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A001555
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1^n + 2^n + ... + 8^n.
(Formerly M4520 N1914)
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2
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8, 36, 204, 1296, 8772, 61776, 446964, 3297456, 24684612, 186884496, 1427557524, 10983260016, 84998999652, 660994932816, 5161010498484, 40433724284976, 317685943157892, 2502137235710736, 19748255868485844, 156142792528260336
(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 a 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 368
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FORMULA
| From Wolfdieter Lang, Oct 15 2011 (Start)
E.g.f.: (1-exp(8*x))/(exp(-x)-1) = sum(exp(j*x),j=1..8) (trivial).
O.g.f.: 4*(2-9*x)*(1-27*x+288*x^2-1539*x^3+4299*x^4-5886*x^5+3044*x^6)/product(1-j*x,j=1..8). From the e.g.f. via Laplace transformation. See the proof in a link under A196837.
(End)
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CROSSREFS
| Column 8 of array A103438.
Sequence in context: A019022 A079819 A030112 * A032770 A032794 A000757
Adjacent sequences: A001552 A001553 A001554 * A001556 A001557 A001558
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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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