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%I #42 Sep 08 2022 08:44:35
%S 0,1,4096,531441,16777216,244140625,2176782336,13841287201,
%T 68719476736,282429536481,1000000000000,3138428376721,8916100448256,
%U 23298085122481,56693912375296,129746337890625,281474976710656,582622237229761
%N 12th powers: a(n) = n^12.
%C Numbers which are square, cubic and quartic. - _Doug Bell_, Jun 03 2017
%H Vincenzo Librandi, <a href="/A008456/b008456.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
%F Multiplicative with a(p^e) = p^(12*e). - _David W. Wilson_, Aug 01 2001
%F a(n) = A000290(n)^6 = A000578(n)^4 = A000583(n)^3 = A001014(n)^2. - _Doug Bell_, Jun 03 2017
%F From _Amiram Eldar_, Oct 08 2020: (Start)
%F Sum_{n>=1} 1/a(n) = zeta(12) = 691*Pi^12/638512875 (A013670).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 2047*zeta(12)/2048 = 1414477*Pi^12/1307674368000. (End)
%F a(n) = 13*a(n-1)-78*a(n-2)+286*a(n-3)-715*a(n-4)+1287*a(n-5)-1716*a(n-6)+1716*a(n-7)-1287*a(n-8)+715*a(n-9)-286*a(n-10)+78*a(n-11)-13*a(n-12)+a(n-13). - _Wesley Ivan Hurt_, Dec 02 2021
%t Range[0,30]^12 (* _Vladimir Joseph Stephan Orlovsky_, May 05 2011 *)
%o (Magma) [n^12: n in [0..30]]; // _Vincenzo Librandi_, May 06 2011
%Y a(n) = A123868(n) + 1.
%Y Cf. A000290, A000578, A000583, A001014, A013670.
%K nonn,easy,mult
%O 0,3
%A _N. J. A. Sloane_
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