Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A000541
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A000541 Sum of 7th powers: 1^7 + 2^7 + ... + n^7.
(Formerly M5394 N2343)
+0
5
0, 1, 129, 2316, 18700, 96825, 376761, 1200304, 3297456, 8080425, 18080425, 37567596, 73399404, 136147921, 241561425, 412420800, 680856256, 1091194929, 1703414961, 2597286700, 3877286700, 5678375241, 8172733129, 11577558576, 16164030000, 22267545625 (list; graph; listen)
OFFSET

0,3

COMMENT

a(n) is divisible by A000537(n) if and only n is congruent to 1 mod 3 (see A016777) - Artur Jasinski (grafix(AT)csl.pl), Oct 10 2007

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^2*(n+1)^2*(3*n^4+6*n^3-n^2-4*n+2)/24.

a(n) = Sqrt[Sum[Sum[(i*j)^7, {i, 1, n}], {j, 1, n}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 26 2004

Jacobi formula: a(n) = 2(A000217(n))^4 - A000539(n) - Artur Jasinski (grafix(AT)csl.pl), Oct 10 2007

MAPLE

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^7 od: seq(a[n], n=0..25); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008

MATHEMATICA

Table[Sum[k^7, {k, 1, n}], {n, 0, 100}] - Artur Jasinski (grafix(AT)csl.pl), Oct 10 2007

s = 0; lst = {s}; Do[s += n^7; AppendTo[lst, s], {n, 1, 30, 1}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]

CROSSREFS

Row 7 of array A103438.

Cf. A000217, A000537, A000539, A119617, A134153, A134154, A134157, A134158, A134159, A134160.

Sequence in context: A017677 A013955 A036085 this_sequence A023876 A143006 A138586

Adjacent sequences: A000538 A000539 A000540 this_sequence A000542 A000543 A000544

KEYWORD

easy,nonn

AUTHOR

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

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified December 16 13:01 EST 2009. Contains 170825 sequences.


AT&T Labs Research