A010807 19th powers: a(n) = n^19.
0, 1, 524288, 1162261467, 274877906944, 19073486328125, 609359740010496, 11398895185373143, 144115188075855872, 1350851717672992089, 10000000000000000000, 61159090448414546291, 319479999370622926848, 1461920290375446110677, 5976303958948914397184
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (20, -190, 1140, -4845, 15504, -38760, 77520, -125970, 167960, -184756, 167960, -125970, 77520, -38760, 15504, -4845, 1140, -190, 20, -1).
Programs
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Haskell
a010807 = (^ 19) -- Reinhard Zumkeller, Sep 29 2014
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Magma
[n^19: n in [0..15]]; // Vincenzo Librandi, Jun 19 2011
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Maple
A010807:=n->n^19: seq(A010807(n), n=0..20); # Wesley Ivan Hurt, Jul 13 2014
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Mathematica
Range[0, 20]^19 (* Wesley Ivan Hurt, Jul 13 2014 *)
Formula
a(n) is a totally multiplicative sequence (and is therefore multiplicative as well). - Jaroslav Krizek, Nov 01 2009
From Ilya Gutkovskiy, Feb 27 2017: (Start)
Dirichlet g.f.: zeta(s-19).
Sum_{n>=1} 1/a(n) = zeta(19) = A013677. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 262143*zeta(19)/262144. - Amiram Eldar, Oct 09 2020