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A093762 Numerators of 1-2*HarmonicNumber(n)/(n+1). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

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

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

EXAMPLE

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

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 *)

PROG

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

CROSSREFS

Cf. A002548.

Sequence in context: A212316 A292996 A107814 * A156677 A097398 A225210

Adjacent sequences:  A093759 A093760 A093761 * A093763 A093764 A093765

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Apr 15 2004

STATUS

approved

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Last modified June 22 03:25 EDT 2021. Contains 345367 sequences. (Running on oeis4.)