A093762 Numerators of 1-2*HarmonicNumber(n)/(n+1).

0, 0, 1, 1, 43, 3, 197, 499, 5471, 589, 82609, 7243, 1376527, 1530967, 1687123, 217033, 68127937, 1290761, 500679401, 107119657, 38046795, 1756445, 983477669, 622806889, 81955769933, 86074407533, 811851812797, 29280696293

Offset: 1

Author

Eric W. Weisstein, Apr 15 2004

Keywords

• nonn
• frac

Comments

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

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..2296
• Eric Weisstein's World of Mathematics, Triangle Point Picking
• Eric Weisstein's World of Mathematics, Simplex Simplex Picking

Crossrefs

Cf. A002548.

Programs

Maple

h:= 1:
A[1]:= 0:
for n from 2 to 50 do
  h:= h+1/n;
  A[n]:= numer(1-2*h/(n+1));
od:
seq(A[i],i=1..50); # Robert Israel, Oct 17 2018

Mathematica

Table[Numerator[1-2HarmonicNumber[n]/(n+1)],{n,30}] (* Harvey P. Dale, Oct 10 2013 *)

PARI

a(n) = numerator(1-2*sum(i=1, n, 1/i)/(n+1)) \\ Felix Fröhlich, Oct 17 2018