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A001553
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1^n + 2^n + ... + 6^n.
(Formerly M4149 N1723)
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3
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6, 21, 91, 441, 2275, 12201, 67171, 376761, 2142595, 12313161, 71340451, 415998681, 2438235715, 14350108521, 84740914531, 501790686201, 2978035877635, 17706908038281, 105443761093411, 628709267031321, 3752628871164355, 22418196307542441, 134023513204581091
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| For the o.g.f.s of such sequences see the W. Lang link under A196837. The e.g.f.s are trivial. [Wolfdieter Lang, Oct 14 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 366
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FORMULA
| a(n) = sum(k^n,n=1..6),n>=0.
From Wolfdieter Lang, Oct 10 2011 (Start)
E.g.f.: (1-exp(6*x))/(exp(-x)-1) = sum(exp(j*x),j=1..6) (trivial).
O.g.f.:
(2-7*x)*(3-42*x+203*x^2-392*x^3+252*x^4)/product((1-j*x),j=1..6).
From the Laplace transformation of the e.g.f (with argument 1/p, and multiplied with 1/p). which yields the partial fraction decomposition of the given o.g.f., namely sum(1/(1-j*x),j=1..6).
(End)
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MATHEMATICA
| Table[Total[Range[6]^n], {n, 0, 40}] (* T. D. Noe, Oct 10 2011 *)
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CROSSREFS
| Column 6 of array A103438, A001552.
Sequence in context: A005498 A002222 A006359 * A009247 A093774 A151612
Adjacent sequences: A001550 A001551 A001552 * A001554 A001555 A001556
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KEYWORD
| nonn,easy
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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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