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A001557
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1^n + 2^n + ... + 10^n.
(Formerly M4713 N2014)
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4
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10, 55, 385, 3025, 25333, 220825, 1978405, 18080425, 167731333, 1574304985, 14914341925, 142364319625, 1367428536133, 13202860761145, 128037802953445, 1246324856379625, 12170706132009733, 119179318935377305, 1169842891165484965, 11506994510201252425
(list;
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OFFSET
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0,1
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COMMENTS
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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]
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REFERENCES
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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
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T. D. Noe, Table of n, a(n) for n = 0..200
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 370
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FORMULA
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a(n)=sum(j^n,j=1..10), n>=0.
E.g.f.: exp(x)+exp(2*x)+exp(3*x)+exp(4*x)+exp(5*x)+exp(6*x)+exp(7*x)+exp(8*x)+exp(9*x)+exp(10*x). - Vladeta Jovovic, May 08 2002
From Wolfdieter Lang, Oct 15 2011 (Start)
O.g.f.:
(2-11*x)*(5-220*x+4070*x^2-41140*x^3+247049*x^4-896368*x^5+1903836*x^6
-2143152*x^7+966240*x^8)/product((1-j*x),j=1..10).
From the e.g.f. via Laplace transformation. See the proof in a link under A196837.
(End)
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MATHEMATICA
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Table[Total[Range[10]^n], {n, 0, 20}] (* T. D. Noe, Aug 09 2012 *)
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CROSSREFS
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Column 10 of array A103438. A196837.
Sequence in context: A199413 A054629 A030114 * A197357 A164951 A000814
Adjacent sequences: A001554 A001555 A001556 * A001558 A001559 A001560
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Mar 24 2010
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STATUS
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approved
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