A001554 a(n) = 1^n + 2^n + ... + 7^n. (Formerly M4393 N1850)

7, 28, 140, 784, 4676, 29008, 184820, 1200304, 7907396, 52666768, 353815700, 2393325424, 16279522916, 111239118928, 762963987380, 5249352196144, 36210966447236, 250337422025488, 1733857359003860, 12027604452404464, 83544895168776356, 580964060390826448

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.

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

A001554:=n->add(i^n, i=1..7): seq(A001554(n), n=0..30); # Wesley Ivan Hurt, Jul 15 2014

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

Column 7 of array A103438. A196837.

Sequence in context: A238448 A290356 A025030 * A370243 A370103 A359723

Adjacent sequences: A001551 A001552 A001553 * A001555 A001556 A001557

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Jon E. Schoenfield, Mar 24 2010

Status

approved