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Numerators of 1-2*HarmonicNumber(n)/(n+1).
2

%I #21 Oct 18 2018 03:12:49

%S 0,0,1,1,43,3,197,499,5471,589,82609,7243,1376527,1530967,1687123,

%T 217033,68127937,1290761,500679401,107119657,38046795,1756445,

%U 983477669,622806889,81955769933,86074407533,811851812797,29280696293

%N Numerators of 1-2*HarmonicNumber(n)/(n+1).

%C Expected area of the convex hull of n points picked at random inside a triangle with unit area.

%H Robert Israel, <a href="/A093762/b093762.txt">Table of n, a(n) for n = 1..2296</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TrianglePointPicking.html">Triangle Point Picking</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SimplexSimplexPicking.html">Simplex Simplex Picking</a>

%e 0, 0, 1/12, 1/6, 43/180, 3/10, 197/560, 499/1260, 5471/12600, ...

%p h:= 1:

%p A[1]:= 0:

%p for n from 2 to 50 do

%p h:= h+1/n;

%p A[n]:= numer(1-2*h/(n+1));

%p od:

%p seq(A[i],i=1..50); # _Robert Israel_, Oct 17 2018

%t Table[Numerator[1-2HarmonicNumber[n]/(n+1)],{n,30}] (* _Harvey P. Dale_, Oct 10 2013 *)

%o (PARI) a(n) = numerator(1-2*sum(i=1, n, 1/i)/(n+1)) \\ _Felix Fröhlich_, Oct 17 2018

%Y Cf. A002548.

%K nonn,frac

%O 1,5

%A _Eric W. Weisstein_, Apr 15 2004