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

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