A001553 a(n) = 1^n + 2^n + ... + 6^n. (Formerly M4149 N1723)

6, 21, 91, 441, 2275, 12201, 67171, 376761, 2142595, 12313161, 71340451, 415998681, 2438235715, 14350108521, 84740914531, 501790686201, 2978035877635, 17706908038281, 105443761093411, 628709267031321, 3752628871164355, 22418196307542441, 134023513204581091

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

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

Column 6 of array A103438, A001552.

Sequence in context: A002222 A290355 A006359 * A369556 A009247 A093774

Adjacent sequences: A001550 A001551 A001552 * A001554 A001555 A001556

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Jon E. Schoenfield, Mar 24 2010

Status

approved