A093531 - OEIS

A093531

Denominators of the average length of a line segment picked at random in the unit n-ball for odd n.

3, 35, 693, 1287, 230945, 96577, 11700675, 6678671, 371255535, 1204952175, 74182976285, 1860438674025, 6771996773451, 78736520890181, 22884013460693, 315208830571481, 424299741297447197, 108494411640283617, 1355691431937597989, 15176059956710358055

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..20.

Eric Weisstein's World of Mathematics, Ball Line Picking.

EXAMPLE

2/3, 128/(45*Pi), 36/35, 16384/(4725*Pi), 800/693, ...

MATHEMATICA

B[z_, a_, b_] := z^a/a*HypergeometricPFQ[{a, 1 - b}, {a + 1}, z]; a[n_] := Integrate[ n*s^n*B[1 - s^2/4, (n + 1)/2, 1/2]/B[1, (n + 1)/2, 1/2], {s, 0, 2}]; Table[a[n], {n, 1, 21, 2}] // Denominator (* Jean-François Alcover, Oct 31 2012, after Maple program in A093530 *)

CROSSREFS

Cf. A093530, A093532, A093533.

Sequence in context: A046032 A304191 A009071 * A129505 A185752 A210897

Adjacent sequences: A093528 A093529 A093530 * A093532 A093533 A093534

KEYWORD

nonn,frac

AUTHOR

Eric W. Weisstein, Mar 30 2004

EXTENSIONS

a(10)-a(11) from Max Alekseyev, Dec 12 2011

a(12)-a(14) from Robert G. Wilson v, Nov 04 2013

a(15)-a(20) from Alois P. Heinz, Nov 04 2013

STATUS

approved