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%I #28 Sep 08 2022 08:44:37
%S 0,1,524288,1162261467,274877906944,19073486328125,609359740010496,
%T 11398895185373143,144115188075855872,1350851717672992089,
%U 10000000000000000000,61159090448414546291,319479999370622926848,1461920290375446110677,5976303958948914397184
%N 19th powers: a(n) = n^19.
%H Vincenzo Librandi, <a href="/A010807/b010807.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).
%F a(n) is a totally multiplicative sequence (and is therefore multiplicative as well). - _Jaroslav Krizek_, Nov 01 2009
%F From _Ilya Gutkovskiy_, Feb 27 2017: (Start)
%F Dirichlet g.f.: zeta(s-19).
%F Sum_{n>=1} 1/a(n) = zeta(19) = A013677. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 262143*zeta(19)/262144. - _Amiram Eldar_, Oct 09 2020
%p A010807:=n->n^19: seq(A010807(n), n=0..20); # _Wesley Ivan Hurt_, Jul 13 2014
%t Range[0, 20]^19 (* _Wesley Ivan Hurt_, Jul 13 2014 *)
%o (Magma) [n^19: n in [0..15]]; // _Vincenzo Librandi_, Jun 19 2011
%o (Haskell)
%o a010807 = (^ 19) -- _Reinhard Zumkeller_, Sep 29 2014
%Y Cf. A013677, A247894 ([sqrt(a(n)]).
%K nonn,mult,easy
%O 0,3
%A _N. J. A. Sloane_.
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