|
| |
|
|
A000541
|
|
Sum of 7th powers: 1^7 + 2^7 + ... + n^7.
(Formerly M5394 N2343)
|
|
8
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| 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
a(n) = n*A000540(n) - sum [i = 0 ... n-1] A000540(i) [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Apr 26 2010]
|
|
|
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).
|
|
|
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]
|
|
|
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 * A023876 A189608 A168067
Adjacent sequences: A000538 A000539 A000540 * A000542 A000543 A000544
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
