This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A093762 #22 Feb 16 2025 08:32:53
%S A093762 0,0,1,1,43,3,197,499,5471,589,82609,7243,1376527,1530967,1687123,
%T A093762 217033,68127937,1290761,500679401,107119657,38046795,1756445,
%U A093762 983477669,622806889,81955769933,86074407533,811851812797,29280696293
%N A093762 Numerators of 1-2*HarmonicNumber(n)/(n+1).
%C A093762 Expected area of the convex hull of n points picked at random inside a triangle with unit area.
%H A093762 Robert Israel, <a href="/A093762/b093762.txt">Table of n, a(n) for n = 1..2296</a>
%H A093762 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TrianglePointPicking.html">Triangle Point Picking</a>
%H A093762 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SimplexSimplexPicking.html">Simplex Simplex Picking</a>
%e A093762 0, 0, 1/12, 1/6, 43/180, 3/10, 197/560, 499/1260, 5471/12600, ...
%p A093762 h:= 1:
%p A093762 A[1]:= 0:
%p A093762 for n from 2 to 50 do
%p A093762 h:= h+1/n;
%p A093762 A[n]:= numer(1-2*h/(n+1));
%p A093762 od:
%p A093762 seq(A[i],i=1..50); # _Robert Israel_, Oct 17 2018
%t A093762 Table[Numerator[1-2HarmonicNumber[n]/(n+1)],{n,30}] (* _Harvey P. Dale_, Oct 10 2013 *)
%o A093762 (PARI) a(n) = numerator(1-2*sum(i=1, n, 1/i)/(n+1)) \\ _Felix Fröhlich_, Oct 17 2018
%Y A093762 Cf. A002548.
%K A093762 nonn,frac
%O A093762 1,5
%A A093762 _Eric W. Weisstein_, Apr 15 2004