cp's OEIS Frontend

A103932 Numerators of first difference of squares of harmonic numbers.

%I A103932 #31 Sep 28 2023 04:15:27
%S A103932 1,5,10,47,131,71,353,1487,6989,1451,82451,42433,1132133,1158863,
%T A103932 236749,4828073,41781863,42482563,273253759,277235737,56204647,
%U A103932 18975625,441730115,670193263,33874048171,34224132367,311048966203,313970420453
%N A103932 Numerators of first difference of squares of harmonic numbers.
%C A103932 The corresponding denominators are given in A103933.
%C A103932 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 A103932 Robert Israel, <a href="/A103932/b103932.txt">Table of n, a(n) for n = 1..2296</a>
%H A103932 Wolfdieter Lang, <a href="/A103932/a103932.txt">Rationals</a>.
%F A103932 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 A103932 G.f. for r(n): (log(1-x))^2 + dilog(1-x) where dilog(1-x) = polylog(2, x).
%F A103932 a(n) = numerator(h(n) + h(n-1)), where h(n) is the n-th harmonic number. - _Gary Detlefs_, May 25 2012
%p A103932 H:= Vector(51):
%p A103932 for i from 2 to 51 do H[i]:= H[i-1]+1/(i-1) od:
%p A103932 HS:= map(t -> t^2, H):
%p A103932 convert(map(numer, HS[2..-1]-HS[1..-2]),list); # _Robert Israel_, Sep 27 2023
%t A103932 Array[ HarmonicNumber[#]^2&, 29, 0] // Differences // Numerator (* _Jean-François Alcover_, Jul 09 2013 *)
%K A103932 nonn,easy,frac
%O A103932 1,2
%A A103932 _Wolfdieter Lang_, Mar 24 2005