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A000539
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Sum of 5th powers: 0^5 + 1^5 + 2^5 + ... + n^5.
(Formerly M5241 N2280)
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46
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0, 1, 33, 276, 1300, 4425, 12201, 29008, 61776, 120825, 220825, 381876, 630708, 1002001, 1539825, 2299200, 3347776, 4767633, 6657201, 9133300, 12333300, 16417401, 21571033, 28007376, 35970000, 45735625, 57617001, 71965908, 89176276, 109687425, 133987425
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) = n*A000538(n) - sum [i = 0 ... n-1] A000538(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. 813.
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]
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index to sequences with linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
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FORMULA
| a(n) = n^2*(n+1)^2*(2*n^2+2*n-1)/12.
a(n) = Sqrt[Sum[Sum[(i*j)^5, {i, 1, n}], {j, 1, n}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 26 2004
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MAPLE
| A000539:=-(1+26*z+66*z**2+26*z**3+z**4)/(z-1)**7; [S. Plouffe in his 1992 dissertation.]
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^5 od: seq(a[n], n=0..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
a:=n->sum(j^5, j=0..n): seq(a(n), n=0..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2008
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MATHEMATICA
| lst={}; s=0; Do[s=s+n^5; AppendTo[lst, s], {n, 10^2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 14 2008]
s = 0; lst = {s}; Do[s += n^5; AppendTo[lst, s], {n, 1, 30, 1}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
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PROG
| (PARI) a(n)=n^2*(n+1)^2*(2*n^2+2*n-1)/12 \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Partial sums of A000584. Row 5 of array A103438.
Cf. A101092.
Sequence in context: A119782 A008515 A179995 * A023874 A020291 A024400
Adjacent sequences: A000536 A000537 A000538 * A000540 A000541 A000542
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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