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A103932 Numerators of first difference of squares of harmonic numbers. 3

%I

%S 1,5,10,47,131,71,353,1487,6989,1451,82451,42433,1132133,1158863,

%T 236749,4828073,41781863,42482563,273253759,277235737,56204647,

%U 18975625,441730115,670193263,33874048171,34224132367,311048966203,313970420453

%N Numerators of first difference of squares of harmonic numbers.

%C The corresponding denominators are given in A103933.

%C h(n+1) + h(n) = (n+1)*(h(n+1)^2 - h(n)^2), where h(n) is the n-th harmonic number. - _Gary Detlefs_, May 25 2012

%H W. Lang: <a href="/A103932/a103932.txt">Rationals</a>.

%F a(n)=numerator(r(n)), with the rationals r(n)=H(n)^2-H(n-1)^2 where H(n)= A001008(n)/A002805(n), n>=1, H(0):=0.

%F G.f. for r(n): (log(1-x))^2 + dilog(1-x) where dilog(1-x)=polylog(2, x).

%F a(n)= Numerator(h(n)+h(n-1)), where h(n) is the n-th harmonic number. - _Gary Detlefs_, May 25 2012

%t Array[ HarmonicNumber[#]^2&, 29, 0] // Differences // Numerator (* _Jean-Fran├žois Alcover_, Jul 09 2013 *)

%K nonn,easy,frac

%O 1,2

%A _Wolfdieter Lang_, Mar 24 2005

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Last modified April 20 03:02 EDT 2021. Contains 343121 sequences. (Running on oeis4.)