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A000542 Sum of 8th powers: 1^8 + 2^8 + ... + n^8.
(Formerly M5427 N2358)
+0
4
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; listen)
OFFSET

0,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

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].

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.

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

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]

PROGRAM

(Other) sage: [bernoulli_polynomial(n, 9)/9 for n in xrange(1, 25)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2009]

CROSSREFS

Row 8 of array A103438.

Sequence in context: A017679 A013956 A036086 this_sequence A023877 A086022 A125649

Adjacent sequences: A000539 A000540 A000541 this_sequence A000543 A000544 A000545

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified December 18 21:37 EST 2009. Contains 171024 sequences.


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