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Search: id:A000539
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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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+0
42
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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; listen)
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OFFSET
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0,3
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REFERENCES
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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. 813.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 155.
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LINKS
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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].
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.
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FORMULA
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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
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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
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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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CROSSREFS
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Partial sums of A000584. Row 5 of array A103438.
Cf. A101092.
Sequence in context: A061223 A119782 A008515 this_sequence A023874 A020291 A024400
Adjacent sequences: A000536 A000537 A000538 this_sequence A000540 A000541 A000542
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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