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A001556
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1^n + 2^n + ... + 9^n.
(Formerly M4627 N1977)
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2
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9, 45, 285, 2025, 15333, 120825, 978405, 8080425, 67731333, 574304985, 4914341925, 42364319625, 367428536133, 3202860761145, 28037802953445, 246324856379625, 2170706132009733, 19179318935377305, 169842891165484965
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Conjectures for o.g.f.s for this type of sequences appear in the PhD thesis by S. Plouffe. See A001552 for the reference. These conjectures are proved in the link given in A196837. [Wolfdieter Lang, Oct 15, 2011]
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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).
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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].
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 369
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FORMULA
| a(n)=sum(j^n,j=1..9), 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((1-j*x),j=1..9).
From the e.g.f.via Laplace transformation. See the proof in a link under A196837.
(End)
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CROSSREFS
| Column 9 of array A103438. A196837.
Sequence in context: A132133 A009410 A030113 * A009432 A145757 A058824
Adjacent sequences: A001553 A001554 A001555 * A001557 A001558 A001559
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Mar 24 2010
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