More on A103932, first difference of square of harmonic numbers H(n)=A001008(n)/A002805(n), n>=1, H(0):=0.

The rationals r(n):=A103932(n)/A103933(n) are, for n=1..30:

[1, 5/4, 10/9, 47/48, 131/150, 71/90, 353/490, 1487/2240, 6989/11340, 1451/2520, 82451/152460, 42433/83160, 

1132133/2342340, 1158863/2522520, 236749/540540, 4828073/11531520, 41781863/104144040, 42482563/110270160, 

273253759/737176440, 277235737/775975200, 56204647/162954792, 18975625/56904848, 441730115/1368302936, 

670193263/2141691552, 33874048171/111546435000, 34224132367/116008292400, 311048966203/1084231348200, 

313970420453/1124388064800, 9186889794787/33771798660600, 9265864670767/34936343442000]


r(n)=H(n)^2-H(n-1)^2, n>=1.

G.f.: (ln(1-x))^2 + dilog(1-x) where dilog(1-x)=polylog(2,x). 


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