523/b022523.txt">Table of n, a(n) for n = 0..10000</a>
%H H. D. Nguyen, D. Taggart, <a href="http://www.rowan.edu/colleges/csm/departments/math/facultystaff/nguyen/talks/Ten_Experimental_Conjectures_JMM_2013.pdf">Mining the OEIS: Ten Experimental Conjectures</a>, 2013; http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.391.2522&rep=rep1&type=pdf. Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F 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
%F 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
%t q=7;lst={};Do[AppendTo[lst,(n+1)^q-n^q],{n,0,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 23 2009 *)
%t Table[(n+1)^7-n^7,{n,0,20}] (* _Vincenzo Librandi_, Nov 22 2011 *)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,127,2059,14197,61741,201811,543607},30] (* _Harvey P. Dale_, Apr 17 2017 *)
%t Differences[Range[0,50]^7] (* _Harvey P. Dale_, Jun 07 2023 *)
%o (Magma) [(n+1)^7-n^7: n in [0..30]]; // _Vincenzo Librandi_, Nov 22 2011
%o (PARI) a(n)=(n+1)^7-n^7 \\ _Charles R Greathouse IV_, Sep 28 2015
%Y First differences of A001015.
%Y Cf. A008292, A022522, A022524.
%Y Column k=6 of array A047969.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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