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A007487
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Sum of 9th powers.
(Formerly M5460)
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6
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0, 1, 513, 20196, 282340, 2235465, 12313161, 52666768, 186884496, 574304985, 1574304985, 3932252676, 9092033028, 19696532401, 40357579185, 78800938560, 147520415296, 266108291793, 464467582161, 787155279940, 1299155279940, 2093435326521, 3300704544313
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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. 815.
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)), where Ar(m) is the m-th term of a sequence Ar: website Matem@ticamente (in Italian).
Eric Weisstein's World of Mathematics, Power Sum.
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FORMULA
| a(n) = n^2*(n+1)^2*(n^2+n-1)*(2*n^4+4*n^3-n^2-3*n+3)/20 (see MathWorld, Power Sum, formula 39). a(n) = n*A000542(n)-sum(i=0..n-1, A000542(i)). - Bruno Berselli, Apr 26 2010
G.f.: x*(1+502*x+14608*x^2+88234*x^3+156190*x^4+88234*x^5+14608*x^6+502*x^7+x^8)/(1-x)^11. a(n) = a(-n-1). - Bruno Berselli, Aug 23 2011
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MAPLE
| [seq(add(i^9, i=1..n), n=0..40)];
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^9 od: seq(a[n], n=0..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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MATHEMATICA
| lst={}; s=0; Do[s=s+n^9; AppendTo[lst, s], {n, 10^2}]; lst..or..Table[Sum[k^9, {k, 1, n}], {n, 0, 100}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 14 2008]
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PROG
| (MAGMA) [&+[n^9: n in [0..m]]: m in [0..22]]; // Bruno Berselli, Aug 23 2011
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CROSSREFS
| Row 9 of array A103438.
Sequence in context: A017681 A013957 A036087 * A023878 A168118 A086030
Adjacent sequences: A007484 A007485 A007486 * A007488 A007489 A007490
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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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