A093532 Numerators of the average length of a line segment picked at random in the unit n-ball for even n.

128, 16384, 131072, 134217728, 2684354560, 68719476736, 3848290697216, 4503599627370496, 27021597764222976, 1152921504606846976, 101457092405402533888, 9444732965739290427392, 491126114218443102224384, 4835703278458516698824704, 38685626227668133590597632, 2535301200456458802993406410752

Offset

1,1

Links

Table of n, a(n) for n=1..16.

Bernhard Burgstaller and Friedrich Pillichshammer, The Average Distance Between Two Points, Bulletin of the Australian Mathematical Society, 2009;80(3):353-359.

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

Wikipedia, Mean line segment length

Example

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

Prog

(PARI) betae(n) = 2^(3*n+1)*(n\2)!^2*n!/((n+1)*(2*n)!);
a093532(n) = my(m=2*n); numerator(2*m*betae(m)/(2*m+1)); \\ Hugo Pfoertner, Jan 19 2026

Crossrefs

Cf. A093530, A093531, A093533 (denominators).

Sequence in context: A184760 A228985 A282315 * A016747 A189269 A223674

Adjacent sequences: A093529 A093530 A093531 * A093533 A093534 A093535

Keyword

nonn,frac

Author

Eric W. Weisstein, Mar 30 2004

Extensions

More terms from Hugo Pfoertner, Jan 19 2026

Status

approved