OFFSET
0,1
COMMENTS
For the o.g.f.s of such sequences see the W. Lang link under A196837. The e.g.f.s are trivial. - Wolfdieter Lang, Oct 14 2011
a(n) is divisible by 7 iff n is not divisible by 6 (see De Koninck & Mercier reference). Example: a(5)= 12201 = 7 * 1743 and a(6) = 67171 = 9595 * 7 + 6. - Bernard Schott, Mar 06 2020
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.
J.-M. De Koninck and A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 289 pp. 45, 194, Ellipses, Paris, (2004).
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 366
Index entries for linear recurrences with constant coefficients, signature (21, -175, 735, -1624, 1764, -720).
FORMULA
a(n) = Sum_{k=1..6} k^n.
From Wolfdieter Lang, Oct 10 2011: (Start)
E.g.f.: (1-exp(6*x))/(exp(-x)-1) = Sum_{j=1..6} exp(j*x) (trivial).
O.g.f.: (2 - 7*x)*(3 - 42*x + 203*x^2 - 392*x^3 + 252*x^4)/Product_{j=1..6} (1 - j*x).
From the Laplace transformation of the e.g.f. (with argument 1/p, and multiplied with 1/p), which yields the partial fraction decomposition of the given o.g.f., namely Sum_{j=1..6} 1/(1 - j*x).
(End)
MATHEMATICA
Table[Total[Range[6]^n], {n, 0, 40}] (* T. D. Noe, Oct 10 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Jon E. Schoenfield, Mar 24 2010
STATUS
approved