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A001554
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1^n + 2^n + ... + 7^n.
(Formerly M4393 N1850)
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2
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7, 28, 140, 784, 4676, 29008, 184820, 1200304, 7907396, 52666768, 353815700, 2393325424, 16279522916, 111239118928, 762963987380, 5249352196144, 36210966447236, 250337422025488, 1733857359003860, 12027604452404464
(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 367
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FORMULA
| From Wolfdieter Lang, Oct 15 2011 (Start)
E.g.f.: (1-exp(7*x))/(exp(-x)-1) = sum(exp(j*x),j=1..7) (trivial).
O.g.f.:
(7-168*x+1610*x^2-7840*x^3+20307*x^4-26264*x^5+13068*x^6)/product((1-j*x),j=1..7).
From the e.g.f. via Laplace transformation. See the proof in a link under A196837.
(End)
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CROSSREFS
| Column 7 of array A103438. A196837.
Sequence in context: A037702 A054626 A025030 * A026664 A203296 A058822
Adjacent sequences: A001551 A001552 A001553 * A001555 A001556 A001557
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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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