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A000540 Sum of 6th powers: 1^6 + 2^6 + ... + n^6.
(Formerly M5335 N2322)
+0
12
0, 1, 65, 794, 4890, 20515, 67171, 184820, 446964, 978405, 1978405, 3749966, 6735950, 11562759, 19092295, 30482920, 47260136, 71397705, 105409929, 152455810, 216455810, 302221931, 415601835, 563637724, 754740700, 998881325, 1307797101, 1695217590 (list; graph; listen)
OFFSET

0,3

REFERENCES

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.

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.

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, December 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.

FORMULA

a(n) = n*(n+1)*(2*n+1)*(3*n^4+6*n^3-3*n+1)/42.

a(n) = Sqrt[Sum[Sum[(i*j)^6, {i, 1, n}], {j, 1, n}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 26 2004

MAPLE

a:=n->sum (j^6, j=0..n): seq(a(n), n=0..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2007

A000540:=(z+1)*(z**4+56*z**3+246*z**2+56*z+1)/(z-1)**8; [Conjectured by 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^6 od: seq(a[n], n=0..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 05 2008

CROSSREFS

Cf. A101093.

Row 6 of array A103438.

Sequence in context: A013954 A116277 A008516 this_sequence A023875 A027463 A086021

Adjacent sequences: A000537 A000538 A000539 this_sequence A000541 A000542 A000543

KEYWORD

nonn

AUTHOR

njas

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Last modified July 26 13:41 EDT 2008. Contains 142293 sequences.


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