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A120076
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Numerators of row sums of rational triangle A120072/A120073.
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6
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3, 37, 169, 4549, 4769, 241481, 989549, 9072541, 1841321, 225467009, 227698469, 38801207261, 39076419341, 196577627041, 790503882349, 229526961468061, 230480866420061, 83512167402400421, 3351610394325821
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OFFSET
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2,1
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COMMENTS
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The corresponding denominators are given by A120077.
See the W. Lang link under A120072 for more details.
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LINKS
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FORMULA
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a(n) = numerator(r(m)), with the rationals r(m) = Sum_{n=1..m-1} A120072(m,n)/A120073(m,n), m >= 2.
The rationals are r(m) = Zeta(2; m-1) - (m-1)/m^2, m >= 2, with the partial sums Zeta(2; n) = Sum_{k=1..n} 1/k^2. See the W. Lang link in A103345.
O.g.f. for the rationals r(m), m>=2: log(1-x) + polylog(2,x)/(1-x).
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EXAMPLE
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The rationals a(m)/A120077(m), m>=2, begin with (3/4, 37/36, 169/144, 4549/3600, 4769/3600, ...).
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MATHEMATICA
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Table[Numerator[HarmonicNumber[n, 2] -1/n], {n, 2, 40}] (* G. C. Greubel, Apr 24 2023 *)
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PROG
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(Magma)
A120076:= func< n | Numerator( (&+[1/k^2: k in [1..n]]) -1/n) >;
(SageMath)
def A120076(n): return numerator(harmonic_number(n, 2) - 1/n)
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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STATUS
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approved
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