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A120076 Numerators of row sums of rational triangle A120072/A120073. 3

%I

%S 3,37,169,4549,4769,241481,989549,9072541,1841321,225467009,227698469,

%T 38801207261,39076419341,196577627041,790503882349,229526961468061,

%U 230480866420061,83512167402400421,3351610394325821

%N Numerators of row sums of rational triangle A120072/A120073.

%C The corresponding denominators are given by A120077.

%C See the W. Lang link under A120072 for more details.

%F a(n)=numerator(r(m)), with the rationals r(m):=sum(A120072(m,n)/A120073(m,n),n=1..m-1),m>=2.

%F The rationals are r(m)= Zeta(2;m-1) - (m-1)/m^2, m>=2, with the partial sums Zeta(2;n):=sum(1/k^2,k=1..n). See the W. Lang link under A103345.

%F O.g.f. for the rationals r(m), m>=2: log(1-x) + polylog(2,x)/(1-x).

%e The rationals A120076(m)/A120077(m), m>=2, begin with [3/4, 37/36,

%e 169/144, 4549/3600, 4769/3600,..].

%K nonn,easy,frac

%O 2,1

%A _Wolfdieter Lang_, Jul 20 2006

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)