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A023002
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Sum of 10th powers.
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6
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0, 1, 1025, 60074, 1108650, 10874275, 71340451, 353815700, 1427557524, 4914341925, 14914341925, 40851766526, 102769130750, 240627622599, 529882277575, 1106532668200, 2206044295976, 4222038196425, 7792505423049, 13923571680850
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..1000
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*(n+1)*(2*n+1)*(n^2+n-1)(3*n^6+9*n^5+2*n^4-11*n^3+3*n^2+10*n-5)/66 (see MathWorld, Power Sum, formula 40). - Bruno Berselli, Apr 26 2010
a(n) = n*A007487(n)-sum(i=0..n-1, A007487(i)). - From Bruno Berselli, Apr 27 2010
G.f.: x*(1+x)*(1+1012*x+46828*x^2+408364*x^3+901990*x^4+408364*x^5+46828*x^6+1012*x^7+x^8)/(1-x)^12. a(n) = -a(-n-1). - Bruno Berselli, Aug 23 2011
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MATHEMATICA
| lst={}; s=0; Do[s=s+n^10; AppendTo[lst, s], {n, 10^2}]; lst..or..Table[Sum[k^10, {k, 1, n}], {n, 0, 10^2}] [From Vladimir Orlovsky, Aug 14 2008]
Accumulate[Range[0, 20]^10] (* From Harvey P. Dale, Aug 23 2011 *)
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PROG
| (Other) sage: [bernoulli_polynomial(n, 11)/11 for n in xrange(2, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2009]
(MAGMA) [&+[n^10: n in [0..m]]: m in [0..19]]; // Bruno Berselli, Aug 23 2011
(PARI) a(n)=(6*x^11+33*x^10+55*x^9-66*x^7+66*x^5-33*x^3+5*x)/66 \\ Charles R Greathouse IV, Aug 23 2011
(PARI) a(n)=sum(i=0, 10, binomial(11, i)*bernfrac(i)*n^(11-i))/11+n^10 \\ Charles R Greathouse IV, Aug 23 2011
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CROSSREFS
| Row 10 of array A103438.
Sequence in context: A017683 A013958 A036088 * A168119 A180270 A103716
Adjacent sequences: A022999 A023000 A023001 * A023003 A023004 A023005
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KEYWORD
| nonn,easy
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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