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A001556
a(n) = 1^n + 2^n + ... + 9^n.
(Formerly M4627 N1977)
4
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
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].
Index entries for linear recurrences with constant coefficients, signature (45, -870, 9450, -63273, 269325, -723680, 1172700, -1026576, 362880).
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
KEYWORD
nonn,changed
EXTENSIONS
More terms from Jon E. Schoenfield, Mar 24 2010
STATUS
approved