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A022528 Nexus numbers (n+1)^12-n^12.

%I A022528 #30 Sep 08 2022 08:44:46
%S A022528 1,4095,527345,16245775,227363409,1932641711,11664504865,54878189535,
%T A022528 213710059745,717570463519,2138428376721,5777672071535,14381984674225,
%U A022528 33395827252815,73052425515329,151728638820031,301147260519105,574209144196415
%N A022528 Nexus numbers (n+1)^12-n^12.
%D A022528 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.
%H A022528 Vincenzo Librandi, <a href="/A022528/b022528.txt">Table of n, a(n) for n = 0..10000</a>
%H A022528 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A022528 a(n) = A008456(n+1) - A008456(n). - _Colin Barker_, Nov 30 2014
%F A022528 G.f.: (x +1)*(x^10 +4082*x^9 +474189*x^8 +9713496*x^7 +56604978*x^6 +105907308*x^5 +56604978*x^4 +9713496*x^3 +474189*x^2 +4082*x +1) / (x -1)^12. - _Colin Barker_, Nov 30 2014
%F A022528 G.f.: polylog(-12, x)*(1-x)/x. See the g.f. of _Colin Barker_ (with expanded numerator), and the g.f. of the rows of A008292 by _Vladeta Jovovic_, Sep 02 2002. - _Wolfdieter Lang_, May 10 2021
%t A022528 lst={};Do[a=n^6;b=(n+1)^6;s=(a+b)*(b-a);AppendTo[lst,s],{n,0,4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 23 2009 *)
%t A022528 Table[(n+1)^12-n^12,{n,0,20}] (* _Vincenzo Librandi_, Nov 22 2011 *)
%t A022528 LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{1,4095,527345,16245775,227363409,1932641711,11664504865,54878189535,213710059745,717570463519,2138428376721,5777672071535},20] (* _Harvey P. Dale_, Apr 23 2019 *)
%o A022528 (Magma) [(n+1)^12-n^12: n in [0..20]]; // _Vincenzo Librandi_, Nov 22 2011
%o A022528 (PARI) vector(30, n, n--; (n+1)^12-n^12) \\ _Colin Barker_, Nov 30 2014
%Y A022528 Column k=11 of array A047969.
%Y A022528 Cf. A008292, A022527, A022529.
%K A022528 nonn,easy
%O A022528 0,2
%A A022528 _N. J. A. Sloane_