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Search: id:A080779
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| A080779 |
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Triangle read by rows: n-th row gives expansion of the series for HarmonicNumber[n, -p]. |
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+0
1
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| 1, 1, 1, 1, 3, 2, 0, 6, 12, 6, -4, 0, 40, 60, 24, 0, -60, 0, 300, 360, 120, 120, 0, -840, 0, 2520, 2520, 720, 0, 3360, 0, -11760, 0, 23520, 20160, 5040, -12096, 0, 80640, 0, -169344, 0, 241920, 181440, 40320, 0, -544320, 0, 1814400, 0, -2540160, 0, 2721600, 1814400, 362880
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are n!, last element in row is (n-1)!
Alternative description using Bernoulli polynomials: Let p[x,n]=Sum[k^n,{k,1,x}]; 1/x /. NSolve[p[x,n]-Zeta[n]==0,x] where n>=2. Then t(n,m)=CoefficientList[Expand[n!*(BernoulliB[n + 1, x + 1] - BernoulliB[n + 1])/x], x]. - Roger Bagula (rlbagulatftn(AT)yahoo.com) and njas, Feb 18 2008
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EXAMPLE
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1; 1,1; 1,3,2; 0,6,12,6; -4,0,40,60,24; 0,-60,0,300,360,120; ...
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MATHEMATICA
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Table[(p+1)! CoefficientList[ Sum[k^p, {k, 0, n}]/n, n], {p, 1, 12}]
a = Join[{{1}}, Table[CoefficientList[Expand[n!*(BernoulliB[n + 1, x + 1] - BernoulliB[n + 1])/x], x], {n, 1, 10}]] Flatten[a] - Roger Bagula (rlbagulatftn(AT)yahoo.com) and njas, Feb 18 2008
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CROSSREFS
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Sequence in context: A114376 A058096 A049780 this_sequence A010604 A067585 A116191
Adjacent sequences: A080776 A080777 A080778 this_sequence A080780 A080781 A080782
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Mar 11 2003
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