A001556 a(n) = 1^n + 2^n + ... + 9^n. (Formerly M4627 N1977)

9, 45, 285, 2025, 15333, 120825, 978405, 8080425, 67731333, 574304985, 4914341925, 42364319625, 367428536133, 3202860761145, 28037802953445, 246324856379625, 2170706132009733, 19179318935377305, 169842891165484965, 1506994510201252425

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 the 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 369

Formula

a(n) = sum_{j=1..9} j^n, n>=0.

From Wolfdieter Lang, Oct 15 2011: (Start)

E.g.f.: (1-exp(9*x))/(exp(-x)-1) = sum(exp(j*x),j=1..9) (trivial).

O.g.f.: (9 - 360*x + 6090*x^2 - 56700*x^3 + 316365*x^4 - 1077300*x^5 + 2171040*x^6 - 2345400*x^7 + 1026576*x^8)/product_{j=1..9} (1-j*x).

From the e.g.f. via Laplace transformation. See the proof in a link under A196837.

(End)

a(n) = A001555(n) + A001019(n). - Michel Marcus, Jul 26 2013

Mathematica

Table[Total[Range[9]^n], {n, 0, 20}] (* T. D. Noe, Aug 09 2012 *)

Crossrefs

Column 9 of array A103438. A196837.

Sequence in context: A009410 A290358 A030113 * A230063 A009432 A145757

Adjacent sequences: A001553 A001554 A001555 * A001557 A001558 A001559

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Jon E. Schoenfield, Mar 24 2010

Status

approved