OFFSET
0,1
COMMENTS
Conjectures for o.g.f.s for this type of sequences 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, Table of n, a(n) for n = 0..200
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 367
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Index entries for linear recurrences with constant coefficients, signature (28, -322, 1960, -6769, 13132, -13068, 5040).
FORMULA
From Wolfdieter Lang, Oct 15 2011: (Start)
E.g.f.: (1-exp(7*x))/(exp(-x)-1) = Sum_{j=1..7} exp(j*x) (trivial).
O.g.f.: (7 - 168*x + 1610*x^2 - 7840*x^3 + 20307*x^4 - 26264*x^5 + 13068*x^6)/Product_{j=1..7} (1 - j*x). From the e.g.f. via Laplace transformation. See the proof in a link under A196837. (End)
MAPLE
MATHEMATICA
Table[Total[Range[7]^n], {n, 0, 20}]
PROG
(Magma) [1+2^n+3^n+4^n+5^n+6^n+7^n : n in [0..30]]; // Wesley Ivan Hurt, Jul 15 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Jon E. Schoenfield, Mar 24 2010
STATUS
approved