OFFSET
0,1
COMMENTS
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]
REFERENCES
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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe and Robert Israel, Table of n, a(n) for n = 0..1000 (n = 0..200 from T. D. Noe)
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 368
FORMULA
From Wolfdieter Lang, Oct 15 2011 (Start)
E.g.f.: (1-exp(8*x))/(exp(-x)-1) = Sum_{j=1..8} exp(j*x) (trivial).
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)
MAPLE
seq(add(j^n, j=1..8), n=0..20); # Robert Israel, Aug 23 2015
MATHEMATICA
Table[Total[Range[8]^n], {n, 0, 20}] (* T. D. Noe, Aug 09 2012 *)
PROG
(PARI) first(m)=vector(m, n, n--; sum(i=1, 8, i^n)) \\ Anders Hellström, Aug 23 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Jon E. Schoenfield, Mar 24 2010
STATUS
approved