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%I #20 Aug 30 2019 03:36:19
%S 1,9,121,625,18769,2401,131769,579121,50822641,54479161,7007531521,
%T 7399612441,1313299956049,1372958223289,1429834803049,5936819760481,
%U 1775966959381729,203755669038601,75787776947048401,3117562300468225
%N Numerators of squares of harmonic numbers A001008/A002805.
%C The corresponding denominators are given in A103931.
%H W. Lang: <a href="/A103930/a103930.txt">Rationals H(n)^2.</a>
%F G.f.: -((d^3/dx^3)((log(1-x))^3))/3 + dilog(1-x)/(1-x) = ((log(1-x)^2) + dilog(1-x))/(1-x) with dilog(1-x)=polylog(2, x).
%F First differences give A103932(n)/A103933(n).
%F a(n) = numerator(H(n)^2), with the harmonic numbers H(n) = A001008(n)/A002805(n), n >= 1.
%p A103930 := n->numer(sum(1/i, i=1..n)^2); seq(A103930(k), k=1..40); # _Wesley Ivan Hurt_, Sep 30 2013
%t a[n_] := HarmonicNumber[n]^2 // Numerator; Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, Sep 16 2013 *)
%K nonn,easy,frac
%O 1,2
%A _Wolfdieter Lang_, Mar 24 2005
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