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%I M4520 N1914 #49 May 08 2018 15:11:53
%S 8,36,204,1296,8772,61776,446964,3297456,24684612,186884496,
%T 1427557524,10983260016,84998999652,660994932816,5161010498484,
%U 40433724284976,317685943157892,2502137235710736,19748255868485844,156142792528260336,1236466399775623332
%N a(n) = 1^n + 2^n + ... + 8^n.
%C Conjectures for o.g.f.s for this type of sequence appear in the PhD thesis by _Simon Plouffe_. See A001552 for the reference. These conjectures are proved in a link given in A196837. [_Wolfdieter Lang_, Oct 15 2011]
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 813.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe and Robert Israel, <a href="/A001555/b001555.txt">Table of n, a(n) for n = 0..1000</a> (n = 0..200 from T. D. Noe)
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=368">Encyclopedia of Combinatorial Structures 368</a>
%F From _Wolfdieter Lang_, Oct 15 2011 (Start)
%F E.g.f.: (1-exp(8*x))/(exp(-x)-1) = Sum_{j=1..8} exp(j*x) (trivial).
%F O.g.f.: 4*(2-9*x)*(1-27*x+288*x^2-1539*x^3+4299*x^4-5886*x^5+3044*x^6) / Product_{j=1..8} (1-j*x). From the e.g.f. via Laplace transformation. See the proof in a link under A196837. (End)
%F a(n) = A001554(n) + A001018(n). - _Michel Marcus_, Jul 26 2013
%p seq(add(j^n,j=1..8), n=0..20); # _Robert Israel_, Aug 23 2015
%t Table[Total[Range[8]^n], {n, 0, 20}] (* _T. D. Noe_, Aug 09 2012 *)
%o (PARI) first(m)=vector(m,n,n--;sum(i=1,8,i^n)) \\ _Anders Hellström_, Aug 23 2015
%Y Column 8 of array A103438.
%Y Cf. A001018, A001552, A001554, A196837.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Jon E. Schoenfield_, Mar 24 2010
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