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A000542
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Sum of 8th powers: 1^8 + 2^8 + ... + n^8.
(Formerly M5427 N2358)
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6
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0, 1, 257, 6818, 72354, 462979, 2142595, 7907396, 24684612, 67731333, 167731333, 382090214, 812071910, 1627802631, 3103591687, 5666482312, 9961449608, 16937207049, 27957167625, 44940730666, 70540730666, 108363590027, 163239463563, 241550448844
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = n*A000541(n) - sum [i = 0 ... n-1] A000541(i) [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Apr 26 2010]
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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. 815.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 155.
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
| T. D. Noe, Table of n, a(n) for n=0..1000
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].
B. Berselli, a description of the recursive method n*Ar(n)-sum[i=0...n-1]Ar(i) (Ar(m) is the m-th term of a sequence): website Matem@ticamente. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Apr 26 2010]
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FORMULA
| a(n) = n*(n+1)*(2*n+1)*(5*n^6+15*n^5+5*n^4-15*n^3-n^2+9*n-3)/90.
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MAPLE
| a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^8 od: seq(a[n], n=0..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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MATHEMATICA
| lst={}; s=0; Do[s=s+n^8; AppendTo[lst, s], {n, 10^2}]; lst..or..Table[Sum[k^8, {k, 1, n}], {n, 0, 100}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 14 2008]
s = 0; lst = {s}; Do[s += n^8; AppendTo[lst, s], {n, 1, 30, 1}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
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PROG
| (Other) sage: [bernoulli_polynomial(n, 9)/9 for n in xrange(1, 25)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2009]
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CROSSREFS
| Row 8 of array A103438.
Sequence in context: A017679 A013956 A036086 * A023877 A168116 A086022
Adjacent sequences: A000539 A000540 A000541 * A000543 A000544 A000545
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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