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 A120076 Numerators of row sums of rational triangle A120072/A120073. 6
 3, 37, 169, 4549, 4769, 241481, 989549, 9072541, 1841321, 225467009, 227698469, 38801207261, 39076419341, 196577627041, 790503882349, 229526961468061, 230480866420061, 83512167402400421, 3351610394325821 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The corresponding denominators are given by A120077. See the W. Lang link under A120072 for more details. LINKS G. C. Greubel, Table of n, a(n) for n = 2..1000 FORMULA 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). EXAMPLE The rationals a(m)/A120077(m), m>=2, begin with (3/4, 37/36, 169/144, 4549/3600, 4769/3600, ...). MATHEMATICA Table[Numerator[HarmonicNumber[n, 2] -1/n], {n, 2, 40}] (* G. C. Greubel, Apr 24 2023 *) PROG (Magma) A120076:= func< n | Numerator( (&+[1/k^2: k in [1..n]]) -1/n) >; [A120076(n): n in [2..30]]; // G. C. Greubel, Apr 24 2023 (SageMath) def A120076(n): return numerator(harmonic_number(n, 2) - 1/n) [A120076(n) for n in range(2, 31)] # G. C. Greubel, Apr 24 2023 CROSSREFS Cf. A120070, A120072, A120073, A120074, A120075, A120077. Sequence in context: A109835 A066364 A106995 * A119938 A232303 A196978 Adjacent sequences: A120073 A120074 A120075 * A120077 A120078 A120079 KEYWORD nonn,easy,frac AUTHOR Wolfdieter Lang, Jul 20 2006 STATUS approved

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Last modified June 3 18:18 EDT 2023. Contains 363116 sequences. (Running on oeis4.)